Lash---1.13.THM-Prf.s

%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : SEU664^1 : TPTP v9.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : lash -P picomus -M modes -p tstp -t %d %s

% Computer : n031.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 Oct  9 02:33:19 PM UTC 2025

% Result   : Theorem 0.50s 0.70s
% Output   : Proof 0.73s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_subset,type,
    subset: $i > $i > $o ).

thf(ty_iskpair,type,
    iskpair: $i > $o ).

thf(ty_setminus,type,
    setminus: $i > $i > $i ).

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

thf(ty_binunion,type,
    binunion: $i > $i > $i ).

thf(ty_kfst,type,
    kfst: $i > $i ).

thf(ty_symdiff,type,
    symdiff: $i > $i > $i ).

thf(ty_eigen__0,type,
    eigen__0: $i ).

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

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

thf(ty_descr,type,
    descr: ( $i > $o ) > $i ).

thf(ty_eigen__2,type,
    eigen__2: $i ).

thf(ty_prop2set,type,
    prop2set: $o > $i ).

thf(ty_binintersect,type,
    binintersect: $i > $i > $i ).

thf(ty_eigen__1,type,
    eigen__1: $i ).

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

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

thf(ty_ksnd,type,
    ksnd: $i > $i ).

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

thf(ty_cartprod,type,
    cartprod: $i > $i > $i ).

thf(ty_set2prop,type,
    set2prop: $i > $o ).

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

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

thf(sP1,plain,
    ( sP1
  <=> ( in @ eigen__2 @ ( cartprod @ eigen__0 @ eigen__1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( iskpair @ eigen__2 ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ! [X1: $i] :
        ( ( in @ X1 @ ( cartprod @ eigen__0 @ eigen__1 ) )
       => ( iskpair @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( sP1
     => sP2 ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ! [X1: $i,X2: $i,X3: $i] :
        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
       => ( iskpair @ X3 ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( sP2
     => ( ( kpair @ ( kfst @ eigen__2 ) @ ( ksnd @ eigen__2 ) )
        = eigen__2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( ( kpair @ ( kfst @ eigen__2 ) @ ( ksnd @ eigen__2 ) )
      = eigen__2 ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ! [X1: $i] :
        ( ( iskpair @ X1 )
       => ( ( kpair @ ( kfst @ X1 ) @ ( ksnd @ X1 ) )
          = X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ! [X1: $i,X2: $i] :
        ( ( in @ X2 @ ( cartprod @ eigen__0 @ X1 ) )
       => ( iskpair @ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(def_exu,definition,
    ( exu
    = ( ^ [X1: $i > $o] :
        ? [X2: $i] :
          ( ( X1 @ X2 )
          & ! [X3: $i] :
              ( ^ [X4: $o,X5: $o] :
                  ( X4
                 => X5 )
              @ ( X1 @ X3 )
              @ ( X2 = X3 ) ) ) ) ) ).

thf(def_setextAx,definition,
    ( setextAx
    = ( ! [X1: $i,X2: $i] :
          ( ^ [X3: $o,X4: $o] :
              ( X3
             => X4 )
          @ ! [X3: $i] :
              ( ( in @ X3 @ X1 )
            <=> ( in @ X3 @ X2 ) )
          @ ( X1 = X2 ) ) ) ) ).

thf(def_emptysetAx,definition,
    ( emptysetAx
    = ( ! [X1: $i] : ( (~) @ ( in @ X1 @ emptyset ) ) ) ) ).

thf(def_setadjoinAx,definition,
    ( setadjoinAx
    = ( ! [X1: $i,X2: $i,X3: $i] :
          ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
        <=> ( ( X3 = X1 )
            | ( in @ X3 @ X2 ) ) ) ) ) ).

thf(def_powersetAx,definition,
    ( powersetAx
    = ( ! [X1: $i,X2: $i] :
          ( ( in @ X2 @ ( powerset @ X1 ) )
        <=> ! [X3: $i] :
              ( ^ [X4: $o,X5: $o] :
                  ( X4
                 => X5 )
              @ ( in @ X3 @ X2 )
              @ ( in @ X3 @ X1 ) ) ) ) ) ).

thf(def_setunionAx,definition,
    ( setunionAx
    = ( ! [X1: $i,X2: $i] :
          ( ( in @ X2 @ ( setunion @ X1 ) )
        <=> ? [X3: $i] :
              ( ( in @ X2 @ X3 )
              & ( in @ X3 @ X1 ) ) ) ) ) ).

thf(def_omega0Ax,definition,
    ( omega0Ax
    = ( in @ emptyset @ omega ) ) ).

thf(def_omegaSAx,definition,
    ( omegaSAx
    = ( ! [X1: $i] :
          ( ^ [X2: $o,X3: $o] :
              ( X2
             => X3 )
          @ ( in @ X1 @ omega )
          @ ( in @ ( setadjoin @ X1 @ X1 ) @ omega ) ) ) ) ).

thf(def_omegaIndAx,definition,
    ( omegaIndAx
    = ( ! [X1: $i] :
          ( ^ [X2: $o,X3: $o] :
              ( X2
             => X3 )
          @ ( ( in @ emptyset @ X1 )
            & ! [X2: $i] :
                ( ^ [X3: $o,X4: $o] :
                    ( X3
                   => X4 )
                @ ( ( in @ X2 @ omega )
                  & ( in @ X2 @ X1 ) )
                @ ( in @ ( setadjoin @ X2 @ X2 ) @ X1 ) ) )
          @ ! [X2: $i] :
              ( ^ [X3: $o,X4: $o] :
                  ( X3
                 => X4 )
              @ ( in @ X2 @ omega )
              @ ( in @ X2 @ X1 ) ) ) ) ) ).

thf(def_replAx,definition,
    ( replAx
    = ( ! [X1: $i > $i > $o,X2: $i] :
          ( ^ [X3: $o,X4: $o] :
              ( X3
             => X4 )
          @ ! [X3: $i] :
              ( ^ [X4: $o,X5: $o] :
                  ( X4
                 => X5 )
              @ ( in @ X3 @ X2 )
              @ ( exu
                @ ^ [X4: $i] : ( X1 @ X3 @ X4 ) ) )
          @ ? [X3: $i] :
            ! [X4: $i] :
              ( ( in @ X4 @ X3 )
            <=> ? [X5: $i] :
                  ( ( in @ X5 @ X2 )
                  & ( X1 @ X5 @ X4 ) ) ) ) ) ) ).

thf(def_foundationAx,definition,
    ( foundationAx
    = ( ! [X1: $i] :
          ( ^ [X2: $o,X3: $o] :
              ( X2
             => X3 )
          @ ? [X2: $i] : ( in @ X2 @ X1 )
          @ ? [X2: $i] :
              ( ( in @ X2 @ X1 )
              & ( (~)
                @ ? [X3: $i] :
                    ( ( in @ X3 @ X2 )
                    & ( in @ X3 @ X1 ) ) ) ) ) ) ) ).

thf(def_wellorderingAx,definition,
    ( wellorderingAx
    = ( ! [X1: $i] :
        ? [X2: $i] :
          ( ! [X3: $i] :
              ( ^ [X4: $o,X5: $o] :
                  ( X4
                 => X5 )
              @ ( in @ X3 @ X2 )
              @ ! [X4: $i] :
                  ( ^ [X5: $o,X6: $o] :
                      ( X5
                     => X6 )
                  @ ( in @ X4 @ X3 )
                  @ ( in @ X4 @ X1 ) ) )
          & ! [X3: $i,X4: $i] :
              ( ^ [X5: $o,X6: $o] :
                  ( X5
                 => X6 )
              @ ( ( in @ X3 @ X1 )
                & ( in @ X4 @ X1 ) )
              @ ( ^ [X5: $o,X6: $o] :
                    ( X5
                   => X6 )
                @ ! [X5: $i] :
                    ( ^ [X6: $o,X7: $o] :
                        ( X6
                       => X7 )
                    @ ( in @ X5 @ X2 )
                    @ ( ( in @ X3 @ X5 )
                    <=> ( in @ X4 @ X5 ) ) )
                @ ( X3 = X4 ) ) )
          & ! [X3: $i,X4: $i] :
              ( ^ [X5: $o,X6: $o] :
                  ( X5
                 => X6 )
              @ ( ( in @ X3 @ X2 )
                & ( in @ X4 @ X2 ) )
              @ ( ! [X5: $i] :
                    ( ^ [X6: $o,X7: $o] :
                        ( X6
                       => X7 )
                    @ ( in @ X5 @ X3 )
                    @ ( in @ X5 @ X4 ) )
                | ! [X5: $i] :
                    ( ^ [X6: $o,X7: $o] :
                        ( X6
                       => X7 )
                    @ ( in @ X5 @ X4 )
                    @ ( in @ X5 @ X3 ) ) ) )
          & ! [X3: $i] :
              ( ^ [X4: $o,X5: $o] :
                  ( X4
                 => X5 )
              @ ( ! [X4: $i] :
                    ( ^ [X5: $o,X6: $o] :
                        ( X5
                       => X6 )
                    @ ( in @ X4 @ X3 )
                    @ ( in @ X4 @ X1 ) )
                & ? [X4: $i] : ( in @ X4 @ X3 ) )
              @ ? [X4: $i,X5: $i] :
                  ( ( in @ X4 @ X2 )
                  & ( in @ X5 @ X3 )
                  & ( (~)
                    @ ? [X6: $i] :
                        ( ( in @ X6 @ X4 )
                        & ( in @ X6 @ X3 ) ) )
                  & ! [X6: $i] :
                      ( ^ [X7: $o,X8: $o] :
                          ( X7
                         => X8 )
                      @ ( in @ X6 @ X2 )
                      @ ( ! [X7: $i] :
                            ( ^ [X8: $o,X9: $o] :
                                ( X8
                               => X9 )
                            @ ( in @ X7 @ X6 )
                            @ ( in @ X7 @ X4 ) )
                        | ( in @ X5 @ X6 ) ) ) ) ) ) ) ) ).

thf(def_descrp,definition,
    ( descrp
    = ( ! [X1: $i > $o] :
          ( ^ [X2: $o,X3: $o] :
              ( X2
             => X3 )
          @ ( exu
            @ ^ [X2: $i] : ( X1 @ X2 ) )
          @ ( X1
            @ ( descr
              @ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ) ) ).

thf(def_dsetconstrI,definition,
    ( dsetconstrI
    = ( ! [X1: $i,X2: $i > $o,X3: $i] :
          ( ^ [X4: $o,X5: $o] :
              ( X4
             => X5 )
          @ ( in @ X3 @ X1 )
          @ ( ^ [X4: $o,X5: $o] :
                ( X4
               => X5 )
            @ ( X2 @ X3 )
            @ ( in @ X3
              @ ( dsetconstr @ X1
                @ ^ [X4: $i] : ( X2 @ X4 ) ) ) ) ) ) ) ).

thf(def_dsetconstrEL,definition,
    ( dsetconstrEL
    = ( ! [X1: $i,X2: $i > $o,X3: $i] :
          ( ^ [X4: $o,X5: $o] :
              ( X4
             => X5 )
          @ ( in @ X3
            @ ( dsetconstr @ X1
              @ ^ [X4: $i] : ( X2 @ X4 ) ) )
          @ ( in @ X3 @ X1 ) ) ) ) ).

thf(def_dsetconstrER,definition,
    ( dsetconstrER
    = ( ! [X1: $i,X2: $i > $o,X3: $i] :
          ( ^ [X4: $o,X5: $o] :
              ( X4
             => X5 )
          @ ( in @ X3
            @ ( dsetconstr @ X1
              @ ^ [X4: $i] : ( X2 @ X4 ) ) )
          @ ( X2 @ X3 ) ) ) ) ).

thf(def_exuE1,definition,
    ( exuE1
    = ( ! [X1: $i > $o] :
          ( ^ [X2: $o,X3: $o] :
              ( X2
             => X3 )
          @ ( exu
            @ ^ [X2: $i] : ( X1 @ X2 ) )
          @ ? [X2: $i] :
              ( ( X1 @ X2 )
              & ! [X3: $i] :
                  ( ^ [X4: $o,X5: $o] :
                      ( X4
                     => X5 )
                  @ ( X1 @ X3 )
                  @ ( X2 = X3 ) ) ) ) ) ) ).

thf(def_prop2setE,definition,
    ( prop2setE
    = ( ! [X1: $o,X2: $i] :
          ( ^ [X3: $o,X4: $o] :
              ( X3
             => X4 )
          @ ( in @ X2 @ ( prop2set @ X1 ) )
          @ X1 ) ) ) ).

thf(def_emptysetE,definition,
    ( emptysetE
    = ( ! [X1: $i] :
          ( ^ [X2: $o,X3: $o] :
              ( X2
             => X3 )
          @ ( in @ X1 @ emptyset )
          @ ! [X2: $o] : X2 ) ) ) ).

thf(def_emptysetimpfalse,definition,
    ( emptysetimpfalse
    = ( ! [X1: $i] :
          ( ^ [X2: $o,X3: $o] :
              ( X2
             => X3 )
          @ ( in @ X1 @ emptyset )
          @ $false ) ) ) ).

thf(def_notinemptyset,definition,
    ( notinemptyset
    = ( ! [X1: $i] : ( (~) @ ( in @ X1 @ emptyset ) ) ) ) ).

thf(def_exuE3e,definition,
    ( exuE3e
    = ( ! [X1: $i > $o] :
          ( ^ [X2: $o,X3: $o] :
              ( X2
             => X3 )
          @ ( exu
            @ ^ [X2: $i] : ( X1 @ X2 ) )
          @ ? [X2: $i] : ( X1 @ X2 ) ) ) ) ).

thf(def_setext,definition,
    ( setext
    = ( ! [X1: $i,X2: $i] :
          ( ^ [X3: $o,X4: $o] :
              ( X3
             => X4 )
          @ ! [X3: $i] :
              ( ^ [X4: $o,X5: $o] :
                  ( X4
                 => X5 )
              @ ( in @ X3 @ X1 )
              @ ( in @ X3 @ X2 ) )
          @ ( ^ [X3: $o,X4: $o] :
                ( X3
               => X4 )
            @ ! [X3: $i] :
                ( ^ [X4: $o,X5: $o] :
                    ( X4
                   => X5 )
                @ ( in @ X3 @ X2 )
                @ ( in @ X3 @ X1 ) )
            @ ( X1 = X2 ) ) ) ) ) ).

thf(def_emptyI,definition,
    ( emptyI
    = ( ! [X1: $i] :
          ( ^ [X2: $o,X3: $o] :
              ( X2
             => X3 )
          @ ! [X2: $i] : ( (~) @ ( in @ X2 @ X1 ) )
          @ ( X1 = emptyset ) ) ) ) ).

thf(def_noeltsimpempty,definition,
    ( noeltsimpempty
    = ( ! [X1: $i] :
          ( ^ [X2: $o,X3: $o] :
              ( X2
             => X3 )
          @ ! [X2: $i] : ( (~) @ ( in @ X2 @ X1 ) )
          @ ( X1 = emptyset ) ) ) ) ).

thf(def_setbeta,definition,
    ( setbeta
    = ( ! [X1: $i,X2: $i > $o,X3: $i] :
          ( ^ [X4: $o,X5: $o] :
              ( X4
             => X5 )
          @ ( in @ X3 @ X1 )
          @ ( ( in @ X3
              @ ( dsetconstr @ X1
                @ ^ [X4: $i] : ( X2 @ X4 ) ) )
          <=> ( X2 @ X3 ) ) ) ) ) ).

thf(def_nonempty,definition,
    ( nonempty
    = ( ^ [X1: $i] : ( (~) @ ( X1 = emptyset ) ) ) ) ).

thf(def_nonemptyE1,definition,
    ( nonemptyE1
    = ( ! [X1: $i] :
          ( ^ [X2: $o,X3: $o] :
              ( X2
             => X3 )
          @ ( nonempty @ X1 )
          @ ? [X2: $i] : ( in @ X2 @ X1 ) ) ) ) ).

thf(def_nonemptyI,definition,
    ( nonemptyI
    = ( ! [X1: $i,X2: $i > $o,X3: $i] :
          ( ^ [X4: $o,X5: $o] :
              ( X4
             => X5 )
          @ ( in @ X3 @ X1 )
          @ ( ^ [X4: $o,X5: $o] :
                ( X4
               => X5 )
            @ ( X2 @ X3 )
            @ ( nonempty
              @ ( dsetconstr @ X1
                @ ^ [X4: $i] : ( X2 @ X4 ) ) ) ) ) ) ) ).

thf(def_nonemptyI1,definition,
    ( nonemptyI1
    = ( ! [X1: $i] :
          ( ^ [X2: $o,X3: $o] :
              ( X2
             => X3 )
          @ ? [X2: $i] : ( in @ X2 @ X1 )
          @ ( nonempty @ X1 ) ) ) ) ).

thf(def_setadjoinIL,definition,
    ( setadjoinIL
    = ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) ) ) ) ).

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

thf(def_setadjoinIR,definition,
    ( setadjoinIR
    = ( ! [X1: $i,X2: $i,X3: $i] :
          ( ^ [X4: $o,X5: $o] :
              ( X4
             => X5 )
          @ ( in @ X3 @ X2 )
          @ ( in @ X3 @ ( setadjoin @ X1 @ X2 ) ) ) ) ) ).

thf(def_setadjoinE,definition,
    ( setadjoinE
    = ( ! [X1: $i,X2: $i,X3: $i] :
          ( ^ [X4: $o,X5: $o] :
              ( X4
             => X5 )
          @ ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
          @ ! [X4: $o] :
              ( ^ [X5: $o,X6: $o] :
                  ( X5
                 => X6 )
              @ ( ^ [X5: $o,X6: $o] :
                    ( X5
                   => X6 )
                @ ( X3 = X1 )
                @ X4 )
              @ ( ^ [X5: $o,X6: $o] :
                    ( X5
                   => X6 )
                @ ( ^ [X5: $o,X6: $o] :
                      ( X5
                     => X6 )
                  @ ( in @ X3 @ X2 )
                  @ X4 )
                @ X4 ) ) ) ) ) ).

thf(def_setadjoinOr,definition,
    ( setadjoinOr
    = ( ! [X1: $i,X2: $i,X3: $i] :
          ( ^ [X4: $o,X5: $o] :
              ( X4
             => X5 )
          @ ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
          @ ( ( X3 = X1 )
            | ( in @ X3 @ X2 ) ) ) ) ) ).

thf(def_setoftrueEq,definition,
    ( setoftrueEq
    = ( ! [X1: $i] :
          ( ( dsetconstr @ X1
            @ ^ [X2: $i] : $true )
          = X1 ) ) ) ).

thf(def_powersetI,definition,
    ( powersetI
    = ( ! [X1: $i,X2: $i] :
          ( ^ [X3: $o,X4: $o] :
              ( X3
             => X4 )
          @ ! [X3: $i] :
              ( ^ [X4: $o,X5: $o] :
                  ( X4
                 => X5 )
              @ ( in @ X3 @ X2 )
              @ ( in @ X3 @ X1 ) )
          @ ( in @ X2 @ ( powerset @ X1 ) ) ) ) ) ).

thf(def_emptyinPowerset,definition,
    ( emptyinPowerset
    = ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) ) ) ) ).

thf(def_emptyInPowerset,definition,
    ( emptyInPowerset
    = ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) ) ) ) ).

thf(def_powersetE,definition,
    ( powersetE
    = ( ! [X1: $i,X2: $i,X3: $i] :
          ( ^ [X4: $o,X5: $o] :
              ( X4
             => X5 )
          @ ( in @ X2 @ ( powerset @ X1 ) )
          @ ( ^ [X4: $o,X5: $o] :
                ( X4
               => X5 )
            @ ( in @ X3 @ X2 )
            @ ( in @ X3 @ X1 ) ) ) ) ) ).

thf(def_setunionI,definition,
    ( setunionI
    = ( ! [X1: $i,X2: $i,X3: $i] :
          ( ^ [X4: $o,X5: $o] :
              ( X4
             => X5 )
          @ ( in @ X2 @ X3 )
          @ ( ^ [X4: $o,X5: $o] :
                ( X4
               => X5 )
            @ ( in @ X3 @ X1 )
            @ ( in @ X2 @ ( setunion @ X1 ) ) ) ) ) ) ).

thf(def_setunionE,definition,
    ( setunionE
    = ( ! [X1: $i,X2: $i] :
          ( ^ [X3: $o,X4: $o] :
              ( X3
             => X4 )
          @ ( in @ X2 @ ( setunion @ X1 ) )
          @ ! [X3: $o] :
              ( ^ [X4: $o,X5: $o] :
                  ( X4
                 => X5 )
              @ ! [X4: $i] :
                  ( ^ [X5: $o,X6: $o] :
                      ( X5
                     => X6 )
                  @ ( in @ X2 @ X4 )
                  @ ( ^ [X5: $o,X6: $o] :
                        ( X5
                       => X6 )
                    @ ( in @ X4 @ X1 )
                    @ X3 ) )
              @ X3 ) ) ) ) ).

thf(def_subPowSU,definition,
    ( subPowSU
    = ( ! [X1: $i,X2: $i] :
          ( ^ [X3: $o,X4: $o] :
              ( X3
             => X4 )
          @ ( in @ X2 @ X1 )
          @ ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) ) ) ) ).

thf(def_exuE2,definition,
    ( exuE2
    = ( ! [X1: $i > $o] :
          ( ^ [X2: $o,X3: $o] :
              ( X2
             => X3 )
          @ ( exu
            @ ^ [X2: $i] : ( X1 @ X2 ) )
          @ ? [X2: $i] :
            ! [X3: $i] :
              ( ( X1 @ X3 )
            <=> ( X3 = X2 ) ) ) ) ) ).

thf(def_nonemptyImpWitness,definition,
    ( nonemptyImpWitness
    = ( ! [X1: $i] :
          ( ^ [X2: $o,X3: $o] :
              ( X2
             => X3 )
          @ ( nonempty @ X1 )
          @ ? [X2: $i] :
              ( ( in @ X2 @ X1 )
              & $true ) ) ) ) ).

thf(def_uniqinunit,definition,
    ( uniqinunit
    = ( ! [X1: $i,X2: $i] :
          ( ^ [X3: $o,X4: $o] :
              ( X3
             => X4 )
          @ ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
          @ ( X1 = X2 ) ) ) ) ).

thf(def_notinsingleton,definition,
    ( notinsingleton
    = ( ! [X1: $i,X2: $i] :
          ( ^ [X3: $o,X4: $o] :
              ( X3
             => X4 )
          @ ( (~) @ ( X1 = X2 ) )
          @ ( (~) @ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) ) ) ) ) ).

thf(def_eqinunit,definition,
    ( eqinunit
    = ( ! [X1: $i,X2: $i] :
          ( ^ [X3: $o,X4: $o] :
              ( X3
             => X4 )
          @ ( X1 = X2 )
          @ ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ) ) ) ).

thf(def_singletonsswitch,definition,
    ( singletonsswitch
    = ( ! [X1: $i,X2: $i] :
          ( ^ [X3: $o,X4: $o] :
              ( X3
             => X4 )
          @ ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
          @ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) ) ) ) ).

thf(def_upairsetE,definition,
    ( upairsetE
    = ( ! [X1: $i,X2: $i,X3: $i] :
          ( ^ [X4: $o,X5: $o] :
              ( X4
             => X5 )
          @ ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
          @ ( ( X3 = X1 )
            | ( X3 = X2 ) ) ) ) ) ).

thf(def_upairsetIL,definition,
    ( upairsetIL
    = ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ) ) ) ).

thf(def_upairsetIR,definition,
    ( upairsetIR
    = ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ) ) ) ).

thf(def_emptyE1,definition,
    ( emptyE1
    = ( ! [X1: $i,X2: $i > $o] :
          ( ^ [X3: $o,X4: $o] :
              ( X3
             => X4 )
          @ ? [X3: $i] :
              ( ( in @ X3 @ X1 )
              & ( X2 @ X3 ) )
          @ ( ^ [X3: $o,X4: $o] :
                ( X3
               => X4 )
            @ ( ( dsetconstr @ X1
                @ ^ [X3: $i] : ( X2 @ X3 ) )
              = emptyset )
            @ $false ) ) ) ) ).

thf(def_vacuousDall,definition,
    ( vacuousDall
    = ( ! [X1: $i > $o,X2: $i] :
          ( ^ [X3: $o,X4: $o] :
              ( X3
             => X4 )
          @ ( in @ X2 @ emptyset )
          @ ( X1 @ X2 ) ) ) ) ).

thf(def_quantDeMorgan1,definition,
    ( quantDeMorgan1
    = ( ! [X1: $i,X2: $i > $o] :
          ( ^ [X3: $o,X4: $o] :
              ( X3
             => X4 )
          @ ( (~)
            @ ! [X3: $i] :
                ( ^ [X4: $o,X5: $o] :
                    ( X4
                   => X5 )
                @ ( in @ X3 @ X1 )
                @ ( X2 @ X3 ) ) )
          @ ? [X3: $i] :
              ( ( in @ X3 @ X1 )
              & ( (~) @ ( X2 @ X3 ) ) ) ) ) ) ).

thf(def_quantDeMorgan2,definition,
    ( quantDeMorgan2
    = ( ! [X1: $i,X2: $i > $o] :
          ( ^ [X3: $o,X4: $o] :
              ( X3
             => X4 )
          @ ! [X3: $i] :
              ( ^ [X4: $o,X5: $o] :
                  ( X4
                 => X5 )
              @ ( in @ X3 @ X1 )
              @ ( (~) @ ( X2 @ X3 ) ) )
          @ ( (~)
            @ ? [X3: $i] :
                ( ( in @ X3 @ X1 )
                & ( X2 @ X3 ) ) ) ) ) ) ).

thf(def_quantDeMorgan3,definition,
    ( quantDeMorgan3
    = ( ! [X1: $i,X2: $i > $o] :
          ( ^ [X3: $o,X4: $o] :
              ( X3
             => X4 )
          @ ( (~)
            @ ? [X3: $i] :
                ( ( in @ X3 @ X1 )
                & ( X2 @ X3 ) ) )
          @ ! [X3: $i] :
              ( ^ [X4: $o,X5: $o] :
                  ( X4
                 => X5 )
              @ ( in @ X3 @ X1 )
              @ ( (~) @ ( X2 @ X3 ) ) ) ) ) ) ).

thf(def_quantDeMorgan4,definition,
    ( quantDeMorgan4
    = ( ! [X1: $i,X2: $i > $o] :
          ( ^ [X3: $o,X4: $o] :
              ( X3
             => X4 )
          @ ? [X3: $i] :
              ( ( in @ X3 @ X1 )
              & ( (~) @ ( X2 @ X3 ) ) )
          @ ( (~)
            @ ! [X3: $i] :
                ( ^ [X4: $o,X5: $o] :
                    ( X4
                   => X5 )
                @ ( in @ X3 @ X1 )
                @ ( X2 @ X3 ) ) ) ) ) ) ).

thf(def_prop2setI,definition,
    ( prop2setI
    = ( ! [X1: $o] :
          ( ^ [X2: $o,X3: $o] :
              ( X2
             => X3 )
          @ X1
          @ ( in @ emptyset @ ( prop2set @ X1 ) ) ) ) ) ).

thf(def_prop2set2propI,definition,
    ( prop2set2propI
    = ( ! [X1: $o] :
          ( ^ [X2: $o,X3: $o] :
              ( X2
             => X3 )
          @ X1
          @ ( set2prop @ ( prop2set @ X1 ) ) ) ) ) ).

thf(def_notdexE,definition,
    ( notdexE
    = ( ! [X1: $i,X2: $i > $o] :
          ( ^ [X3: $o,X4: $o] :
              ( X3
             => X4 )
          @ ( (~)
            @ ? [X3: $i] :
                ( ( in @ X3 @ X1 )
                & ( X2 @ X3 ) ) )
          @ ! [X3: $i] :
              ( ^ [X4: $o,X5: $o] :
                  ( X4
                 => X5 )
              @ ( in @ X3 @ X1 )
              @ ( (~) @ ( X2 @ X3 ) ) ) ) ) ) ).

thf(def_notdallE,definition,
    ( notdallE
    = ( ! [X1: $i,X2: $i > $o] :
          ( ^ [X3: $o,X4: $o] :
              ( X3
             => X4 )
          @ ( (~)
            @ ! [X3: $i] :
                ( ^ [X4: $o,X5: $o] :
                    ( X4
                   => X5 )
                @ ( in @ X3 @ X1 )
                @ ( X2 @ X3 ) ) )
          @ ? [X3: $i] :
              ( ( in @ X3 @ X1 )
              & ( (~) @ ( X2 @ X3 ) ) ) ) ) ) ).

thf(def_exuI1,definition,
    ( exuI1
    = ( ! [X1: $i > $o] :
          ( ^ [X2: $o,X3: $o] :
              ( X2
             => X3 )
          @ ? [X2: $i] :
              ( ( X1 @ X2 )
              & ! [X3: $i] :
                  ( ^ [X4: $o,X5: $o] :
                      ( X4
                     => X5 )
                  @ ( X1 @ X3 )
                  @ ( X2 = X3 ) ) )
          @ ( exu
            @ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ) ).

thf(def_exuI3,definition,
    ( exuI3
    = ( ! [X1: $i > $o] :
          ( ^ [X2: $o,X3: $o] :
              ( X2
             => X3 )
          @ ? [X2: $i] : ( X1 @ X2 )
          @ ( ^ [X2: $o,X3: $o] :
                ( X2
               => X3 )
            @ ! [X2: $i,X3: $i] :
                ( ^ [X4: $o,X5: $o] :
                    ( X4
                   => X5 )
                @ ( X1 @ X2 )
                @ ( ^ [X4: $o,X5: $o] :
                      ( X4
                     => X5 )
                  @ ( X1 @ X3 )
                  @ ( X2 = X3 ) ) )
            @ ( exu
              @ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ) ) ).

thf(def_exuI2,definition,
    ( exuI2
    = ( ! [X1: $i > $o] :
          ( ^ [X2: $o,X3: $o] :
              ( X2
             => X3 )
          @ ? [X2: $i] :
            ! [X3: $i] :
              ( ( X1 @ X3 )
            <=> ( X3 = X2 ) )
          @ ( exu
            @ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ) ).

thf(def_inCongP,definition,
    ( inCongP
    = ( ! [X1: $i,X2: $i] :
          ( ^ [X3: $o,X4: $o] :
              ( X3
             => X4 )
          @ ( X1 = X2 )
          @ ! [X3: $i,X4: $i] :
              ( ^ [X5: $o,X6: $o] :
                  ( X5
                 => X6 )
              @ ( X3 = X4 )
              @ ( ^ [X5: $o,X6: $o] :
                    ( X5
                   => X6 )
                @ ( in @ X3 @ X1 )
                @ ( in @ X4 @ X2 ) ) ) ) ) ) ).

thf(def_in__Cong,definition,
    ( in__Cong
    = ( ! [X1: $i,X2: $i] :
          ( ^ [X3: $o,X4: $o] :
              ( X3
             => X4 )
          @ ( X1 = X2 )
          @ ! [X3: $i,X4: $i] :
              ( ^ [X5: $o,X6: $o] :
                  ( X5
                 => X6 )
              @ ( X3 = X4 )
              @ ( ( in @ X3 @ X1 )
              <=> ( in @ X4 @ X2 ) ) ) ) ) ) ).

thf(def_exuE3u,definition,
    ( exuE3u
    = ( ! [X1: $i > $o] :
          ( ^ [X2: $o,X3: $o] :
              ( X2
             => X3 )
          @ ( exu
            @ ^ [X2: $i] : ( X1 @ X2 ) )
          @ ! [X2: $i,X3: $i] :
              ( ^ [X4: $o,X5: $o] :
                  ( X4
                 => X5 )
              @ ( X1 @ X2 )
              @ ( ^ [X4: $o,X5: $o] :
                    ( X4
                   => X5 )
                @ ( X1 @ X3 )
                @ ( X2 = X3 ) ) ) ) ) ) ).

thf(def_exu__Cong,definition,
    ( exu__Cong
    = ( ! [X1: $i > $o,X2: $i > $o] :
          ( ^ [X3: $o,X4: $o] :
              ( X3
             => X4 )
          @ ! [X3: $i,X4: $i] :
              ( ^ [X5: $o,X6: $o] :
                  ( X5
                 => X6 )
              @ ( X3 = X4 )
              @ ( ( X1 @ X3 )
              <=> ( X2 @ X4 ) ) )
          @ ( ( exu
              @ ^ [X3: $i] : ( X1 @ X3 ) )
          <=> ( exu
              @ ^ [X3: $i] : ( X2 @ X3 ) ) ) ) ) ) ).

thf(def_emptyset__Cong,definition,
    ( emptyset__Cong
    = ( emptyset = emptyset ) ) ).

thf(def_setadjoin__Cong,definition,
    ( setadjoin__Cong
    = ( ! [X1: $i,X2: $i] :
          ( ^ [X3: $o,X4: $o] :
              ( X3
             => X4 )
          @ ( X1 = X2 )
          @ ! [X3: $i,X4: $i] :
              ( ^ [X5: $o,X6: $o] :
                  ( X5
                 => X6 )
              @ ( X3 = X4 )
              @ ( ( setadjoin @ X1 @ X3 )
                = ( setadjoin @ X2 @ X4 ) ) ) ) ) ) ).

thf(def_powerset__Cong,definition,
    ( powerset__Cong
    = ( ! [X1: $i,X2: $i] :
          ( ^ [X3: $o,X4: $o] :
              ( X3
             => X4 )
          @ ( X1 = X2 )
          @ ( ( powerset @ X1 )
            = ( powerset @ X2 ) ) ) ) ) ).

thf(def_setunion__Cong,definition,
    ( setunion__Cong
    = ( ! [X1: $i,X2: $i] :
          ( ^ [X3: $o,X4: $o] :
              ( X3
             => X4 )
          @ ( X1 = X2 )
          @ ( ( setunion @ X1 )
            = ( setunion @ X2 ) ) ) ) ) ).

thf(def_omega__Cong,definition,
    ( omega__Cong
    = ( omega = omega ) ) ).

thf(def_exuEu,definition,
    ( exuEu
    = ( ! [X1: $i > $o] :
          ( ^ [X2: $o,X3: $o] :
              ( X2
             => X3 )
          @ ( exu
            @ ^ [X2: $i] : ( X1 @ X2 ) )
          @ ! [X2: $i,X3: $i] :
              ( ^ [X4: $o,X5: $o] :
                  ( X4
                 => X5 )
              @ ( X1 @ X2 )
              @ ( ^ [X4: $o,X5: $o] :
                    ( X4
                   => X5 )
                @ ( X1 @ X3 )
                @ ( X2 = X3 ) ) ) ) ) ) ).

thf(def_descr__Cong,definition,
    ( descr__Cong
    = ( ! [X1: $i > $o,X2: $i > $o] :
          ( ^ [X3: $o,X4: $o] :
              ( X3
             => X4 )
          @ ! [X3: $i,X4: $i] :
              ( ^ [X5: $o,X6: $o] :
                  ( X5
                 => X6 )
              @ ( X3 = X4 )
              @ ( ( X1 @ X3 )
              <=> ( X2 @ X4 ) ) )
          @ ( ^ [X3: $o,X4: $o] :
                ( X3
               => X4 )
            @ ( exu
              @ ^ [X3: $i] : ( X1 @ X3 ) )
            @ ( ^ [X3: $o,X4: $o] :
                  ( X3
                 => X4 )
              @ ( exu
                @ ^ [X3: $i] : ( X2 @ X3 ) )
              @ ( ( descr
                  @ ^ [X3: $i] : ( X1 @ X3 ) )
                = ( descr
                  @ ^ [X3: $i] : ( X2 @ X3 ) ) ) ) ) ) ) ) ).

thf(def_dsetconstr__Cong,definition,
    ( dsetconstr__Cong
    = ( ! [X1: $i,X2: $i] :
          ( ^ [X3: $o,X4: $o] :
              ( X3
             => X4 )
          @ ( X1 = X2 )
          @ ! [X3: $i > $o,X4: $i > $o] :
              ( ^ [X5: $o,X6: $o] :
                  ( X5
                 => X6 )
              @ ! [X5: $i] :
                  ( ^ [X6: $o,X7: $o] :
                      ( X6
                     => X7 )
                  @ ( in @ X5 @ X1 )
                  @ ! [X6: $i] :
                      ( ^ [X7: $o,X8: $o] :
                          ( X7
                         => X8 )
                      @ ( in @ X6 @ X2 )
                      @ ( ^ [X7: $o,X8: $o] :
                            ( X7
                           => X8 )
                        @ ( X5 = X6 )
                        @ ( ( X3 @ X5 )
                        <=> ( X4 @ X6 ) ) ) ) )
              @ ( ( dsetconstr @ X1
                  @ ^ [X5: $i] : ( X3 @ X5 ) )
                = ( dsetconstr @ X2
                  @ ^ [X5: $i] : ( X4 @ X5 ) ) ) ) ) ) ) ).

thf(def_subsetI1,definition,
    ( subsetI1
    = ( ! [X1: $i,X2: $i] :
          ( ^ [X3: $o,X4: $o] :
              ( X3
             => X4 )
          @ ! [X3: $i] :
              ( ^ [X4: $o,X5: $o] :
                  ( X4
                 => X5 )
              @ ( in @ X3 @ X1 )
              @ ( in @ X3 @ X2 ) )
          @ ( subset @ X1 @ X2 ) ) ) ) ).

thf(def_eqimpsubset2,definition,
    ( eqimpsubset2
    = ( ! [X1: $i,X2: $i] :
          ( ^ [X3: $o,X4: $o] :
              ( X3
             => X4 )
          @ ( X1 = X2 )
          @ ( subset @ X2 @ X1 ) ) ) ) ).

thf(def_eqimpsubset1,definition,
    ( eqimpsubset1
    = ( ! [X1: $i,X2: $i] :
          ( ^ [X3: $o,X4: $o] :
              ( X3
             => X4 )
          @ ( X1 = X2 )
          @ ( subset @ X1 @ X2 ) ) ) ) ).

thf(def_subsetI2,definition,
    ( subsetI2
    = ( ! [X1: $i,X2: $i] :
          ( ^ [X3: $o,X4: $o] :
              ( X3
             => X4 )
          @ ! [X3: $i] :
              ( ^ [X4: $o,X5: $o] :
                  ( X4
                 => X5 )
              @ ( in @ X3 @ X1 )
              @ ( in @ X3 @ X2 ) )
          @ ( subset @ X1 @ X2 ) ) ) ) ).

thf(def_emptysetsubset,definition,
    ( emptysetsubset
    = ( ! [X1: $i] : ( subset @ emptyset @ X1 ) ) ) ).

thf(def_subsetE,definition,
    ( subsetE
    = ( ! [X1: $i,X2: $i,X3: $i] :
          ( ^ [X4: $o,X5: $o] :
              ( X4
             => X5 )
          @ ( subset @ X1 @ X2 )
          @ ( ^ [X4: $o,X5: $o] :
                ( X4
               => X5 )
            @ ( in @ X3 @ X1 )
            @ ( in @ X3 @ X2 ) ) ) ) ) ).

thf(def_subsetE2,definition,
    ( subsetE2
    = ( ! [X1: $i,X2: $i,X3: $i] :
          ( ^ [X4: $o,X5: $o] :
              ( X4
             => X5 )
          @ ( subset @ X1 @ X2 )
          @ ( ^ [X4: $o,X5: $o] :
                ( X4
               => X5 )
            @ ( (~) @ ( in @ X3 @ X2 ) )
            @ ( (~) @ ( in @ X3 @ X1 ) ) ) ) ) ) ).

thf(def_notsubsetI,definition,
    ( notsubsetI
    = ( ! [X1: $i,X2: $i,X3: $i] :
          ( ^ [X4: $o,X5: $o] :
              ( X4
             => X5 )
          @ ( in @ X3 @ X1 )
          @ ( ^ [X4: $o,X5: $o] :
                ( X4
               => X5 )
            @ ( (~) @ ( in @ X3 @ X2 ) )
            @ ( (~) @ ( subset @ X1 @ X2 ) ) ) ) ) ) ).

thf(def_notequalI1,definition,
    ( notequalI1
    = ( ! [X1: $i,X2: $i] :
          ( ^ [X3: $o,X4: $o] :
              ( X3
             => X4 )
          @ ( (~) @ ( subset @ X1 @ X2 ) )
          @ ( (~) @ ( X1 = X2 ) ) ) ) ) ).

thf(def_notequalI2,definition,
    ( notequalI2
    = ( ! [X1: $i,X2: $i,X3: $i] :
          ( ^ [X4: $o,X5: $o] :
              ( X4
             => X5 )
          @ ( in @ X3 @ X1 )
          @ ( ^ [X4: $o,X5: $o] :
                ( X4
               => X5 )
            @ ( (~) @ ( in @ X3 @ X2 ) )
            @ ( (~) @ ( X1 = X2 ) ) ) ) ) ) ).

thf(def_subsetRefl,definition,
    ( subsetRefl
    = ( ! [X1: $i] : ( subset @ X1 @ X1 ) ) ) ).

thf(def_subsetTrans,definition,
    ( subsetTrans
    = ( ! [X1: $i,X2: $i,X3: $i] :
          ( ^ [X4: $o,X5: $o] :
              ( X4
             => X5 )
          @ ( subset @ X1 @ X2 )
          @ ( ^ [X4: $o,X5: $o] :
                ( X4
               => X5 )
            @ ( subset @ X2 @ X3 )
            @ ( subset @ X1 @ X3 ) ) ) ) ) ).

thf(def_setadjoinSub,definition,
    ( setadjoinSub
    = ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) ) ) ) ).

thf(def_setadjoinSub2,definition,
    ( setadjoinSub2
    = ( ! [X1: $i,X2: $i,X3: $i] :
          ( ^ [X4: $o,X5: $o] :
              ( X4
             => X5 )
          @ ( subset @ X1 @ X3 )
          @ ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) ) ) ) ).

thf(def_subset2powerset,definition,
    ( subset2powerset
    = ( ! [X1: $i,X2: $i] :
          ( ^ [X3: $o,X4: $o] :
              ( X3
             => X4 )
          @ ( subset @ X1 @ X2 )
          @ ( in @ X1 @ ( powerset @ X2 ) ) ) ) ) ).

thf(def_setextsub,definition,
    ( setextsub
    = ( ! [X1: $i,X2: $i] :
          ( ^ [X3: $o,X4: $o] :
              ( X3
             => X4 )
          @ ( subset @ X1 @ X2 )
          @ ( ^ [X3: $o,X4: $o] :
                ( X3
               => X4 )
            @ ( subset @ X2 @ X1 )
            @ ( X1 = X2 ) ) ) ) ) ).

thf(def_subsetemptysetimpeq,definition,
    ( subsetemptysetimpeq
    = ( ! [X1: $i] :
          ( ^ [X2: $o,X3: $o] :
              ( X2
             => X3 )
          @ ( subset @ X1 @ emptyset )
          @ ( X1 = emptyset ) ) ) ) ).

thf(def_powersetI1,definition,
    ( powersetI1
    = ( ! [X1: $i,X2: $i] :
          ( ^ [X3: $o,X4: $o] :
              ( X3
             => X4 )
          @ ( subset @ X2 @ X1 )
          @ ( in @ X2 @ ( powerset @ X1 ) ) ) ) ) ).

thf(def_powersetE1,definition,
    ( powersetE1
    = ( ! [X1: $i,X2: $i] :
          ( ^ [X3: $o,X4: $o] :
              ( X3
             => X4 )
          @ ( in @ X2 @ ( powerset @ X1 ) )
          @ ( subset @ X2 @ X1 ) ) ) ) ).

thf(def_inPowerset,definition,
    ( inPowerset
    = ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) ) ) ) ).

thf(def_powersetsubset,definition,
    ( powersetsubset
    = ( ! [X1: $i,X2: $i] :
          ( ^ [X3: $o,X4: $o] :
              ( X3
             => X4 )
          @ ( subset @ X1 @ X2 )
          @ ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) ) ) ) ).

thf(def_sepInPowerset,definition,
    ( sepInPowerset
    = ( ! [X1: $i,X2: $i > $o] :
          ( in
          @ ( dsetconstr @ X1
            @ ^ [X3: $i] : ( X2 @ X3 ) )
          @ ( powerset @ X1 ) ) ) ) ).

thf(def_sepSubset,definition,
    ( sepSubset
    = ( ! [X1: $i,X2: $i > $o] :
          ( subset
          @ ( dsetconstr @ X1
            @ ^ [X3: $i] : ( X2 @ X3 ) )
          @ X1 ) ) ) ).

thf(def_binunionIL,definition,
    ( binunionIL
    = ( ! [X1: $i,X2: $i,X3: $i] :
          ( ^ [X4: $o,X5: $o] :
              ( X4
             => X5 )
          @ ( in @ X3 @ X1 )
          @ ( in @ X3 @ ( binunion @ X1 @ X2 ) ) ) ) ) ).

thf(def_upairset2IR,definition,
    ( upairset2IR
    = ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ) ) ) ).

thf(def_binunionIR,definition,
    ( binunionIR
    = ( ! [X1: $i,X2: $i,X3: $i] :
          ( ^ [X4: $o,X5: $o] :
              ( X4
             => X5 )
          @ ( in @ X3 @ X2 )
          @ ( in @ X3 @ ( binunion @ X1 @ X2 ) ) ) ) ) ).

thf(def_binunionEcases,definition,
    ( binunionEcases
    = ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
          ( ^ [X5: $o,X6: $o] :
              ( X5
             => X6 )
          @ ( in @ X3 @ ( binunion @ X1 @ X2 ) )
          @ ( ^ [X5: $o,X6: $o] :
                ( X5
               => X6 )
            @ ( ^ [X5: $o,X6: $o] :
                  ( X5
                 => X6 )
              @ ( in @ X3 @ X1 )
              @ X4 )
            @ ( ^ [X5: $o,X6: $o] :
                  ( X5
                 => X6 )
              @ ( ^ [X5: $o,X6: $o] :
                    ( X5
                   => X6 )
                @ ( in @ X3 @ X2 )
                @ X4 )
              @ X4 ) ) ) ) ) ).

thf(def_binunionE,definition,
    ( binunionE
    = ( ! [X1: $i,X2: $i,X3: $i] :
          ( ^ [X4: $o,X5: $o] :
              ( X4
             => X5 )
          @ ( in @ X3 @ ( binunion @ X1 @ X2 ) )
          @ ( ( in @ X3 @ X1 )
            | ( in @ X3 @ X2 ) ) ) ) ) ).

thf(def_binunionLsub,definition,
    ( binunionLsub
    = ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) ) ) ) ).

thf(def_binunionRsub,definition,
    ( binunionRsub
    = ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) ) ) ) ).

thf(def_binintersectI,definition,
    ( binintersectI
    = ( ! [X1: $i,X2: $i,X3: $i] :
          ( ^ [X4: $o,X5: $o] :
              ( X4
             => X5 )
          @ ( in @ X3 @ X1 )
          @ ( ^ [X4: $o,X5: $o] :
                ( X4
               => X5 )
            @ ( in @ X3 @ X2 )
            @ ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) ) ) ) ).

thf(def_binintersectSubset5,definition,
    ( binintersectSubset5
    = ( ! [X1: $i,X2: $i,X3: $i] :
          ( ^ [X4: $o,X5: $o] :
              ( X4
             => X5 )
          @ ( subset @ X3 @ X1 )
          @ ( ^ [X4: $o,X5: $o] :
                ( X4
               => X5 )
            @ ( subset @ X3 @ X2 )
            @ ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) ) ) ) ).

thf(def_binintersectEL,definition,
    ( binintersectEL
    = ( ! [X1: $i,X2: $i,X3: $i] :
          ( ^ [X4: $o,X5: $o] :
              ( X4
             => X5 )
          @ ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
          @ ( in @ X3 @ X1 ) ) ) ) ).

thf(def_binintersectLsub,definition,
    ( binintersectLsub
    = ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 ) ) ) ).

thf(def_binintersectSubset2,definition,
    ( binintersectSubset2
    = ( ! [X1: $i,X2: $i] :
          ( ^ [X3: $o,X4: $o] :
              ( X3
             => X4 )
          @ ( subset @ X1 @ X2 )
          @ ( ( binintersect @ X1 @ X2 )
            = X1 ) ) ) ) ).

thf(def_binintersectSubset3,definition,
    ( binintersectSubset3
    = ( ! [X1: $i,X2: $i] :
          ( ^ [X3: $o,X4: $o] :
              ( X3
             => X4 )
          @ ( ( binintersect @ X1 @ X2 )
            = X2 )
          @ ( subset @ X2 @ X1 ) ) ) ) ).

thf(def_binintersectER,definition,
    ( binintersectER
    = ( ! [X1: $i,X2: $i,X3: $i] :
          ( ^ [X4: $o,X5: $o] :
              ( X4
             => X5 )
          @ ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
          @ ( in @ X3 @ X2 ) ) ) ) ).

thf(def_disjointsetsI1,definition,
    ( disjointsetsI1
    = ( ! [X1: $i,X2: $i] :
          ( ^ [X3: $o,X4: $o] :
              ( X3
             => X4 )
          @ ( (~)
            @ ? [X3: $i] :
                ( ( in @ X3 @ X1 )
                & ( in @ X3 @ X2 ) ) )
          @ ( ( binintersect @ X1 @ X2 )
            = emptyset ) ) ) ) ).

thf(def_binintersectRsub,definition,
    ( binintersectRsub
    = ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 ) ) ) ).

thf(def_binintersectSubset4,definition,
    ( binintersectSubset4
    = ( ! [X1: $i,X2: $i] :
          ( ^ [X3: $o,X4: $o] :
              ( X3
             => X4 )
          @ ( subset @ X2 @ X1 )
          @ ( ( binintersect @ X1 @ X2 )
            = X2 ) ) ) ) ).

thf(def_binintersectSubset1,definition,
    ( binintersectSubset1
    = ( ! [X1: $i,X2: $i] :
          ( ^ [X3: $o,X4: $o] :
              ( X3
             => X4 )
          @ ( ( binintersect @ X1 @ X2 )
            = X1 )
          @ ( subset @ X1 @ X2 ) ) ) ) ).

thf(def_bs114d,definition,
    ( bs114d
    = ( ! [X1: $i,X2: $i,X3: $i] :
          ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
          = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) ) ) ) ).

thf(def_setminusI,definition,
    ( setminusI
    = ( ! [X1: $i,X2: $i,X3: $i] :
          ( ^ [X4: $o,X5: $o] :
              ( X4
             => X5 )
          @ ( in @ X3 @ X1 )
          @ ( ^ [X4: $o,X5: $o] :
                ( X4
               => X5 )
            @ ( (~) @ ( in @ X3 @ X2 ) )
            @ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) ) ) ) ).

thf(def_setminusEL,definition,
    ( setminusEL
    = ( ! [X1: $i,X2: $i,X3: $i] :
          ( ^ [X4: $o,X5: $o] :
              ( X4
             => X5 )
          @ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
          @ ( in @ X3 @ X1 ) ) ) ) ).

thf(def_setminusER,definition,
    ( setminusER
    = ( ! [X1: $i,X2: $i,X3: $i] :
          ( ^ [X4: $o,X5: $o] :
              ( X4
             => X5 )
          @ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
          @ ( (~) @ ( in @ X3 @ X2 ) ) ) ) ) ).

thf(def_setminusSubset2,definition,
    ( setminusSubset2
    = ( ! [X1: $i,X2: $i] :
          ( ^ [X3: $o,X4: $o] :
              ( X3
             => X4 )
          @ ( subset @ X1 @ X2 )
          @ ( ( setminus @ X1 @ X2 )
            = emptyset ) ) ) ) ).

thf(def_setminusERneg,definition,
    ( setminusERneg
    = ( ! [X1: $i,X2: $i,X3: $i] :
          ( ^ [X4: $o,X5: $o] :
              ( X4
             => X5 )
          @ ( (~) @ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
          @ ( ^ [X4: $o,X5: $o] :
                ( X4
               => X5 )
            @ ( in @ X3 @ X1 )
            @ ( in @ X3 @ X2 ) ) ) ) ) ).

thf(def_setminusELneg,definition,
    ( setminusELneg
    = ( ! [X1: $i,X2: $i,X3: $i] :
          ( ^ [X4: $o,X5: $o] :
              ( X4
             => X5 )
          @ ( (~) @ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
          @ ( ^ [X4: $o,X5: $o] :
                ( X4
               => X5 )
            @ ( (~) @ ( in @ X3 @ X2 ) )
            @ ( (~) @ ( in @ X3 @ X1 ) ) ) ) ) ) ).

thf(def_setminusILneg,definition,
    ( setminusILneg
    = ( ! [X1: $i,X2: $i,X3: $i] :
          ( ^ [X4: $o,X5: $o] :
              ( X4
             => X5 )
          @ ( (~) @ ( in @ X3 @ X1 ) )
          @ ( (~) @ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) ) ) ) ).

thf(def_setminusIRneg,definition,
    ( setminusIRneg
    = ( ! [X1: $i,X2: $i,X3: $i] :
          ( ^ [X4: $o,X5: $o] :
              ( X4
             => X5 )
          @ ( in @ X3 @ X2 )
          @ ( (~) @ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) ) ) ) ).

thf(def_setminusLsub,definition,
    ( setminusLsub
    = ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 ) ) ) ).

thf(def_setminusSubset1,definition,
    ( setminusSubset1
    = ( ! [X1: $i,X2: $i] :
          ( ^ [X3: $o,X4: $o] :
              ( X3
             => X4 )
          @ ( ( setminus @ X1 @ X2 )
            = emptyset )
          @ ( subset @ X1 @ X2 ) ) ) ) ).

thf(def_symdiffE,definition,
    ( symdiffE
    = ( ! [X1: $i,X2: $i,X3: $i] :
          ( ^ [X4: $o,X5: $o] :
              ( X4
             => X5 )
          @ ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
          @ ! [X4: $o] :
              ( ^ [X5: $o,X6: $o] :
                  ( X5
                 => X6 )
              @ ( ^ [X5: $o,X6: $o] :
                    ( X5
                   => X6 )
                @ ( in @ X3 @ X1 )
                @ ( ^ [X5: $o,X6: $o] :
                      ( X5
                     => X6 )
                  @ ( (~) @ ( in @ X3 @ X2 ) )
                  @ X4 ) )
              @ ( ^ [X5: $o,X6: $o] :
                    ( X5
                   => X6 )
                @ ( ^ [X5: $o,X6: $o] :
                      ( X5
                     => X6 )
                  @ ( (~) @ ( in @ X3 @ X1 ) )
                  @ ( ^ [X5: $o,X6: $o] :
                        ( X5
                       => X6 )
                    @ ( in @ X3 @ X2 )
                    @ X4 ) )
                @ X4 ) ) ) ) ) ).

thf(def_symdiffI1,definition,
    ( symdiffI1
    = ( ! [X1: $i,X2: $i,X3: $i] :
          ( ^ [X4: $o,X5: $o] :
              ( X4
             => X5 )
          @ ( in @ X3 @ X1 )
          @ ( ^ [X4: $o,X5: $o] :
                ( X4
               => X5 )
            @ ( (~) @ ( in @ X3 @ X2 ) )
            @ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) ) ) ) ).

thf(def_symdiffI2,definition,
    ( symdiffI2
    = ( ! [X1: $i,X2: $i,X3: $i] :
          ( ^ [X4: $o,X5: $o] :
              ( X4
             => X5 )
          @ ( (~) @ ( in @ X3 @ X1 ) )
          @ ( ^ [X4: $o,X5: $o] :
                ( X4
               => X5 )
            @ ( in @ X3 @ X2 )
            @ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) ) ) ) ).

thf(def_symdiffIneg1,definition,
    ( symdiffIneg1
    = ( ! [X1: $i,X2: $i,X3: $i] :
          ( ^ [X4: $o,X5: $o] :
              ( X4
             => X5 )
          @ ( in @ X3 @ X1 )
          @ ( ^ [X4: $o,X5: $o] :
                ( X4
               => X5 )
            @ ( in @ X3 @ X2 )
            @ ( (~) @ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) ) ) ) ) ).

thf(def_symdiffIneg2,definition,
    ( symdiffIneg2
    = ( ! [X1: $i,X2: $i,X3: $i] :
          ( ^ [X4: $o,X5: $o] :
              ( X4
             => X5 )
          @ ( (~) @ ( in @ X3 @ X1 ) )
          @ ( ^ [X4: $o,X5: $o] :
                ( X4
               => X5 )
            @ ( (~) @ ( in @ X3 @ X2 ) )
            @ ( (~) @ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) ) ) ) ) ).

thf(def_secondinupair,definition,
    ( secondinupair
    = ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ) ) ) ).

thf(def_setukpairIL,definition,
    ( setukpairIL
    = ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).

thf(def_setukpairIR,definition,
    ( setukpairIR
    = ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).

thf(def_kpairiskpair,definition,
    ( kpairiskpair
    = ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) ) ) ).

thf(def_kpairp,definition,
    ( kpairp
    = ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) ) ) ) ).

thf(def_singletonsubset,definition,
    ( singletonsubset
    = ( ! [X1: $i,X2: $i] :
          ( ^ [X3: $o,X4: $o] :
              ( X3
             => X4 )
          @ ( in @ X2 @ X1 )
          @ ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) ) ) ) ).

thf(def_singletoninpowerset,definition,
    ( singletoninpowerset
    = ( ! [X1: $i,X2: $i] :
          ( ^ [X3: $o,X4: $o] :
              ( X3
             => X4 )
          @ ( in @ X2 @ X1 )
          @ ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) ) ) ) ).

thf(def_singletoninpowunion,definition,
    ( singletoninpowunion
    = ( ! [X1: $i,X2: $i,X3: $i] :
          ( ^ [X4: $o,X5: $o] :
              ( X4
             => X5 )
          @ ( in @ X3 @ X1 )
          @ ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) ) ).

thf(def_upairset2E,definition,
    ( upairset2E
    = ( ! [X1: $i,X2: $i,X3: $i] :
          ( ^ [X4: $o,X5: $o] :
              ( X4
             => X5 )
          @ ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
          @ ( ( X3 = X1 )
            | ( X3 = X2 ) ) ) ) ) ).

thf(def_upairsubunion,definition,
    ( upairsubunion
    = ( ! [X1: $i,X2: $i,X3: $i] :
          ( ^ [X4: $o,X5: $o] :
              ( X4
             => X5 )
          @ ( in @ X3 @ X1 )
          @ ! [X4: $i] :
              ( ^ [X5: $o,X6: $o] :
                  ( X5
                 => X6 )
              @ ( in @ X4 @ X2 )
              @ ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) ) ) ) ).

thf(def_upairinpowunion,definition,
    ( upairinpowunion
    = ( ! [X1: $i,X2: $i,X3: $i] :
          ( ^ [X4: $o,X5: $o] :
              ( X4
             => X5 )
          @ ( in @ X3 @ X1 )
          @ ! [X4: $i] :
              ( ^ [X5: $o,X6: $o] :
                  ( X5
                 => X6 )
              @ ( in @ X4 @ X2 )
              @ ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) ) ) ).

thf(def_ubforcartprodlem1,definition,
    ( ubforcartprodlem1
    = ( ! [X1: $i,X2: $i,X3: $i] :
          ( ^ [X4: $o,X5: $o] :
              ( X4
             => X5 )
          @ ( in @ X3 @ X1 )
          @ ! [X4: $i] :
              ( ^ [X5: $o,X6: $o] :
                  ( X5
                 => X6 )
              @ ( in @ X4 @ X2 )
              @ ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) ) ) ).

thf(def_ubforcartprodlem2,definition,
    ( ubforcartprodlem2
    = ( ! [X1: $i,X2: $i,X3: $i] :
          ( ^ [X4: $o,X5: $o] :
              ( X4
             => X5 )
          @ ( in @ X3 @ X1 )
          @ ! [X4: $i] :
              ( ^ [X5: $o,X6: $o] :
                  ( X5
                 => X6 )
              @ ( in @ X4 @ X2 )
              @ ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) ) ) ) ).

thf(def_ubforcartprodlem3,definition,
    ( ubforcartprodlem3
    = ( ! [X1: $i,X2: $i,X3: $i] :
          ( ^ [X4: $o,X5: $o] :
              ( X4
             => X5 )
          @ ( in @ X3 @ X1 )
          @ ! [X4: $i] :
              ( ^ [X5: $o,X6: $o] :
                  ( X5
                 => X6 )
              @ ( in @ X4 @ X2 )
              @ ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) ) ) ) ).

thf(def_cartprodpairin,definition,
    ( cartprodpairin
    = ( ! [X1: $i,X2: $i,X3: $i] :
          ( ^ [X4: $o,X5: $o] :
              ( X4
             => X5 )
          @ ( in @ X3 @ X1 )
          @ ! [X4: $i] :
              ( ^ [X5: $o,X6: $o] :
                  ( X5
                 => X6 )
              @ ( in @ X4 @ X2 )
              @ ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) ) ) ) ).

thf(def_cartprodmempair1,definition,
    ( cartprodmempair1
    = ( ! [X1: $i,X2: $i,X3: $i] :
          ( ^ [X4: $o,X5: $o] :
              ( X4
             => X5 )
          @ ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
          @ ? [X4: $i] :
              ( ( in @ X4 @ X1 )
              & ? [X5: $i] :
                  ( ( in @ X5 @ X2 )
                  & ( X3
                    = ( kpair @ X4 @ X5 ) ) ) ) ) ) ) ).

thf(def_cartprodmempair,definition,
    ( cartprodmempair
    = ( ! [X1: $i,X2: $i,X3: $i] :
          ( ^ [X4: $o,X5: $o] :
              ( X4
             => X5 )
          @ ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
          @ ( iskpair @ X3 ) ) ) ) ).

thf(def_setunionE2,definition,
    ( setunionE2
    = ( ! [X1: $i,X2: $i] :
          ( ^ [X3: $o,X4: $o] :
              ( X3
             => X4 )
          @ ( in @ X2 @ ( setunion @ X1 ) )
          @ ? [X3: $i] :
              ( ( in @ X3 @ X1 )
              & ( in @ X2 @ X3 ) ) ) ) ) ).

thf(def_setunionsingleton1,definition,
    ( setunionsingleton1
    = ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 ) ) ) ).

thf(def_setunionsingleton2,definition,
    ( setunionsingleton2
    = ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) ) ) ) ).

thf(def_setunionsingleton,definition,
    ( setunionsingleton
    = ( ! [X1: $i] :
          ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
          = X1 ) ) ) ).

thf(def_singleton,definition,
    ( singleton
    = ( ^ [X1: $i] :
        ? [X2: $i] :
          ( ( in @ X2 @ X1 )
          & ( X1
            = ( setadjoin @ X2 @ emptyset ) ) ) ) ) ).

thf(def_singletonprop,definition,
    ( singletonprop
    = ( ! [X1: $i,X2: $i > $o] :
          ( ^ [X3: $o,X4: $o] :
              ( X3
             => X4 )
          @ ! [X3: $i] :
              ( ^ [X4: $o,X5: $o] :
                  ( X4
                 => X5 )
              @ ( in @ X3 @ X1 )
              @ ! [X4: $i] :
                  ( ^ [X5: $o,X6: $o] :
                      ( X5
                     => X6 )
                  @ ( in @ X4 @ X1 )
                  @ ( ^ [X5: $o,X6: $o] :
                        ( X5
                       => X6 )
                    @ ( X2 @ X3 )
                    @ ( ^ [X5: $o,X6: $o] :
                          ( X5
                         => X6 )
                      @ ( X2 @ X4 )
                      @ ( X3 = X4 ) ) ) ) )
          @ ( ^ [X3: $o,X4: $o] :
                ( X3
               => X4 )
            @ ? [X3: $i] :
                ( ( in @ X3 @ X1 )
                & ( X2 @ X3 ) )
            @ ( singleton
              @ ( dsetconstr @ X1
                @ ^ [X3: $i] : ( X2 @ X3 ) ) ) ) ) ) ) ).

thf(def_ex1,definition,
    ( ex1
    = ( ^ [X1: $i,X2: $i > $o] :
          ( singleton
          @ ( dsetconstr @ X1
            @ ^ [X3: $i] : ( X2 @ X3 ) ) ) ) ) ).

thf(def_ex1E1,definition,
    ( ex1E1
    = ( ! [X1: $i,X2: $i > $o] :
          ( ^ [X3: $o,X4: $o] :
              ( X3
             => X4 )
          @ ( ex1 @ X1
            @ ^ [X3: $i] : ( X2 @ X3 ) )
          @ ? [X3: $i] :
              ( ( in @ X3 @ X1 )
              & ( X2 @ X3 ) ) ) ) ) ).

thf(def_ex1I,definition,
    ( ex1I
    = ( ! [X1: $i,X2: $i > $o,X3: $i] :
          ( ^ [X4: $o,X5: $o] :
              ( X4
             => X5 )
          @ ( in @ X3 @ X1 )
          @ ( ^ [X4: $o,X5: $o] :
                ( X4
               => X5 )
            @ ( X2 @ X3 )
            @ ( ^ [X4: $o,X5: $o] :
                  ( X4
                 => X5 )
              @ ! [X4: $i] :
                  ( ^ [X5: $o,X6: $o] :
                      ( X5
                     => X6 )
                  @ ( in @ X4 @ X1 )
                  @ ( ^ [X5: $o,X6: $o] :
                        ( X5
                       => X6 )
                    @ ( X2 @ X4 )
                    @ ( X4 = X3 ) ) )
              @ ( ex1 @ X1
                @ ^ [X4: $i] : ( X2 @ X4 ) ) ) ) ) ) ) ).

thf(def_ex1I2,definition,
    ( ex1I2
    = ( ! [X1: $i,X2: $i > $o] :
          ( ^ [X3: $o,X4: $o] :
              ( X3
             => X4 )
          @ ! [X3: $i] :
              ( ^ [X4: $o,X5: $o] :
                  ( X4
                 => X5 )
              @ ( in @ X3 @ X1 )
              @ ! [X4: $i] :
                  ( ^ [X5: $o,X6: $o] :
                      ( X5
                     => X6 )
                  @ ( in @ X4 @ X1 )
                  @ ( ^ [X5: $o,X6: $o] :
                        ( X5
                       => X6 )
                    @ ( X2 @ X3 )
                    @ ( ^ [X5: $o,X6: $o] :
                          ( X5
                         => X6 )
                      @ ( X2 @ X4 )
                      @ ( X3 = X4 ) ) ) ) )
          @ ( ^ [X3: $o,X4: $o] :
                ( X3
               => X4 )
            @ ? [X3: $i] :
                ( ( in @ X3 @ X1 )
                & ( X2 @ X3 ) )
            @ ( ex1 @ X1
              @ ^ [X3: $i] : ( X2 @ X3 ) ) ) ) ) ) ).

thf(def_singletonsuniq,definition,
    ( singletonsuniq
    = ( ! [X1: $i,X2: $i] :
          ( ^ [X3: $o,X4: $o] :
              ( X3
             => X4 )
          @ ( ( setadjoin @ X1 @ emptyset )
            = ( setadjoin @ X2 @ emptyset ) )
          @ ( X1 = X2 ) ) ) ) ).

thf(def_setukpairinjL1,definition,
    ( setukpairinjL1
    = ( ! [X1: $i,X2: $i,X3: $i] :
          ( ^ [X4: $o,X5: $o] :
              ( X4
             => X5 )
          @ ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
          @ ( X1 = X3 ) ) ) ) ).

thf(def_kfstsingleton,definition,
    ( kfstsingleton
    = ( ! [X1: $i] :
          ( ^ [X2: $o,X3: $o] :
              ( X2
             => X3 )
          @ ( iskpair @ X1 )
          @ ( singleton
            @ ( dsetconstr @ ( setunion @ X1 )
              @ ^ [X2: $i] : ( in @ ( setadjoin @ X2 @ emptyset ) @ X1 ) ) ) ) ) ) ).

thf(def_theprop,definition,
    ( theprop
    = ( ! [X1: $i] :
          ( ^ [X2: $o,X3: $o] :
              ( X2
             => X3 )
          @ ( singleton @ X1 )
          @ ( in @ ( setunion @ X1 ) @ X1 ) ) ) ) ).

thf(def_kfstpairEq,definition,
    ( kfstpairEq
    = ( ! [X1: $i,X2: $i] :
          ( ( kfst @ ( kpair @ X1 @ X2 ) )
          = X1 ) ) ) ).

thf(def_cartprodfstin,definition,
    ( cartprodfstin
    = ( ! [X1: $i,X2: $i,X3: $i] :
          ( ^ [X4: $o,X5: $o] :
              ( X4
             => X5 )
          @ ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
          @ ( in @ ( kfst @ X3 ) @ X1 ) ) ) ) ).

thf(def_setukpairinjL2,definition,
    ( setukpairinjL2
    = ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
          ( ^ [X5: $o,X6: $o] :
              ( X5
             => X6 )
          @ ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
            = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
          @ ( X1 = X3 ) ) ) ) ).

thf(def_setukpairinjL,definition,
    ( setukpairinjL
    = ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
          ( ^ [X5: $o,X6: $o] :
              ( X5
             => X6 )
          @ ( ( kpair @ X1 @ X2 )
            = ( kpair @ X3 @ X4 ) )
          @ ( X1 = X3 ) ) ) ) ).

thf(def_setukpairinjR11,definition,
    ( setukpairinjR11
    = ( ! [X1: $i,X2: $i] :
          ( ^ [X3: $o,X4: $o] :
              ( X3
             => X4 )
          @ ( X1 = X2 )
          @ ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
            = ( setadjoin @ X1 @ emptyset ) ) ) ) ) ).

thf(def_setukpairinjR12,definition,
    ( setukpairinjR12
    = ( ! [X1: $i,X2: $i] :
          ( ^ [X3: $o,X4: $o] :
              ( X3
             => X4 )
          @ ( X1 = X2 )
          @ ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
            = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) ) ) ) ).

thf(def_setukpairinjR1,definition,
    ( setukpairinjR1
    = ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
          ( ^ [X5: $o,X6: $o] :
              ( X5
             => X6 )
          @ ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
            = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
          @ ( ^ [X5: $o,X6: $o] :
                ( X5
               => X6 )
            @ ( X3 = X4 )
            @ ( X2 = X4 ) ) ) ) ) ).

thf(def_upairequniteq,definition,
    ( upairequniteq
    = ( ! [X1: $i,X2: $i,X3: $i] :
          ( ^ [X4: $o,X5: $o] :
              ( X4
             => X5 )
          @ ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
            = ( setadjoin @ X3 @ emptyset ) )
          @ ( X1 = X2 ) ) ) ) ).

thf(def_setukpairinjR2,definition,
    ( setukpairinjR2
    = ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
          ( ^ [X5: $o,X6: $o] :
              ( X5
             => X6 )
          @ ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
            = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
          @ ( X2 = X4 ) ) ) ) ).

thf(def_setukpairinjR,definition,
    ( setukpairinjR
    = ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
          ( ^ [X5: $o,X6: $o] :
              ( X5
             => X6 )
          @ ( ( kpair @ X1 @ X2 )
            = ( kpair @ X3 @ X4 ) )
          @ ( X2 = X4 ) ) ) ) ).

thf(def_ksndsingleton,definition,
    ( ksndsingleton
    = ( ! [X1: $i] :
          ( ^ [X2: $o,X3: $o] :
              ( X2
             => X3 )
          @ ( iskpair @ X1 )
          @ ( singleton
            @ ( dsetconstr @ ( setunion @ X1 )
              @ ^ [X2: $i] :
                  ( X1
                  = ( kpair @ ( kfst @ X1 ) @ X2 ) ) ) ) ) ) ) ).

thf(def_ksndpairEq,definition,
    ( ksndpairEq
    = ( ! [X1: $i,X2: $i] :
          ( ( ksnd @ ( kpair @ X1 @ X2 ) )
          = X2 ) ) ) ).

thf(def_kpairsurjEq,definition,
    ( kpairsurjEq
    = ( ! [X1: $i] :
          ( ^ [X2: $o,X3: $o] :
              ( X2
             => X3 )
          @ ( iskpair @ X1 )
          @ ( ( kpair @ ( kfst @ X1 ) @ ( ksnd @ X1 ) )
            = X1 ) ) ) ) ).

thf(def_cartprodsndin,definition,
    ( cartprodsndin
    = ( ! [X1: $i,X2: $i,X3: $i] :
          ( ^ [X4: $o,X5: $o] :
              ( X4
             => X5 )
          @ ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
          @ ( in @ ( ksnd @ X3 ) @ X2 ) ) ) ) ).

thf(def_cartprodpairmemEL,definition,
    ( cartprodpairmemEL
    = ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
          ( ^ [X5: $o,X6: $o] :
              ( X5
             => X6 )
          @ ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
          @ ( in @ X3 @ X1 ) ) ) ) ).

thf(def_cartprodpairmemER,definition,
    ( cartprodpairmemER
    = ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
          ( ^ [X5: $o,X6: $o] :
              ( X5
             => X6 )
          @ ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
          @ ( in @ X4 @ X2 ) ) ) ) ).

thf(def_cartprodmempaircEq,definition,
    ( cartprodmempaircEq
    = ( ! [X1: $i,X2: $i,X3: $i] :
          ( ^ [X4: $o,X5: $o] :
              ( X4
             => X5 )
          @ ( in @ X3 @ X1 )
          @ ! [X4: $i] :
              ( ^ [X5: $o,X6: $o] :
                  ( X5
                 => X6 )
              @ ( in @ X4 @ X2 )
              @ ( ( kpair @ X3 @ X4 )
                = ( kpair @ X3 @ X4 ) ) ) ) ) ) ).

thf(def_cartprodfstpairEq,definition,
    ( cartprodfstpairEq
    = ( ! [X1: $i,X2: $i,X3: $i] :
          ( ^ [X4: $o,X5: $o] :
              ( X4
             => X5 )
          @ ( in @ X3 @ X1 )
          @ ! [X4: $i] :
              ( ^ [X5: $o,X6: $o] :
                  ( X5
                 => X6 )
              @ ( in @ X4 @ X2 )
              @ ( ( kfst @ ( kpair @ X3 @ X4 ) )
                = X3 ) ) ) ) ) ).

thf(def_cartprodsndpairEq,definition,
    ( cartprodsndpairEq
    = ( ! [X1: $i,X2: $i,X3: $i] :
          ( ^ [X4: $o,X5: $o] :
              ( X4
             => X5 )
          @ ( in @ X3 @ X1 )
          @ ! [X4: $i] :
              ( ^ [X5: $o,X6: $o] :
                  ( X5
                 => X6 )
              @ ( in @ X4 @ X2 )
              @ ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                = X4 ) ) ) ) ) ).

thf(cartprodpairsurjEq,conjecture,
    ( ! [X1: $i,X2: $i] :
        ( ! [X3: $i] :
            ( ( in @ X3 @ X1 )
            = ( in @ X3 @ X2 ) )
       => ( X1 = X2 ) )
   => ( ! [X1: $i] :
          ~ ( in @ X1 @ emptyset )
     => ( ! [X1: $i,X2: $i,X3: $i] :
            ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
            = ( ( X3 != X1 )
             => ( in @ X3 @ X2 ) ) )
       => ( ! [X1: $i,X2: $i] :
              ( ( in @ X2 @ ( powerset @ X1 ) )
              = ( ! [X3: $i] :
                    ( ( in @ X3 @ X2 )
                   => ( in @ X3 @ X1 ) ) ) )
         => ( ! [X1: $i,X2: $i] :
                ( ( in @ X2 @ ( setunion @ X1 ) )
                = ( ~ ! [X3: $i] :
                        ( ( in @ X2 @ X3 )
                       => ~ ( in @ X3 @ X1 ) ) ) )
           => ( ( in @ emptyset @ omega )
             => ( ! [X1: $i] :
                    ( ( in @ X1 @ omega )
                   => ( in @ ( setadjoin @ X1 @ X1 ) @ omega ) )
               => ( ! [X1: $i] :
                      ( ~ ( ( in @ emptyset @ X1 )
                         => ~ ! [X2: $i] :
                                ( ~ ( ( in @ X2 @ omega )
                                   => ~ ( in @ X2 @ X1 ) )
                               => ( in @ ( setadjoin @ X2 @ X2 ) @ X1 ) ) )
                     => ! [X2: $i] :
                          ( ( in @ X2 @ omega )
                         => ( in @ X2 @ X1 ) ) )
                 => ( ! [X1: $i > $i > $o,X2: $i] :
                        ( ! [X3: $i] :
                            ( ( in @ X3 @ X2 )
                           => ~ ! [X4: $i] :
                                  ( ( X1 @ X3 @ X4 )
                                 => ~ ! [X5: $i] :
                                        ( ( X1 @ X3 @ X5 )
                                       => ( X4 = X5 ) ) ) )
                       => ~ ! [X3: $i] :
                              ~ ! [X4: $i] :
                                  ( ( in @ X4 @ X3 )
                                  = ( ~ ! [X5: $i] :
                                          ( ( in @ X5 @ X2 )
                                         => ~ ( X1 @ X5 @ X4 ) ) ) ) )
                   => ( ! [X1: $i] :
                          ( ~ ! [X2: $i] :
                                ~ ( in @ X2 @ X1 )
                         => ~ ! [X2: $i] :
                                ( ( in @ X2 @ X1 )
                               => ~ ! [X3: $i] :
                                      ( ( in @ X3 @ X2 )
                                     => ~ ( in @ X3 @ X1 ) ) ) )
                     => ( ! [X1: $i] :
                            ~ ! [X2: $i] :
                                ( ~ ( ~ ( ! [X3: $i] :
                                            ( ( in @ X3 @ X2 )
                                           => ! [X4: $i] :
                                                ( ( in @ X4 @ X3 )
                                               => ( in @ X4 @ X1 ) ) )
                                       => ~ ! [X3: $i,X4: $i] :
                                              ( ~ ( ( in @ X3 @ X1 )
                                                 => ~ ( in @ X4 @ X1 ) )
                                             => ( ! [X5: $i] :
                                                    ( ( in @ X5 @ X2 )
                                                   => ( ( in @ X3 @ X5 )
                                                      = ( in @ X4 @ X5 ) ) )
                                               => ( X3 = X4 ) ) ) )
                                   => ~ ! [X3: $i,X4: $i] :
                                          ( ~ ( ( in @ X3 @ X2 )
                                             => ~ ( in @ X4 @ X2 ) )
                                         => ( ~ ! [X5: $i] :
                                                  ( ( in @ X5 @ X3 )
                                                 => ( in @ X5 @ X4 ) )
                                           => ! [X5: $i] :
                                                ( ( in @ X5 @ X4 )
                                               => ( in @ X5 @ X3 ) ) ) ) )
                               => ~ ! [X3: $i] :
                                      ( ~ ( ! [X4: $i] :
                                              ( ( in @ X4 @ X3 )
                                             => ( in @ X4 @ X1 ) )
                                         => ! [X4: $i] :
                                              ~ ( in @ X4 @ X3 ) )
                                     => ~ ! [X4: $i,X5: $i] :
                                            ( ~ ( ~ ( ( in @ X4 @ X2 )
                                                   => ~ ( in @ X5 @ X3 ) )
                                               => ~ ! [X6: $i] :
                                                      ( ( in @ X6 @ X4 )
                                                     => ~ ( in @ X6 @ X3 ) ) )
                                           => ~ ! [X6: $i] :
                                                  ( ( in @ X6 @ X2 )
                                                 => ( ~ ! [X7: $i] :
                                                          ( ( in @ X7 @ X6 )
                                                         => ( in @ X7 @ X4 ) )
                                                   => ( in @ X5 @ X6 ) ) ) ) ) )
                       => ( ! [X1: $i > $o] :
                              ( ~ ! [X2: $i] :
                                    ( ( X1 @ X2 )
                                   => ~ ! [X3: $i] :
                                          ( ( X1 @ X3 )
                                         => ( X2 = X3 ) ) )
                             => ( X1 @ ( descr @ X1 ) ) )
                         => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                ( ( in @ X3 @ X1 )
                               => ( ( X2 @ X3 )
                                 => ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) ) ) )
                           => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                  ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                 => ( in @ X3 @ X1 ) )
                             => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                    ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                   => ( X2 @ X3 ) )
                               => ( ! [X1: $o,X2: $i] :
                                      ( ( in @ X2 @ ( prop2set @ X1 ) )
                                     => X1 )
                                 => ( ! [X1: $i] :
                                        ( ( in @ X1 @ emptyset )
                                       => ! [X2: $o] : X2 )
                                   => ( ! [X1: $i] :
                                          ~ ( in @ X1 @ emptyset )
                                     => ( ! [X1: $i] :
                                            ~ ( in @ X1 @ emptyset )
                                       => ( ! [X1: $i > $o] :
                                              ( ~ ! [X2: $i] :
                                                    ( ( X1 @ X2 )
                                                   => ~ ! [X3: $i] :
                                                          ( ( X1 @ X3 )
                                                         => ( X2 = X3 ) ) )
                                             => ~ ! [X2: $i] :
                                                    ~ ( X1 @ X2 ) )
                                         => ( ! [X1: $i,X2: $i] :
                                                ( ! [X3: $i] :
                                                    ( ( in @ X3 @ X1 )
                                                   => ( in @ X3 @ X2 ) )
                                               => ( ! [X3: $i] :
                                                      ( ( in @ X3 @ X2 )
                                                     => ( in @ X3 @ X1 ) )
                                                 => ( X1 = X2 ) ) )
                                           => ( ! [X1: $i] :
                                                  ( ! [X2: $i] :
                                                      ~ ( in @ X2 @ X1 )
                                                 => ( X1 = emptyset ) )
                                             => ( ! [X1: $i] :
                                                    ( ! [X2: $i] :
                                                        ~ ( in @ X2 @ X1 )
                                                   => ( X1 = emptyset ) )
                                               => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                      ( ( in @ X3 @ X1 )
                                                     => ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                        = ( X2 @ X3 ) ) )
                                                 => ( ! [X1: $i] :
                                                        ( ( X1 != emptyset )
                                                       => ~ ! [X2: $i] :
                                                              ~ ( in @ X2 @ X1 ) )
                                                   => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                          ( ( in @ X3 @ X1 )
                                                         => ( ( X2 @ X3 )
                                                           => ( ( dsetconstr @ X1 @ X2 )
                                                             != emptyset ) ) )
                                                     => ( ! [X1: $i] :
                                                            ( ~ ! [X2: $i] :
                                                                  ~ ( in @ X2 @ X1 )
                                                           => ( X1 != emptyset ) )
                                                       => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) )
                                                         => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                  ( ( in @ X3 @ X2 )
                                                                 => ( in @ X3 @ ( setadjoin @ X1 @ X2 ) ) )
                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                    ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                                                   => ! [X4: $o] :
                                                                        ( ( ( X3 = X1 )
                                                                         => X4 )
                                                                       => ( ( ( in @ X3 @ X2 )
                                                                           => X4 )
                                                                         => X4 ) ) )
                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                      ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                                                     => ( ( X3 != X1 )
                                                                       => ( in @ X3 @ X2 ) ) )
                                                                 => ( ! [X1: $i] :
                                                                        ( ( dsetconstr @ X1
                                                                          @ ^ [X2: $i] : ~ $false )
                                                                        = X1 )
                                                                   => ( ! [X1: $i,X2: $i] :
                                                                          ( ! [X3: $i] :
                                                                              ( ( in @ X3 @ X2 )
                                                                             => ( in @ X3 @ X1 ) )
                                                                         => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                                     => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                                                       => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                ( ( in @ X2 @ ( powerset @ X1 ) )
                                                                               => ( ( in @ X3 @ X2 )
                                                                                 => ( in @ X3 @ X1 ) ) )
                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                  ( ( in @ X2 @ X3 )
                                                                                 => ( ( in @ X3 @ X1 )
                                                                                   => ( in @ X2 @ ( setunion @ X1 ) ) ) )
                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                    ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                   => ! [X3: $o] :
                                                                                        ( ! [X4: $i] :
                                                                                            ( ( in @ X2 @ X4 )
                                                                                           => ( ( in @ X4 @ X1 )
                                                                                             => X3 ) )
                                                                                       => X3 ) )
                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                      ( ( in @ X2 @ X1 )
                                                                                     => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
                                                                                 => ( ! [X1: $i > $o] :
                                                                                        ( ~ ! [X2: $i] :
                                                                                              ( ( X1 @ X2 )
                                                                                             => ~ ! [X3: $i] :
                                                                                                    ( ( X1 @ X3 )
                                                                                                   => ( X2 = X3 ) ) )
                                                                                       => ~ ! [X2: $i] :
                                                                                              ~ ! [X3: $i] :
                                                                                                  ( ( X1 @ X3 )
                                                                                                  = ( X3 = X2 ) ) )
                                                                                   => ( ! [X1: $i] :
                                                                                          ( ( X1 != emptyset )
                                                                                         => ~ ! [X2: $i] :
                                                                                                ~ ( in @ X2 @ X1 ) )
                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                            ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                           => ( X1 = X2 ) )
                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                              ( ( X1 != X2 )
                                                                                             => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                ( ( X1 = X2 )
                                                                                               => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                  ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                 => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                    ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                   => ( ( X3 != X1 )
                                                                                                     => ( X3 = X2 ) ) )
                                                                                               => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                 => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                                                                          ( ~ ! [X3: $i] :
                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                               => ~ ( X2 @ X3 ) )
                                                                                                         => ( ( dsetconstr @ X1 @ X2 )
                                                                                                           != emptyset ) )
                                                                                                     => ( ! [X1: $i > $o,X2: $i] :
                                                                                                            ( ( in @ X2 @ emptyset )
                                                                                                           => ( X1 @ X2 ) )
                                                                                                       => ( ! [X1: $o] :
                                                                                                              ( X1
                                                                                                             => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                                                                                         => ( ! [X1: $o] :
                                                                                                                ( X1
                                                                                                               => ( set2prop @ ( prop2set @ X1 ) ) )
                                                                                                           => ( ! [X1: $i > $o] :
                                                                                                                  ( ~ ! [X2: $i] :
                                                                                                                        ~ ( X1 @ X2 )
                                                                                                                 => ( ! [X2: $i,X3: $i] :
                                                                                                                        ( ( X1 @ X2 )
                                                                                                                       => ( ( X1 @ X3 )
                                                                                                                         => ( X2 = X3 ) ) )
                                                                                                                   => ~ ! [X2: $i] :
                                                                                                                          ( ( X1 @ X2 )
                                                                                                                         => ~ ! [X3: $i] :
                                                                                                                                ( ( X1 @ X3 )
                                                                                                                               => ( X2 = X3 ) ) ) ) )
                                                                                                             => ( ! [X1: $i > $o] :
                                                                                                                    ( ~ ! [X2: $i] :
                                                                                                                          ~ ! [X3: $i] :
                                                                                                                              ( ( X1 @ X3 )
                                                                                                                              = ( X3 = X2 ) )
                                                                                                                   => ~ ! [X2: $i] :
                                                                                                                          ( ( X1 @ X2 )
                                                                                                                         => ~ ! [X3: $i] :
                                                                                                                                ( ( X1 @ X3 )
                                                                                                                               => ( X2 = X3 ) ) ) )
                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                      ( ( X1 = X2 )
                                                                                                                     => ! [X3: $i,X4: $i] :
                                                                                                                          ( ( X3 = X4 )
                                                                                                                         => ( ( in @ X3 @ X1 )
                                                                                                                           => ( in @ X4 @ X2 ) ) ) )
                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                        ( ( X1 = X2 )
                                                                                                                       => ! [X3: $i,X4: $i] :
                                                                                                                            ( ( X3 = X4 )
                                                                                                                           => ( ( in @ X3 @ X1 )
                                                                                                                              = ( in @ X4 @ X2 ) ) ) )
                                                                                                                   => ( ! [X1: $i > $o] :
                                                                                                                          ( ~ ! [X2: $i] :
                                                                                                                                ( ( X1 @ X2 )
                                                                                                                               => ~ ! [X3: $i] :
                                                                                                                                      ( ( X1 @ X3 )
                                                                                                                                     => ( X2 = X3 ) ) )
                                                                                                                         => ! [X2: $i,X3: $i] :
                                                                                                                              ( ( X1 @ X2 )
                                                                                                                             => ( ( X1 @ X3 )
                                                                                                                               => ( X2 = X3 ) ) ) )
                                                                                                                     => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                                                            ( ! [X3: $i,X4: $i] :
                                                                                                                                ( ( X3 = X4 )
                                                                                                                               => ( ( X1 @ X3 )
                                                                                                                                  = ( X2 @ X4 ) ) )
                                                                                                                           => ( ( ~ ! [X3: $i] :
                                                                                                                                      ( ( X1 @ X3 )
                                                                                                                                     => ~ ! [X4: $i] :
                                                                                                                                            ( ( X1 @ X4 )
                                                                                                                                           => ( X3 = X4 ) ) ) )
                                                                                                                              = ( ~ ! [X3: $i] :
                                                                                                                                      ( ( X2 @ X3 )
                                                                                                                                     => ~ ! [X4: $i] :
                                                                                                                                            ( ( X2 @ X4 )
                                                                                                                                           => ( X3 = X4 ) ) ) ) ) )
                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                              ( ( X1 = X2 )
                                                                                                                             => ! [X3: $i,X4: $i] :
                                                                                                                                  ( ( X3 = X4 )
                                                                                                                                 => ( ( setadjoin @ X1 @ X3 )
                                                                                                                                    = ( setadjoin @ X2 @ X4 ) ) ) )
                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                ( ( X1 = X2 )
                                                                                                                               => ( ( powerset @ X1 )
                                                                                                                                  = ( powerset @ X2 ) ) )
                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                  ( ( X1 = X2 )
                                                                                                                                 => ( ( setunion @ X1 )
                                                                                                                                    = ( setunion @ X2 ) ) )
                                                                                                                             => ( ! [X1: $i > $o] :
                                                                                                                                    ( ~ ! [X2: $i] :
                                                                                                                                          ( ( X1 @ X2 )
                                                                                                                                         => ~ ! [X3: $i] :
                                                                                                                                                ( ( X1 @ X3 )
                                                                                                                                               => ( X2 = X3 ) ) )
                                                                                                                                   => ! [X2: $i,X3: $i] :
                                                                                                                                        ( ( X1 @ X2 )
                                                                                                                                       => ( ( X1 @ X3 )
                                                                                                                                         => ( X2 = X3 ) ) ) )
                                                                                                                               => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                                                                      ( ! [X3: $i,X4: $i] :
                                                                                                                                          ( ( X3 = X4 )
                                                                                                                                         => ( ( X1 @ X3 )
                                                                                                                                            = ( X2 @ X4 ) ) )
                                                                                                                                     => ( ~ ! [X3: $i] :
                                                                                                                                              ( ( X1 @ X3 )
                                                                                                                                             => ~ ! [X4: $i] :
                                                                                                                                                    ( ( X1 @ X4 )
                                                                                                                                                   => ( X3 = X4 ) ) )
                                                                                                                                       => ( ~ ! [X3: $i] :
                                                                                                                                                ( ( X2 @ X3 )
                                                                                                                                               => ~ ! [X4: $i] :
                                                                                                                                                      ( ( X2 @ X4 )
                                                                                                                                                     => ( X3 = X4 ) ) )
                                                                                                                                         => ( ( descr @ X1 )
                                                                                                                                            = ( descr @ X2 ) ) ) ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                        ( ( X1 = X2 )
                                                                                                                                       => ! [X3: $i > $o,X4: $i > $o] :
                                                                                                                                            ( ! [X5: $i] :
                                                                                                                                                ( ( in @ X5 @ X1 )
                                                                                                                                               => ! [X6: $i] :
                                                                                                                                                    ( ( in @ X6 @ X2 )
                                                                                                                                                   => ( ( X5 = X6 )
                                                                                                                                                     => ( ( X3 @ X5 )
                                                                                                                                                        = ( X4 @ X6 ) ) ) ) )
                                                                                                                                           => ( ( dsetconstr @ X1 @ X3 )
                                                                                                                                              = ( dsetconstr @ X2 @ X4 ) ) ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                          ( ! [X3: $i] :
                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                             => ( in @ X3 @ X2 ) )
                                                                                                                                         => ( subset @ X1 @ X2 ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                            ( ( X1 = X2 )
                                                                                                                                           => ( subset @ X2 @ X1 ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                              ( ( X1 = X2 )
                                                                                                                                             => ( subset @ X1 @ X2 ) )
                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                ( ! [X3: $i] :
                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                   => ( in @ X3 @ X2 ) )
                                                                                                                                               => ( subset @ X1 @ X2 ) )
                                                                                                                                           => ( ! [X1: $i] : ( subset @ emptyset @ X1 )
                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                    ( ( subset @ X1 @ X2 )
                                                                                                                                                   => ( ( in @ X3 @ X1 )
                                                                                                                                                     => ( in @ X3 @ X2 ) ) )
                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                      ( ( subset @ X1 @ X2 )
                                                                                                                                                     => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                       => ~ ( in @ X3 @ X1 ) ) )
                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                       => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                         => ~ ( subset @ X1 @ X2 ) ) )
                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                          ( ~ ( subset @ X1 @ X2 )
                                                                                                                                                         => ( X1 != X2 ) )
                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                           => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                             => ( X1 != X2 ) ) )
                                                                                                                                                       => ( ! [X1: $i] : ( subset @ X1 @ X1 )
                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                ( ( subset @ X1 @ X2 )
                                                                                                                                                               => ( ( subset @ X2 @ X3 )
                                                                                                                                                                 => ( subset @ X1 @ X3 ) ) )
                                                                                                                                                           => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) )
                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                    ( ( subset @ X1 @ X3 )
                                                                                                                                                                   => ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                      ( ( subset @ X1 @ X2 )
                                                                                                                                                                     => ( in @ X1 @ ( powerset @ X2 ) ) )
                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                        ( ( subset @ X1 @ X2 )
                                                                                                                                                                       => ( ( subset @ X2 @ X1 )
                                                                                                                                                                         => ( X1 = X2 ) ) )
                                                                                                                                                                   => ( ! [X1: $i] :
                                                                                                                                                                          ( ( subset @ X1 @ emptyset )
                                                                                                                                                                         => ( X1 = emptyset ) )
                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                            ( ( subset @ X2 @ X1 )
                                                                                                                                                                           => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                              ( ( in @ X2 @ ( powerset @ X1 ) )
                                                                                                                                                                             => ( subset @ X2 @ X1 ) )
                                                                                                                                                                         => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                  ( ( subset @ X1 @ X2 )
                                                                                                                                                                                 => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
                                                                                                                                                                             => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                                                                                                                                                                               => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                       => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                            ( ( in @ X3 @ X2 )
                                                                                                                                                                                           => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                                                                                                                                                                              ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                                                             => ( ( ( in @ X3 @ X1 )
                                                                                                                                                                                                 => X4 )
                                                                                                                                                                                               => ( ( ( in @ X3 @ X2 )
                                                                                                                                                                                                   => X4 )
                                                                                                                                                                                                 => X4 ) ) )
                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                                                               => ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                 => ( in @ X3 @ X2 ) ) )
                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                     => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                       => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                        ( ( subset @ X3 @ X1 )
                                                                                                                                                                                                       => ( ( subset @ X3 @ X2 )
                                                                                                                                                                                                         => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                          ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                                                                                         => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                              ( ( subset @ X1 @ X2 )
                                                                                                                                                                                                             => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                                                = X1 ) )
                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                                                  = X2 )
                                                                                                                                                                                                               => ( subset @ X2 @ X1 ) )
                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                  ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                                                                                                 => ( in @ X3 @ X2 ) )
                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                    ( ! [X3: $i] :
                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                       => ~ ( in @ X3 @ X2 ) )
                                                                                                                                                                                                                   => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                                                      = emptyset ) )
                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                        ( ( subset @ X2 @ X1 )
                                                                                                                                                                                                                       => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                                                          = X2 ) )
                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                          ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                                                            = X1 )
                                                                                                                                                                                                                         => ( subset @ X1 @ X2 ) )
                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                            ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                                                                                                                                                                                            = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                             => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                               => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                                               => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                  ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                                                 => ~ ( in @ X3 @ X2 ) )
                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                    ( ( subset @ X1 @ X2 )
                                                                                                                                                                                                                                   => ( ( setminus @ X1 @ X2 )
                                                                                                                                                                                                                                      = emptyset ) )
                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                      ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                                                     => ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                       => ( in @ X3 @ X2 ) ) )
                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                        ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                                                       => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                                         => ~ ( in @ X3 @ X1 ) ) )
                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                          ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                                         => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                            ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                                           => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                ( ( ( setminus @ X1 @ X2 )
                                                                                                                                                                                                                                                  = emptyset )
                                                                                                                                                                                                                                               => ( subset @ X1 @ X2 ) )
                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                  ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                                                                                                                                                                                 => ! [X4: $o] :
                                                                                                                                                                                                                                                      ( ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                       => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                                                         => X4 ) )
                                                                                                                                                                                                                                                     => ( ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                         => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                                                           => X4 ) )
                                                                                                                                                                                                                                                       => X4 ) ) )
                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                   => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                                                     => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                      ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                     => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                                                       => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                       => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                                                         => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                          ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                         => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                                                           => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                      ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                                                     => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                        ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                                                       => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                         => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                            ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                                                           => ( ( X3 != X1 )
                                                                                                                                                                                                                                                                             => ( X3 = X2 ) ) )
                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                 => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                   => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                     => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                       => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                         => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                           => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                         => ~ ! [X4: $i] :
                                                                                                                                                                                                                                                                                                ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                                               => ! [X5: $i] :
                                                                                                                                                                                                                                                                                                    ( ( in @ X5 @ X2 )
                                                                                                                                                                                                                                                                                                   => ( X3
                                                                                                                                                                                                                                                                                                     != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                                                                                                                                                                                     => ( sP5
                                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                              ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                                                                                                                                                                                             => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                   => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                                                                                                                                                                                         => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                                                                                                                                                                                           => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                             => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                                    ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                                                                                                                                                                                    = X1 )
                                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                                                                      ( ! [X3: $i] :
                                                                                                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                              ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                                                             => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                                                                               => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                                                                 => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                                                                                                     => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                             => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                                                                                                       => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                                              ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                             => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                               != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                                                                        ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                                              ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                             => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                               != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                       => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                             => ~ ( X2 @ X3 ) ) )
                                                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                         => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                                                                           => ( ! [X4: $i] :
                                                                                                                                                                                                                                                                                                                  ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                                                                 => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                                                                   => ( X4 = X3 ) ) )
                                                                                                                                                                                                                                                                                                             => ~ ! [X4: $i] :
                                                                                                                                                                                                                                                                                                                    ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                   => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                                     != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                                                                            ( ! [X3: $i] :
                                                                                                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                                    ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                                                                   => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                                                                                     => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                                                                       => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                                                                                                           => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                                   => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                                                                                                             => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                                                    ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                   => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                                     != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                              ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                                                                                                                                                                                = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                                                             => ( X1 = X2 ) )
                                                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                               => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                                                           => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                                                  ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                                                                                 => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                                                        ( ( in @ X2
                                                                                                                                                                                                                                                                                                                          @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                                            @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                                                                                                                                                                                       => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                                            @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                                                                                                                         != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                                                                                             => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                                                    ( ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                                                          ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                                                                                                         => ( X1
                                                                                                                                                                                                                                                                                                                           != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                   => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                                      ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                      = X1 )
                                                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                       => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                          ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                                            = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                         => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                            ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                                              = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                                           => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                                              ( ( X1 = X2 )
                                                                                                                                                                                                                                                                                                                             => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                                                                                = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                                                ( ( X1 = X2 )
                                                                                                                                                                                                                                                                                                                               => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                                                  = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                                  ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                                                    = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                                 => ( ( X3 = X4 )
                                                                                                                                                                                                                                                                                                                                   => ( X2 = X4 ) ) )
                                                                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                                    ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                                                                                      = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                                                                                                                                                                                   => ( X1 = X2 ) )
                                                                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                                      ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                                                        = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                                     => ( X2 = X4 ) )
                                                                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                                        ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                                                          = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                                                       => ( X2 = X4 ) )
                                                                                                                                                                                                                                                                                                                                   => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                                                                          ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                                                                                                         => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                                                                                ( ( in @ X2
                                                                                                                                                                                                                                                                                                                                                  @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                                                                    @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                                                                                                        ( X1
                                                                                                                                                                                                                                                                                                                                                        = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                                                                                                                                                                               => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                                                                    @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                                                                                                        ( X1
                                                                                                                                                                                                                                                                                                                                                        = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                                                                                                                                                                                 != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                                                            ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                                            = X2 )
                                                                                                                                                                                                                                                                                                                                       => ( sP8
                                                                                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                                                ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                                               => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                                                  ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                                                 => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                                                    ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                                                   => ( in @ X4 @ X2 ) )
                                                                                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                                                                                         => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                                                                            = X3 ) ) )
                                                                                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                                                                                           => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                                                                              = X4 ) ) )
                                                                                                                                                                                                                                                                                                                                                   => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                                                        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                                                       => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                                                                                                                                                                                          = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

thf(h0,negated_conjecture,
    ~ ( ! [X1: $i,X2: $i] :
          ( ! [X3: $i] :
              ( ( in @ X3 @ X1 )
              = ( in @ X3 @ X2 ) )
         => ( X1 = X2 ) )
     => ( ! [X1: $i] :
            ~ ( in @ X1 @ emptyset )
       => ( ! [X1: $i,X2: $i,X3: $i] :
              ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
              = ( ( X3 != X1 )
               => ( in @ X3 @ X2 ) ) )
         => ( ! [X1: $i,X2: $i] :
                ( ( in @ X2 @ ( powerset @ X1 ) )
                = ( ! [X3: $i] :
                      ( ( in @ X3 @ X2 )
                     => ( in @ X3 @ X1 ) ) ) )
           => ( ! [X1: $i,X2: $i] :
                  ( ( in @ X2 @ ( setunion @ X1 ) )
                  = ( ~ ! [X3: $i] :
                          ( ( in @ X2 @ X3 )
                         => ~ ( in @ X3 @ X1 ) ) ) )
             => ( ( in @ emptyset @ omega )
               => ( ! [X1: $i] :
                      ( ( in @ X1 @ omega )
                     => ( in @ ( setadjoin @ X1 @ X1 ) @ omega ) )
                 => ( ! [X1: $i] :
                        ( ~ ( ( in @ emptyset @ X1 )
                           => ~ ! [X2: $i] :
                                  ( ~ ( ( in @ X2 @ omega )
                                     => ~ ( in @ X2 @ X1 ) )
                                 => ( in @ ( setadjoin @ X2 @ X2 ) @ X1 ) ) )
                       => ! [X2: $i] :
                            ( ( in @ X2 @ omega )
                           => ( in @ X2 @ X1 ) ) )
                   => ( ! [X1: $i > $i > $o,X2: $i] :
                          ( ! [X3: $i] :
                              ( ( in @ X3 @ X2 )
                             => ~ ! [X4: $i] :
                                    ( ( X1 @ X3 @ X4 )
                                   => ~ ! [X5: $i] :
                                          ( ( X1 @ X3 @ X5 )
                                         => ( X4 = X5 ) ) ) )
                         => ~ ! [X3: $i] :
                                ~ ! [X4: $i] :
                                    ( ( in @ X4 @ X3 )
                                    = ( ~ ! [X5: $i] :
                                            ( ( in @ X5 @ X2 )
                                           => ~ ( X1 @ X5 @ X4 ) ) ) ) )
                     => ( ! [X1: $i] :
                            ( ~ ! [X2: $i] :
                                  ~ ( in @ X2 @ X1 )
                           => ~ ! [X2: $i] :
                                  ( ( in @ X2 @ X1 )
                                 => ~ ! [X3: $i] :
                                        ( ( in @ X3 @ X2 )
                                       => ~ ( in @ X3 @ X1 ) ) ) )
                       => ( ! [X1: $i] :
                              ~ ! [X2: $i] :
                                  ( ~ ( ~ ( ! [X3: $i] :
                                              ( ( in @ X3 @ X2 )
                                             => ! [X4: $i] :
                                                  ( ( in @ X4 @ X3 )
                                                 => ( in @ X4 @ X1 ) ) )
                                         => ~ ! [X3: $i,X4: $i] :
                                                ( ~ ( ( in @ X3 @ X1 )
                                                   => ~ ( in @ X4 @ X1 ) )
                                               => ( ! [X5: $i] :
                                                      ( ( in @ X5 @ X2 )
                                                     => ( ( in @ X3 @ X5 )
                                                        = ( in @ X4 @ X5 ) ) )
                                                 => ( X3 = X4 ) ) ) )
                                     => ~ ! [X3: $i,X4: $i] :
                                            ( ~ ( ( in @ X3 @ X2 )
                                               => ~ ( in @ X4 @ X2 ) )
                                           => ( ~ ! [X5: $i] :
                                                    ( ( in @ X5 @ X3 )
                                                   => ( in @ X5 @ X4 ) )
                                             => ! [X5: $i] :
                                                  ( ( in @ X5 @ X4 )
                                                 => ( in @ X5 @ X3 ) ) ) ) )
                                 => ~ ! [X3: $i] :
                                        ( ~ ( ! [X4: $i] :
                                                ( ( in @ X4 @ X3 )
                                               => ( in @ X4 @ X1 ) )
                                           => ! [X4: $i] :
                                                ~ ( in @ X4 @ X3 ) )
                                       => ~ ! [X4: $i,X5: $i] :
                                              ( ~ ( ~ ( ( in @ X4 @ X2 )
                                                     => ~ ( in @ X5 @ X3 ) )
                                                 => ~ ! [X6: $i] :
                                                        ( ( in @ X6 @ X4 )
                                                       => ~ ( in @ X6 @ X3 ) ) )
                                             => ~ ! [X6: $i] :
                                                    ( ( in @ X6 @ X2 )
                                                   => ( ~ ! [X7: $i] :
                                                            ( ( in @ X7 @ X6 )
                                                           => ( in @ X7 @ X4 ) )
                                                     => ( in @ X5 @ X6 ) ) ) ) ) )
                         => ( ! [X1: $i > $o] :
                                ( ~ ! [X2: $i] :
                                      ( ( X1 @ X2 )
                                     => ~ ! [X3: $i] :
                                            ( ( X1 @ X3 )
                                           => ( X2 = X3 ) ) )
                               => ( X1 @ ( descr @ X1 ) ) )
                           => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                  ( ( in @ X3 @ X1 )
                                 => ( ( X2 @ X3 )
                                   => ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) ) ) )
                             => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                    ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                   => ( in @ X3 @ X1 ) )
                               => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                      ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                     => ( X2 @ X3 ) )
                                 => ( ! [X1: $o,X2: $i] :
                                        ( ( in @ X2 @ ( prop2set @ X1 ) )
                                       => X1 )
                                   => ( ! [X1: $i] :
                                          ( ( in @ X1 @ emptyset )
                                         => ! [X2: $o] : X2 )
                                     => ( ! [X1: $i] :
                                            ~ ( in @ X1 @ emptyset )
                                       => ( ! [X1: $i] :
                                              ~ ( in @ X1 @ emptyset )
                                         => ( ! [X1: $i > $o] :
                                                ( ~ ! [X2: $i] :
                                                      ( ( X1 @ X2 )
                                                     => ~ ! [X3: $i] :
                                                            ( ( X1 @ X3 )
                                                           => ( X2 = X3 ) ) )
                                               => ~ ! [X2: $i] :
                                                      ~ ( X1 @ X2 ) )
                                           => ( ! [X1: $i,X2: $i] :
                                                  ( ! [X3: $i] :
                                                      ( ( in @ X3 @ X1 )
                                                     => ( in @ X3 @ X2 ) )
                                                 => ( ! [X3: $i] :
                                                        ( ( in @ X3 @ X2 )
                                                       => ( in @ X3 @ X1 ) )
                                                   => ( X1 = X2 ) ) )
                                             => ( ! [X1: $i] :
                                                    ( ! [X2: $i] :
                                                        ~ ( in @ X2 @ X1 )
                                                   => ( X1 = emptyset ) )
                                               => ( ! [X1: $i] :
                                                      ( ! [X2: $i] :
                                                          ~ ( in @ X2 @ X1 )
                                                     => ( X1 = emptyset ) )
                                                 => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                        ( ( in @ X3 @ X1 )
                                                       => ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                          = ( X2 @ X3 ) ) )
                                                   => ( ! [X1: $i] :
                                                          ( ( X1 != emptyset )
                                                         => ~ ! [X2: $i] :
                                                                ~ ( in @ X2 @ X1 ) )
                                                     => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                            ( ( in @ X3 @ X1 )
                                                           => ( ( X2 @ X3 )
                                                             => ( ( dsetconstr @ X1 @ X2 )
                                                               != emptyset ) ) )
                                                       => ( ! [X1: $i] :
                                                              ( ~ ! [X2: $i] :
                                                                    ~ ( in @ X2 @ X1 )
                                                             => ( X1 != emptyset ) )
                                                         => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) )
                                                           => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                    ( ( in @ X3 @ X2 )
                                                                   => ( in @ X3 @ ( setadjoin @ X1 @ X2 ) ) )
                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                      ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                                                     => ! [X4: $o] :
                                                                          ( ( ( X3 = X1 )
                                                                           => X4 )
                                                                         => ( ( ( in @ X3 @ X2 )
                                                                             => X4 )
                                                                           => X4 ) ) )
                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                        ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                                                       => ( ( X3 != X1 )
                                                                         => ( in @ X3 @ X2 ) ) )
                                                                   => ( ! [X1: $i] :
                                                                          ( ( dsetconstr @ X1
                                                                            @ ^ [X2: $i] : ~ $false )
                                                                          = X1 )
                                                                     => ( ! [X1: $i,X2: $i] :
                                                                            ( ! [X3: $i] :
                                                                                ( ( in @ X3 @ X2 )
                                                                               => ( in @ X3 @ X1 ) )
                                                                           => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                                       => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                                                         => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                  ( ( in @ X2 @ ( powerset @ X1 ) )
                                                                                 => ( ( in @ X3 @ X2 )
                                                                                   => ( in @ X3 @ X1 ) ) )
                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                    ( ( in @ X2 @ X3 )
                                                                                   => ( ( in @ X3 @ X1 )
                                                                                     => ( in @ X2 @ ( setunion @ X1 ) ) ) )
                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                      ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                     => ! [X3: $o] :
                                                                                          ( ! [X4: $i] :
                                                                                              ( ( in @ X2 @ X4 )
                                                                                             => ( ( in @ X4 @ X1 )
                                                                                               => X3 ) )
                                                                                         => X3 ) )
                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                        ( ( in @ X2 @ X1 )
                                                                                       => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
                                                                                   => ( ! [X1: $i > $o] :
                                                                                          ( ~ ! [X2: $i] :
                                                                                                ( ( X1 @ X2 )
                                                                                               => ~ ! [X3: $i] :
                                                                                                      ( ( X1 @ X3 )
                                                                                                     => ( X2 = X3 ) ) )
                                                                                         => ~ ! [X2: $i] :
                                                                                                ~ ! [X3: $i] :
                                                                                                    ( ( X1 @ X3 )
                                                                                                    = ( X3 = X2 ) ) )
                                                                                     => ( ! [X1: $i] :
                                                                                            ( ( X1 != emptyset )
                                                                                           => ~ ! [X2: $i] :
                                                                                                  ~ ( in @ X2 @ X1 ) )
                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                              ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                             => ( X1 = X2 ) )
                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                ( ( X1 != X2 )
                                                                                               => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                  ( ( X1 = X2 )
                                                                                                 => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                    ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                   => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                      ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                     => ( ( X3 != X1 )
                                                                                                       => ( X3 = X2 ) ) )
                                                                                                 => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                   => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                                                                            ( ~ ! [X3: $i] :
                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                 => ~ ( X2 @ X3 ) )
                                                                                                           => ( ( dsetconstr @ X1 @ X2 )
                                                                                                             != emptyset ) )
                                                                                                       => ( ! [X1: $i > $o,X2: $i] :
                                                                                                              ( ( in @ X2 @ emptyset )
                                                                                                             => ( X1 @ X2 ) )
                                                                                                         => ( ! [X1: $o] :
                                                                                                                ( X1
                                                                                                               => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                                                                                           => ( ! [X1: $o] :
                                                                                                                  ( X1
                                                                                                                 => ( set2prop @ ( prop2set @ X1 ) ) )
                                                                                                             => ( ! [X1: $i > $o] :
                                                                                                                    ( ~ ! [X2: $i] :
                                                                                                                          ~ ( X1 @ X2 )
                                                                                                                   => ( ! [X2: $i,X3: $i] :
                                                                                                                          ( ( X1 @ X2 )
                                                                                                                         => ( ( X1 @ X3 )
                                                                                                                           => ( X2 = X3 ) ) )
                                                                                                                     => ~ ! [X2: $i] :
                                                                                                                            ( ( X1 @ X2 )
                                                                                                                           => ~ ! [X3: $i] :
                                                                                                                                  ( ( X1 @ X3 )
                                                                                                                                 => ( X2 = X3 ) ) ) ) )
                                                                                                               => ( ! [X1: $i > $o] :
                                                                                                                      ( ~ ! [X2: $i] :
                                                                                                                            ~ ! [X3: $i] :
                                                                                                                                ( ( X1 @ X3 )
                                                                                                                                = ( X3 = X2 ) )
                                                                                                                     => ~ ! [X2: $i] :
                                                                                                                            ( ( X1 @ X2 )
                                                                                                                           => ~ ! [X3: $i] :
                                                                                                                                  ( ( X1 @ X3 )
                                                                                                                                 => ( X2 = X3 ) ) ) )
                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                        ( ( X1 = X2 )
                                                                                                                       => ! [X3: $i,X4: $i] :
                                                                                                                            ( ( X3 = X4 )
                                                                                                                           => ( ( in @ X3 @ X1 )
                                                                                                                             => ( in @ X4 @ X2 ) ) ) )
                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                          ( ( X1 = X2 )
                                                                                                                         => ! [X3: $i,X4: $i] :
                                                                                                                              ( ( X3 = X4 )
                                                                                                                             => ( ( in @ X3 @ X1 )
                                                                                                                                = ( in @ X4 @ X2 ) ) ) )
                                                                                                                     => ( ! [X1: $i > $o] :
                                                                                                                            ( ~ ! [X2: $i] :
                                                                                                                                  ( ( X1 @ X2 )
                                                                                                                                 => ~ ! [X3: $i] :
                                                                                                                                        ( ( X1 @ X3 )
                                                                                                                                       => ( X2 = X3 ) ) )
                                                                                                                           => ! [X2: $i,X3: $i] :
                                                                                                                                ( ( X1 @ X2 )
                                                                                                                               => ( ( X1 @ X3 )
                                                                                                                                 => ( X2 = X3 ) ) ) )
                                                                                                                       => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                                                              ( ! [X3: $i,X4: $i] :
                                                                                                                                  ( ( X3 = X4 )
                                                                                                                                 => ( ( X1 @ X3 )
                                                                                                                                    = ( X2 @ X4 ) ) )
                                                                                                                             => ( ( ~ ! [X3: $i] :
                                                                                                                                        ( ( X1 @ X3 )
                                                                                                                                       => ~ ! [X4: $i] :
                                                                                                                                              ( ( X1 @ X4 )
                                                                                                                                             => ( X3 = X4 ) ) ) )
                                                                                                                                = ( ~ ! [X3: $i] :
                                                                                                                                        ( ( X2 @ X3 )
                                                                                                                                       => ~ ! [X4: $i] :
                                                                                                                                              ( ( X2 @ X4 )
                                                                                                                                             => ( X3 = X4 ) ) ) ) ) )
                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                ( ( X1 = X2 )
                                                                                                                               => ! [X3: $i,X4: $i] :
                                                                                                                                    ( ( X3 = X4 )
                                                                                                                                   => ( ( setadjoin @ X1 @ X3 )
                                                                                                                                      = ( setadjoin @ X2 @ X4 ) ) ) )
                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                  ( ( X1 = X2 )
                                                                                                                                 => ( ( powerset @ X1 )
                                                                                                                                    = ( powerset @ X2 ) ) )
                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                    ( ( X1 = X2 )
                                                                                                                                   => ( ( setunion @ X1 )
                                                                                                                                      = ( setunion @ X2 ) ) )
                                                                                                                               => ( ! [X1: $i > $o] :
                                                                                                                                      ( ~ ! [X2: $i] :
                                                                                                                                            ( ( X1 @ X2 )
                                                                                                                                           => ~ ! [X3: $i] :
                                                                                                                                                  ( ( X1 @ X3 )
                                                                                                                                                 => ( X2 = X3 ) ) )
                                                                                                                                     => ! [X2: $i,X3: $i] :
                                                                                                                                          ( ( X1 @ X2 )
                                                                                                                                         => ( ( X1 @ X3 )
                                                                                                                                           => ( X2 = X3 ) ) ) )
                                                                                                                                 => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                                                                        ( ! [X3: $i,X4: $i] :
                                                                                                                                            ( ( X3 = X4 )
                                                                                                                                           => ( ( X1 @ X3 )
                                                                                                                                              = ( X2 @ X4 ) ) )
                                                                                                                                       => ( ~ ! [X3: $i] :
                                                                                                                                                ( ( X1 @ X3 )
                                                                                                                                               => ~ ! [X4: $i] :
                                                                                                                                                      ( ( X1 @ X4 )
                                                                                                                                                     => ( X3 = X4 ) ) )
                                                                                                                                         => ( ~ ! [X3: $i] :
                                                                                                                                                  ( ( X2 @ X3 )
                                                                                                                                                 => ~ ! [X4: $i] :
                                                                                                                                                        ( ( X2 @ X4 )
                                                                                                                                                       => ( X3 = X4 ) ) )
                                                                                                                                           => ( ( descr @ X1 )
                                                                                                                                              = ( descr @ X2 ) ) ) ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                          ( ( X1 = X2 )
                                                                                                                                         => ! [X3: $i > $o,X4: $i > $o] :
                                                                                                                                              ( ! [X5: $i] :
                                                                                                                                                  ( ( in @ X5 @ X1 )
                                                                                                                                                 => ! [X6: $i] :
                                                                                                                                                      ( ( in @ X6 @ X2 )
                                                                                                                                                     => ( ( X5 = X6 )
                                                                                                                                                       => ( ( X3 @ X5 )
                                                                                                                                                          = ( X4 @ X6 ) ) ) ) )
                                                                                                                                             => ( ( dsetconstr @ X1 @ X3 )
                                                                                                                                                = ( dsetconstr @ X2 @ X4 ) ) ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                            ( ! [X3: $i] :
                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                               => ( in @ X3 @ X2 ) )
                                                                                                                                           => ( subset @ X1 @ X2 ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                              ( ( X1 = X2 )
                                                                                                                                             => ( subset @ X2 @ X1 ) )
                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                ( ( X1 = X2 )
                                                                                                                                               => ( subset @ X1 @ X2 ) )
                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                  ( ! [X3: $i] :
                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                     => ( in @ X3 @ X2 ) )
                                                                                                                                                 => ( subset @ X1 @ X2 ) )
                                                                                                                                             => ( ! [X1: $i] : ( subset @ emptyset @ X1 )
                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                      ( ( subset @ X1 @ X2 )
                                                                                                                                                     => ( ( in @ X3 @ X1 )
                                                                                                                                                       => ( in @ X3 @ X2 ) ) )
                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                        ( ( subset @ X1 @ X2 )
                                                                                                                                                       => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                         => ~ ( in @ X3 @ X1 ) ) )
                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                         => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                           => ~ ( subset @ X1 @ X2 ) ) )
                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                            ( ~ ( subset @ X1 @ X2 )
                                                                                                                                                           => ( X1 != X2 ) )
                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                             => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                               => ( X1 != X2 ) ) )
                                                                                                                                                         => ( ! [X1: $i] : ( subset @ X1 @ X1 )
                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                  ( ( subset @ X1 @ X2 )
                                                                                                                                                                 => ( ( subset @ X2 @ X3 )
                                                                                                                                                                   => ( subset @ X1 @ X3 ) ) )
                                                                                                                                                             => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) )
                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                      ( ( subset @ X1 @ X3 )
                                                                                                                                                                     => ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                        ( ( subset @ X1 @ X2 )
                                                                                                                                                                       => ( in @ X1 @ ( powerset @ X2 ) ) )
                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                          ( ( subset @ X1 @ X2 )
                                                                                                                                                                         => ( ( subset @ X2 @ X1 )
                                                                                                                                                                           => ( X1 = X2 ) ) )
                                                                                                                                                                     => ( ! [X1: $i] :
                                                                                                                                                                            ( ( subset @ X1 @ emptyset )
                                                                                                                                                                           => ( X1 = emptyset ) )
                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                              ( ( subset @ X2 @ X1 )
                                                                                                                                                                             => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                ( ( in @ X2 @ ( powerset @ X1 ) )
                                                                                                                                                                               => ( subset @ X2 @ X1 ) )
                                                                                                                                                                           => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                    ( ( subset @ X1 @ X2 )
                                                                                                                                                                                   => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
                                                                                                                                                                               => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                                                                                                                                                                                 => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                         => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                              ( ( in @ X3 @ X2 )
                                                                                                                                                                                             => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                                                                                                                                                                                ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                                                               => ( ( ( in @ X3 @ X1 )
                                                                                                                                                                                                   => X4 )
                                                                                                                                                                                                 => ( ( ( in @ X3 @ X2 )
                                                                                                                                                                                                     => X4 )
                                                                                                                                                                                                   => X4 ) ) )
                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                  ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                                                                 => ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                   => ( in @ X3 @ X2 ) ) )
                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                       => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                         => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                          ( ( subset @ X3 @ X1 )
                                                                                                                                                                                                         => ( ( subset @ X3 @ X2 )
                                                                                                                                                                                                           => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                            ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                                                                                           => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                ( ( subset @ X1 @ X2 )
                                                                                                                                                                                                               => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                                                  = X1 ) )
                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                  ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                                                    = X2 )
                                                                                                                                                                                                                 => ( subset @ X2 @ X1 ) )
                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                    ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                                                                                                   => ( in @ X3 @ X2 ) )
                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                      ( ! [X3: $i] :
                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                         => ~ ( in @ X3 @ X2 ) )
                                                                                                                                                                                                                     => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                                                        = emptyset ) )
                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                          ( ( subset @ X2 @ X1 )
                                                                                                                                                                                                                         => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                                                            = X2 ) )
                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                            ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                                                              = X1 )
                                                                                                                                                                                                                           => ( subset @ X1 @ X2 ) )
                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                              ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                                                                                                                                                                                              = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                               => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                                 => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                  ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                                                 => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                    ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                                                   => ~ ( in @ X3 @ X2 ) )
                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                      ( ( subset @ X1 @ X2 )
                                                                                                                                                                                                                                     => ( ( setminus @ X1 @ X2 )
                                                                                                                                                                                                                                        = emptyset ) )
                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                        ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                                                       => ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                         => ( in @ X3 @ X2 ) ) )
                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                          ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                                                         => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                                           => ~ ( in @ X3 @ X1 ) ) )
                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                            ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                                           => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                              ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                                             => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                  ( ( ( setminus @ X1 @ X2 )
                                                                                                                                                                                                                                                    = emptyset )
                                                                                                                                                                                                                                                 => ( subset @ X1 @ X2 ) )
                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                    ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                                                                                                                                                                                   => ! [X4: $o] :
                                                                                                                                                                                                                                                        ( ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                         => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                                                           => X4 ) )
                                                                                                                                                                                                                                                       => ( ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                           => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                                                             => X4 ) )
                                                                                                                                                                                                                                                         => X4 ) ) )
                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                     => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                                                       => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                        ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                       => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                                                         => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                         => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                                                           => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                            ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                           => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                                                             => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                        ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                                                       => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                          ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                                                         => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                           => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                              ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                                                             => ( ( X3 != X1 )
                                                                                                                                                                                                                                                                               => ( X3 = X2 ) ) )
                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                   => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                     => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                       => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                         => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                           => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                             => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                            ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                           => ~ ! [X4: $i] :
                                                                                                                                                                                                                                                                                                  ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                                                 => ! [X5: $i] :
                                                                                                                                                                                                                                                                                                      ( ( in @ X5 @ X2 )
                                                                                                                                                                                                                                                                                                     => ( X3
                                                                                                                                                                                                                                                                                                       != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                                                                                                                                                                                       => ( sP5
                                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                                                                                                                                                                                               => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                     => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                                                                                                                                                                                           => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                                                                                                                                                                                             => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                               => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                                      ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                                                                                                                                                                                      = X1 )
                                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                                                                        ( ! [X3: $i] :
                                                                                                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                                ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                                                               => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                                                                                 => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                                                                   => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                                                                                                       => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                               => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                                                                                                         => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                                                ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                               => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                                 != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                                                                          ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                                                ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                               => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                                 != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                         => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                               => ~ ( X2 @ X3 ) ) )
                                                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                           => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                                                                             => ( ! [X4: $i] :
                                                                                                                                                                                                                                                                                                                    ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                                                                   => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                                                                     => ( X4 = X3 ) ) )
                                                                                                                                                                                                                                                                                                               => ~ ! [X4: $i] :
                                                                                                                                                                                                                                                                                                                      ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                     => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                                       != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                                                                              ( ! [X3: $i] :
                                                                                                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                                      ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                                                                     => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                                                                                       => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                                                                         => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                                                                                                             => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                                     => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                                                                                                               => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                                                      ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                     => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                                       != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                                ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                                                                                                                                                                                  = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                                                               => ( X1 = X2 ) )
                                                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                  ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                 => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                                                             => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                                                    ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                                                                                   => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                                                          ( ( in @ X2
                                                                                                                                                                                                                                                                                                                            @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                                              @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                                                                                                                                                                                         => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                                              @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                                                                                                                           != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                                                                                               => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                                                      ( ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                                                            ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                                                                                                           => ( X1
                                                                                                                                                                                                                                                                                                                             != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                     => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                                        ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                        = X1 )
                                                                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                         => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                            ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                                              = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                           => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                              ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                                                = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                                             => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                                                ( ( X1 = X2 )
                                                                                                                                                                                                                                                                                                                               => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                                                                                  = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                                                  ( ( X1 = X2 )
                                                                                                                                                                                                                                                                                                                                 => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                                                    = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                                    ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                                                      = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                                   => ( ( X3 = X4 )
                                                                                                                                                                                                                                                                                                                                     => ( X2 = X4 ) ) )
                                                                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                                      ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                                                                                        = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                                                                                                                                                                                     => ( X1 = X2 ) )
                                                                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                                        ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                                                          = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                                       => ( X2 = X4 ) )
                                                                                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                                          ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                                                            = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                                                         => ( X2 = X4 ) )
                                                                                                                                                                                                                                                                                                                                     => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                                                                            ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                                                                                                           => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X2
                                                                                                                                                                                                                                                                                                                                                    @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                                                                      @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                                                                                                          ( X1
                                                                                                                                                                                                                                                                                                                                                          = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                                                                                                                                                                                 => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                                                                      @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                                                                                                          ( X1
                                                                                                                                                                                                                                                                                                                                                          = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                                                                                                                                                                                   != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                                                              ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                                              = X2 )
                                                                                                                                                                                                                                                                                                                                         => ( sP8
                                                                                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                                                 => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                                                    ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                                                   => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                                                      ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                                                     => ( in @ X4 @ X2 ) )
                                                                                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                                                                                           => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                                                                              = X3 ) ) )
                                                                                                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                                                                                             => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                                                                                = X4 ) ) )
                                                                                                                                                                                                                                                                                                                                                     => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                                                         => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                                                                                                                                                                                            = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(assume_negation,[status(cth)],[cartprodpairsurjEq]) ).

thf(h1,assumption,
    ! [X1: $i,X2: $i] :
      ( ! [X3: $i] :
          ( ( in @ X3 @ X1 )
          = ( in @ X3 @ X2 ) )
     => ( X1 = X2 ) ),
    introduced(assumption,[]) ).

thf(h2,assumption,
    ~ ( ! [X1: $i] :
          ~ ( in @ X1 @ emptyset )
     => ( ! [X1: $i,X2: $i,X3: $i] :
            ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
            = ( ( X3 != X1 )
             => ( in @ X3 @ X2 ) ) )
       => ( ! [X1: $i,X2: $i] :
              ( ( in @ X2 @ ( powerset @ X1 ) )
              = ( ! [X3: $i] :
                    ( ( in @ X3 @ X2 )
                   => ( in @ X3 @ X1 ) ) ) )
         => ( ! [X1: $i,X2: $i] :
                ( ( in @ X2 @ ( setunion @ X1 ) )
                = ( ~ ! [X3: $i] :
                        ( ( in @ X2 @ X3 )
                       => ~ ( in @ X3 @ X1 ) ) ) )
           => ( ( in @ emptyset @ omega )
             => ( ! [X1: $i] :
                    ( ( in @ X1 @ omega )
                   => ( in @ ( setadjoin @ X1 @ X1 ) @ omega ) )
               => ( ! [X1: $i] :
                      ( ~ ( ( in @ emptyset @ X1 )
                         => ~ ! [X2: $i] :
                                ( ~ ( ( in @ X2 @ omega )
                                   => ~ ( in @ X2 @ X1 ) )
                               => ( in @ ( setadjoin @ X2 @ X2 ) @ X1 ) ) )
                     => ! [X2: $i] :
                          ( ( in @ X2 @ omega )
                         => ( in @ X2 @ X1 ) ) )
                 => ( ! [X1: $i > $i > $o,X2: $i] :
                        ( ! [X3: $i] :
                            ( ( in @ X3 @ X2 )
                           => ~ ! [X4: $i] :
                                  ( ( X1 @ X3 @ X4 )
                                 => ~ ! [X5: $i] :
                                        ( ( X1 @ X3 @ X5 )
                                       => ( X4 = X5 ) ) ) )
                       => ~ ! [X3: $i] :
                              ~ ! [X4: $i] :
                                  ( ( in @ X4 @ X3 )
                                  = ( ~ ! [X5: $i] :
                                          ( ( in @ X5 @ X2 )
                                         => ~ ( X1 @ X5 @ X4 ) ) ) ) )
                   => ( ! [X1: $i] :
                          ( ~ ! [X2: $i] :
                                ~ ( in @ X2 @ X1 )
                         => ~ ! [X2: $i] :
                                ( ( in @ X2 @ X1 )
                               => ~ ! [X3: $i] :
                                      ( ( in @ X3 @ X2 )
                                     => ~ ( in @ X3 @ X1 ) ) ) )
                     => ( ! [X1: $i] :
                            ~ ! [X2: $i] :
                                ( ~ ( ~ ( ! [X3: $i] :
                                            ( ( in @ X3 @ X2 )
                                           => ! [X4: $i] :
                                                ( ( in @ X4 @ X3 )
                                               => ( in @ X4 @ X1 ) ) )
                                       => ~ ! [X3: $i,X4: $i] :
                                              ( ~ ( ( in @ X3 @ X1 )
                                                 => ~ ( in @ X4 @ X1 ) )
                                             => ( ! [X5: $i] :
                                                    ( ( in @ X5 @ X2 )
                                                   => ( ( in @ X3 @ X5 )
                                                      = ( in @ X4 @ X5 ) ) )
                                               => ( X3 = X4 ) ) ) )
                                   => ~ ! [X3: $i,X4: $i] :
                                          ( ~ ( ( in @ X3 @ X2 )
                                             => ~ ( in @ X4 @ X2 ) )
                                         => ( ~ ! [X5: $i] :
                                                  ( ( in @ X5 @ X3 )
                                                 => ( in @ X5 @ X4 ) )
                                           => ! [X5: $i] :
                                                ( ( in @ X5 @ X4 )
                                               => ( in @ X5 @ X3 ) ) ) ) )
                               => ~ ! [X3: $i] :
                                      ( ~ ( ! [X4: $i] :
                                              ( ( in @ X4 @ X3 )
                                             => ( in @ X4 @ X1 ) )
                                         => ! [X4: $i] :
                                              ~ ( in @ X4 @ X3 ) )
                                     => ~ ! [X4: $i,X5: $i] :
                                            ( ~ ( ~ ( ( in @ X4 @ X2 )
                                                   => ~ ( in @ X5 @ X3 ) )
                                               => ~ ! [X6: $i] :
                                                      ( ( in @ X6 @ X4 )
                                                     => ~ ( in @ X6 @ X3 ) ) )
                                           => ~ ! [X6: $i] :
                                                  ( ( in @ X6 @ X2 )
                                                 => ( ~ ! [X7: $i] :
                                                          ( ( in @ X7 @ X6 )
                                                         => ( in @ X7 @ X4 ) )
                                                   => ( in @ X5 @ X6 ) ) ) ) ) )
                       => ( ! [X1: $i > $o] :
                              ( ~ ! [X2: $i] :
                                    ( ( X1 @ X2 )
                                   => ~ ! [X3: $i] :
                                          ( ( X1 @ X3 )
                                         => ( X2 = X3 ) ) )
                             => ( X1 @ ( descr @ X1 ) ) )
                         => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                ( ( in @ X3 @ X1 )
                               => ( ( X2 @ X3 )
                                 => ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) ) ) )
                           => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                  ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                 => ( in @ X3 @ X1 ) )
                             => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                    ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                   => ( X2 @ X3 ) )
                               => ( ! [X1: $o,X2: $i] :
                                      ( ( in @ X2 @ ( prop2set @ X1 ) )
                                     => X1 )
                                 => ( ! [X1: $i] :
                                        ( ( in @ X1 @ emptyset )
                                       => ! [X2: $o] : X2 )
                                   => ( ! [X1: $i] :
                                          ~ ( in @ X1 @ emptyset )
                                     => ( ! [X1: $i] :
                                            ~ ( in @ X1 @ emptyset )
                                       => ( ! [X1: $i > $o] :
                                              ( ~ ! [X2: $i] :
                                                    ( ( X1 @ X2 )
                                                   => ~ ! [X3: $i] :
                                                          ( ( X1 @ X3 )
                                                         => ( X2 = X3 ) ) )
                                             => ~ ! [X2: $i] :
                                                    ~ ( X1 @ X2 ) )
                                         => ( ! [X1: $i,X2: $i] :
                                                ( ! [X3: $i] :
                                                    ( ( in @ X3 @ X1 )
                                                   => ( in @ X3 @ X2 ) )
                                               => ( ! [X3: $i] :
                                                      ( ( in @ X3 @ X2 )
                                                     => ( in @ X3 @ X1 ) )
                                                 => ( X1 = X2 ) ) )
                                           => ( ! [X1: $i] :
                                                  ( ! [X2: $i] :
                                                      ~ ( in @ X2 @ X1 )
                                                 => ( X1 = emptyset ) )
                                             => ( ! [X1: $i] :
                                                    ( ! [X2: $i] :
                                                        ~ ( in @ X2 @ X1 )
                                                   => ( X1 = emptyset ) )
                                               => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                      ( ( in @ X3 @ X1 )
                                                     => ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                        = ( X2 @ X3 ) ) )
                                                 => ( ! [X1: $i] :
                                                        ( ( X1 != emptyset )
                                                       => ~ ! [X2: $i] :
                                                              ~ ( in @ X2 @ X1 ) )
                                                   => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                          ( ( in @ X3 @ X1 )
                                                         => ( ( X2 @ X3 )
                                                           => ( ( dsetconstr @ X1 @ X2 )
                                                             != emptyset ) ) )
                                                     => ( ! [X1: $i] :
                                                            ( ~ ! [X2: $i] :
                                                                  ~ ( in @ X2 @ X1 )
                                                           => ( X1 != emptyset ) )
                                                       => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) )
                                                         => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                  ( ( in @ X3 @ X2 )
                                                                 => ( in @ X3 @ ( setadjoin @ X1 @ X2 ) ) )
                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                    ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                                                   => ! [X4: $o] :
                                                                        ( ( ( X3 = X1 )
                                                                         => X4 )
                                                                       => ( ( ( in @ X3 @ X2 )
                                                                           => X4 )
                                                                         => X4 ) ) )
                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                      ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                                                     => ( ( X3 != X1 )
                                                                       => ( in @ X3 @ X2 ) ) )
                                                                 => ( ! [X1: $i] :
                                                                        ( ( dsetconstr @ X1
                                                                          @ ^ [X2: $i] : ~ $false )
                                                                        = X1 )
                                                                   => ( ! [X1: $i,X2: $i] :
                                                                          ( ! [X3: $i] :
                                                                              ( ( in @ X3 @ X2 )
                                                                             => ( in @ X3 @ X1 ) )
                                                                         => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                                     => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                                                       => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                ( ( in @ X2 @ ( powerset @ X1 ) )
                                                                               => ( ( in @ X3 @ X2 )
                                                                                 => ( in @ X3 @ X1 ) ) )
                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                  ( ( in @ X2 @ X3 )
                                                                                 => ( ( in @ X3 @ X1 )
                                                                                   => ( in @ X2 @ ( setunion @ X1 ) ) ) )
                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                    ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                   => ! [X3: $o] :
                                                                                        ( ! [X4: $i] :
                                                                                            ( ( in @ X2 @ X4 )
                                                                                           => ( ( in @ X4 @ X1 )
                                                                                             => X3 ) )
                                                                                       => X3 ) )
                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                      ( ( in @ X2 @ X1 )
                                                                                     => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
                                                                                 => ( ! [X1: $i > $o] :
                                                                                        ( ~ ! [X2: $i] :
                                                                                              ( ( X1 @ X2 )
                                                                                             => ~ ! [X3: $i] :
                                                                                                    ( ( X1 @ X3 )
                                                                                                   => ( X2 = X3 ) ) )
                                                                                       => ~ ! [X2: $i] :
                                                                                              ~ ! [X3: $i] :
                                                                                                  ( ( X1 @ X3 )
                                                                                                  = ( X3 = X2 ) ) )
                                                                                   => ( ! [X1: $i] :
                                                                                          ( ( X1 != emptyset )
                                                                                         => ~ ! [X2: $i] :
                                                                                                ~ ( in @ X2 @ X1 ) )
                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                            ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                           => ( X1 = X2 ) )
                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                              ( ( X1 != X2 )
                                                                                             => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                ( ( X1 = X2 )
                                                                                               => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                  ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                 => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                    ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                   => ( ( X3 != X1 )
                                                                                                     => ( X3 = X2 ) ) )
                                                                                               => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                 => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                                                                          ( ~ ! [X3: $i] :
                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                               => ~ ( X2 @ X3 ) )
                                                                                                         => ( ( dsetconstr @ X1 @ X2 )
                                                                                                           != emptyset ) )
                                                                                                     => ( ! [X1: $i > $o,X2: $i] :
                                                                                                            ( ( in @ X2 @ emptyset )
                                                                                                           => ( X1 @ X2 ) )
                                                                                                       => ( ! [X1: $o] :
                                                                                                              ( X1
                                                                                                             => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                                                                                         => ( ! [X1: $o] :
                                                                                                                ( X1
                                                                                                               => ( set2prop @ ( prop2set @ X1 ) ) )
                                                                                                           => ( ! [X1: $i > $o] :
                                                                                                                  ( ~ ! [X2: $i] :
                                                                                                                        ~ ( X1 @ X2 )
                                                                                                                 => ( ! [X2: $i,X3: $i] :
                                                                                                                        ( ( X1 @ X2 )
                                                                                                                       => ( ( X1 @ X3 )
                                                                                                                         => ( X2 = X3 ) ) )
                                                                                                                   => ~ ! [X2: $i] :
                                                                                                                          ( ( X1 @ X2 )
                                                                                                                         => ~ ! [X3: $i] :
                                                                                                                                ( ( X1 @ X3 )
                                                                                                                               => ( X2 = X3 ) ) ) ) )
                                                                                                             => ( ! [X1: $i > $o] :
                                                                                                                    ( ~ ! [X2: $i] :
                                                                                                                          ~ ! [X3: $i] :
                                                                                                                              ( ( X1 @ X3 )
                                                                                                                              = ( X3 = X2 ) )
                                                                                                                   => ~ ! [X2: $i] :
                                                                                                                          ( ( X1 @ X2 )
                                                                                                                         => ~ ! [X3: $i] :
                                                                                                                                ( ( X1 @ X3 )
                                                                                                                               => ( X2 = X3 ) ) ) )
                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                      ( ( X1 = X2 )
                                                                                                                     => ! [X3: $i,X4: $i] :
                                                                                                                          ( ( X3 = X4 )
                                                                                                                         => ( ( in @ X3 @ X1 )
                                                                                                                           => ( in @ X4 @ X2 ) ) ) )
                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                        ( ( X1 = X2 )
                                                                                                                       => ! [X3: $i,X4: $i] :
                                                                                                                            ( ( X3 = X4 )
                                                                                                                           => ( ( in @ X3 @ X1 )
                                                                                                                              = ( in @ X4 @ X2 ) ) ) )
                                                                                                                   => ( ! [X1: $i > $o] :
                                                                                                                          ( ~ ! [X2: $i] :
                                                                                                                                ( ( X1 @ X2 )
                                                                                                                               => ~ ! [X3: $i] :
                                                                                                                                      ( ( X1 @ X3 )
                                                                                                                                     => ( X2 = X3 ) ) )
                                                                                                                         => ! [X2: $i,X3: $i] :
                                                                                                                              ( ( X1 @ X2 )
                                                                                                                             => ( ( X1 @ X3 )
                                                                                                                               => ( X2 = X3 ) ) ) )
                                                                                                                     => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                                                            ( ! [X3: $i,X4: $i] :
                                                                                                                                ( ( X3 = X4 )
                                                                                                                               => ( ( X1 @ X3 )
                                                                                                                                  = ( X2 @ X4 ) ) )
                                                                                                                           => ( ( ~ ! [X3: $i] :
                                                                                                                                      ( ( X1 @ X3 )
                                                                                                                                     => ~ ! [X4: $i] :
                                                                                                                                            ( ( X1 @ X4 )
                                                                                                                                           => ( X3 = X4 ) ) ) )
                                                                                                                              = ( ~ ! [X3: $i] :
                                                                                                                                      ( ( X2 @ X3 )
                                                                                                                                     => ~ ! [X4: $i] :
                                                                                                                                            ( ( X2 @ X4 )
                                                                                                                                           => ( X3 = X4 ) ) ) ) ) )
                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                              ( ( X1 = X2 )
                                                                                                                             => ! [X3: $i,X4: $i] :
                                                                                                                                  ( ( X3 = X4 )
                                                                                                                                 => ( ( setadjoin @ X1 @ X3 )
                                                                                                                                    = ( setadjoin @ X2 @ X4 ) ) ) )
                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                ( ( X1 = X2 )
                                                                                                                               => ( ( powerset @ X1 )
                                                                                                                                  = ( powerset @ X2 ) ) )
                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                  ( ( X1 = X2 )
                                                                                                                                 => ( ( setunion @ X1 )
                                                                                                                                    = ( setunion @ X2 ) ) )
                                                                                                                             => ( ! [X1: $i > $o] :
                                                                                                                                    ( ~ ! [X2: $i] :
                                                                                                                                          ( ( X1 @ X2 )
                                                                                                                                         => ~ ! [X3: $i] :
                                                                                                                                                ( ( X1 @ X3 )
                                                                                                                                               => ( X2 = X3 ) ) )
                                                                                                                                   => ! [X2: $i,X3: $i] :
                                                                                                                                        ( ( X1 @ X2 )
                                                                                                                                       => ( ( X1 @ X3 )
                                                                                                                                         => ( X2 = X3 ) ) ) )
                                                                                                                               => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                                                                      ( ! [X3: $i,X4: $i] :
                                                                                                                                          ( ( X3 = X4 )
                                                                                                                                         => ( ( X1 @ X3 )
                                                                                                                                            = ( X2 @ X4 ) ) )
                                                                                                                                     => ( ~ ! [X3: $i] :
                                                                                                                                              ( ( X1 @ X3 )
                                                                                                                                             => ~ ! [X4: $i] :
                                                                                                                                                    ( ( X1 @ X4 )
                                                                                                                                                   => ( X3 = X4 ) ) )
                                                                                                                                       => ( ~ ! [X3: $i] :
                                                                                                                                                ( ( X2 @ X3 )
                                                                                                                                               => ~ ! [X4: $i] :
                                                                                                                                                      ( ( X2 @ X4 )
                                                                                                                                                     => ( X3 = X4 ) ) )
                                                                                                                                         => ( ( descr @ X1 )
                                                                                                                                            = ( descr @ X2 ) ) ) ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                        ( ( X1 = X2 )
                                                                                                                                       => ! [X3: $i > $o,X4: $i > $o] :
                                                                                                                                            ( ! [X5: $i] :
                                                                                                                                                ( ( in @ X5 @ X1 )
                                                                                                                                               => ! [X6: $i] :
                                                                                                                                                    ( ( in @ X6 @ X2 )
                                                                                                                                                   => ( ( X5 = X6 )
                                                                                                                                                     => ( ( X3 @ X5 )
                                                                                                                                                        = ( X4 @ X6 ) ) ) ) )
                                                                                                                                           => ( ( dsetconstr @ X1 @ X3 )
                                                                                                                                              = ( dsetconstr @ X2 @ X4 ) ) ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                          ( ! [X3: $i] :
                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                             => ( in @ X3 @ X2 ) )
                                                                                                                                         => ( subset @ X1 @ X2 ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                            ( ( X1 = X2 )
                                                                                                                                           => ( subset @ X2 @ X1 ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                              ( ( X1 = X2 )
                                                                                                                                             => ( subset @ X1 @ X2 ) )
                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                ( ! [X3: $i] :
                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                   => ( in @ X3 @ X2 ) )
                                                                                                                                               => ( subset @ X1 @ X2 ) )
                                                                                                                                           => ( ! [X1: $i] : ( subset @ emptyset @ X1 )
                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                    ( ( subset @ X1 @ X2 )
                                                                                                                                                   => ( ( in @ X3 @ X1 )
                                                                                                                                                     => ( in @ X3 @ X2 ) ) )
                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                      ( ( subset @ X1 @ X2 )
                                                                                                                                                     => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                       => ~ ( in @ X3 @ X1 ) ) )
                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                       => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                         => ~ ( subset @ X1 @ X2 ) ) )
                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                          ( ~ ( subset @ X1 @ X2 )
                                                                                                                                                         => ( X1 != X2 ) )
                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                           => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                             => ( X1 != X2 ) ) )
                                                                                                                                                       => ( ! [X1: $i] : ( subset @ X1 @ X1 )
                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                ( ( subset @ X1 @ X2 )
                                                                                                                                                               => ( ( subset @ X2 @ X3 )
                                                                                                                                                                 => ( subset @ X1 @ X3 ) ) )
                                                                                                                                                           => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) )
                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                    ( ( subset @ X1 @ X3 )
                                                                                                                                                                   => ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                      ( ( subset @ X1 @ X2 )
                                                                                                                                                                     => ( in @ X1 @ ( powerset @ X2 ) ) )
                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                        ( ( subset @ X1 @ X2 )
                                                                                                                                                                       => ( ( subset @ X2 @ X1 )
                                                                                                                                                                         => ( X1 = X2 ) ) )
                                                                                                                                                                   => ( ! [X1: $i] :
                                                                                                                                                                          ( ( subset @ X1 @ emptyset )
                                                                                                                                                                         => ( X1 = emptyset ) )
                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                            ( ( subset @ X2 @ X1 )
                                                                                                                                                                           => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                              ( ( in @ X2 @ ( powerset @ X1 ) )
                                                                                                                                                                             => ( subset @ X2 @ X1 ) )
                                                                                                                                                                         => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                  ( ( subset @ X1 @ X2 )
                                                                                                                                                                                 => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
                                                                                                                                                                             => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                                                                                                                                                                               => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                       => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                            ( ( in @ X3 @ X2 )
                                                                                                                                                                                           => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                                                                                                                                                                              ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                                                             => ( ( ( in @ X3 @ X1 )
                                                                                                                                                                                                 => X4 )
                                                                                                                                                                                               => ( ( ( in @ X3 @ X2 )
                                                                                                                                                                                                   => X4 )
                                                                                                                                                                                                 => X4 ) ) )
                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                                                               => ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                 => ( in @ X3 @ X2 ) ) )
                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                     => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                       => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                        ( ( subset @ X3 @ X1 )
                                                                                                                                                                                                       => ( ( subset @ X3 @ X2 )
                                                                                                                                                                                                         => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                          ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                                                                                         => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                              ( ( subset @ X1 @ X2 )
                                                                                                                                                                                                             => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                                                = X1 ) )
                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                                                  = X2 )
                                                                                                                                                                                                               => ( subset @ X2 @ X1 ) )
                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                  ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                                                                                                 => ( in @ X3 @ X2 ) )
                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                    ( ! [X3: $i] :
                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                       => ~ ( in @ X3 @ X2 ) )
                                                                                                                                                                                                                   => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                                                      = emptyset ) )
                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                        ( ( subset @ X2 @ X1 )
                                                                                                                                                                                                                       => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                                                          = X2 ) )
                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                          ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                                                            = X1 )
                                                                                                                                                                                                                         => ( subset @ X1 @ X2 ) )
                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                            ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                                                                                                                                                                                            = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                             => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                               => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                                               => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                  ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                                                 => ~ ( in @ X3 @ X2 ) )
                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                    ( ( subset @ X1 @ X2 )
                                                                                                                                                                                                                                   => ( ( setminus @ X1 @ X2 )
                                                                                                                                                                                                                                      = emptyset ) )
                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                      ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                                                     => ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                       => ( in @ X3 @ X2 ) ) )
                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                        ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                                                       => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                                         => ~ ( in @ X3 @ X1 ) ) )
                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                          ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                                         => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                            ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                                           => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                ( ( ( setminus @ X1 @ X2 )
                                                                                                                                                                                                                                                  = emptyset )
                                                                                                                                                                                                                                               => ( subset @ X1 @ X2 ) )
                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                  ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                                                                                                                                                                                 => ! [X4: $o] :
                                                                                                                                                                                                                                                      ( ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                       => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                                                         => X4 ) )
                                                                                                                                                                                                                                                     => ( ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                         => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                                                           => X4 ) )
                                                                                                                                                                                                                                                       => X4 ) ) )
                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                   => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                                                     => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                      ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                     => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                                                       => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                       => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                                                         => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                          ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                         => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                                                           => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                      ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                                                     => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                        ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                                                       => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                         => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                            ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                                                           => ( ( X3 != X1 )
                                                                                                                                                                                                                                                                             => ( X3 = X2 ) ) )
                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                 => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                   => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                     => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                       => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                         => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                           => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                         => ~ ! [X4: $i] :
                                                                                                                                                                                                                                                                                                ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                                               => ! [X5: $i] :
                                                                                                                                                                                                                                                                                                    ( ( in @ X5 @ X2 )
                                                                                                                                                                                                                                                                                                   => ( X3
                                                                                                                                                                                                                                                                                                     != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                                                                                                                                                                                     => ( sP5
                                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                              ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                                                                                                                                                                                             => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                   => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                                                                                                                                                                                         => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                                                                                                                                                                                           => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                             => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                                    ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                                                                                                                                                                                    = X1 )
                                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                                                                      ( ! [X3: $i] :
                                                                                                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                              ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                                                             => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                                                                               => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                                                                 => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                                                                                                     => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                             => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                                                                                                       => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                                              ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                             => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                               != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                                                                        ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                                              ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                             => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                               != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                       => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                             => ~ ( X2 @ X3 ) ) )
                                                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                         => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                                                                           => ( ! [X4: $i] :
                                                                                                                                                                                                                                                                                                                  ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                                                                 => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                                                                   => ( X4 = X3 ) ) )
                                                                                                                                                                                                                                                                                                             => ~ ! [X4: $i] :
                                                                                                                                                                                                                                                                                                                    ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                   => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                                     != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                                                                            ( ! [X3: $i] :
                                                                                                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                                    ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                                                                   => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                                                                                     => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                                                                       => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                                                                                                           => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                                   => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                                                                                                             => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                                                    ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                   => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                                     != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                              ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                                                                                                                                                                                = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                                                             => ( X1 = X2 ) )
                                                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                               => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                                                           => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                                                  ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                                                                                 => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                                                        ( ( in @ X2
                                                                                                                                                                                                                                                                                                                          @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                                            @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                                                                                                                                                                                       => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                                            @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                                                                                                                         != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                                                                                             => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                                                    ( ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                                                          ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                                                                                                         => ( X1
                                                                                                                                                                                                                                                                                                                           != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                   => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                                      ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                      = X1 )
                                                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                       => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                          ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                                            = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                         => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                            ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                                              = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                                           => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                                              ( ( X1 = X2 )
                                                                                                                                                                                                                                                                                                                             => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                                                                                = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                                                ( ( X1 = X2 )
                                                                                                                                                                                                                                                                                                                               => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                                                  = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                                  ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                                                    = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                                 => ( ( X3 = X4 )
                                                                                                                                                                                                                                                                                                                                   => ( X2 = X4 ) ) )
                                                                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                                    ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                                                                                      = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                                                                                                                                                                                   => ( X1 = X2 ) )
                                                                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                                      ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                                                        = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                                     => ( X2 = X4 ) )
                                                                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                                        ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                                                          = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                                                       => ( X2 = X4 ) )
                                                                                                                                                                                                                                                                                                                                   => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                                                                          ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                                                                                                         => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                                                                                ( ( in @ X2
                                                                                                                                                                                                                                                                                                                                                  @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                                                                    @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                                                                                                        ( X1
                                                                                                                                                                                                                                                                                                                                                        = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                                                                                                                                                                               => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                                                                    @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                                                                                                        ( X1
                                                                                                                                                                                                                                                                                                                                                        = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                                                                                                                                                                                 != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                                                            ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                                            = X2 )
                                                                                                                                                                                                                                                                                                                                       => ( sP8
                                                                                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                                                ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                                               => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                                                  ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                                                 => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                                                    ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                                                   => ( in @ X4 @ X2 ) )
                                                                                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                                                                                         => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                                                                            = X3 ) ) )
                                                                                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                                                                                           => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                                                                              = X4 ) ) )
                                                                                                                                                                                                                                                                                                                                                   => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                                                        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                                                       => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                                                                                                                                                                                          = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h3,assumption,
    ! [X1: $i] :
      ~ ( in @ X1 @ emptyset ),
    introduced(assumption,[]) ).

thf(h4,assumption,
    ~ ( ! [X1: $i,X2: $i,X3: $i] :
          ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
          = ( ( X3 != X1 )
           => ( in @ X3 @ X2 ) ) )
     => ( ! [X1: $i,X2: $i] :
            ( ( in @ X2 @ ( powerset @ X1 ) )
            = ( ! [X3: $i] :
                  ( ( in @ X3 @ X2 )
                 => ( in @ X3 @ X1 ) ) ) )
       => ( ! [X1: $i,X2: $i] :
              ( ( in @ X2 @ ( setunion @ X1 ) )
              = ( ~ ! [X3: $i] :
                      ( ( in @ X2 @ X3 )
                     => ~ ( in @ X3 @ X1 ) ) ) )
         => ( ( in @ emptyset @ omega )
           => ( ! [X1: $i] :
                  ( ( in @ X1 @ omega )
                 => ( in @ ( setadjoin @ X1 @ X1 ) @ omega ) )
             => ( ! [X1: $i] :
                    ( ~ ( ( in @ emptyset @ X1 )
                       => ~ ! [X2: $i] :
                              ( ~ ( ( in @ X2 @ omega )
                                 => ~ ( in @ X2 @ X1 ) )
                             => ( in @ ( setadjoin @ X2 @ X2 ) @ X1 ) ) )
                   => ! [X2: $i] :
                        ( ( in @ X2 @ omega )
                       => ( in @ X2 @ X1 ) ) )
               => ( ! [X1: $i > $i > $o,X2: $i] :
                      ( ! [X3: $i] :
                          ( ( in @ X3 @ X2 )
                         => ~ ! [X4: $i] :
                                ( ( X1 @ X3 @ X4 )
                               => ~ ! [X5: $i] :
                                      ( ( X1 @ X3 @ X5 )
                                     => ( X4 = X5 ) ) ) )
                     => ~ ! [X3: $i] :
                            ~ ! [X4: $i] :
                                ( ( in @ X4 @ X3 )
                                = ( ~ ! [X5: $i] :
                                        ( ( in @ X5 @ X2 )
                                       => ~ ( X1 @ X5 @ X4 ) ) ) ) )
                 => ( ! [X1: $i] :
                        ( ~ ! [X2: $i] :
                              ~ ( in @ X2 @ X1 )
                       => ~ ! [X2: $i] :
                              ( ( in @ X2 @ X1 )
                             => ~ ! [X3: $i] :
                                    ( ( in @ X3 @ X2 )
                                   => ~ ( in @ X3 @ X1 ) ) ) )
                   => ( ! [X1: $i] :
                          ~ ! [X2: $i] :
                              ( ~ ( ~ ( ! [X3: $i] :
                                          ( ( in @ X3 @ X2 )
                                         => ! [X4: $i] :
                                              ( ( in @ X4 @ X3 )
                                             => ( in @ X4 @ X1 ) ) )
                                     => ~ ! [X3: $i,X4: $i] :
                                            ( ~ ( ( in @ X3 @ X1 )
                                               => ~ ( in @ X4 @ X1 ) )
                                           => ( ! [X5: $i] :
                                                  ( ( in @ X5 @ X2 )
                                                 => ( ( in @ X3 @ X5 )
                                                    = ( in @ X4 @ X5 ) ) )
                                             => ( X3 = X4 ) ) ) )
                                 => ~ ! [X3: $i,X4: $i] :
                                        ( ~ ( ( in @ X3 @ X2 )
                                           => ~ ( in @ X4 @ X2 ) )
                                       => ( ~ ! [X5: $i] :
                                                ( ( in @ X5 @ X3 )
                                               => ( in @ X5 @ X4 ) )
                                         => ! [X5: $i] :
                                              ( ( in @ X5 @ X4 )
                                             => ( in @ X5 @ X3 ) ) ) ) )
                             => ~ ! [X3: $i] :
                                    ( ~ ( ! [X4: $i] :
                                            ( ( in @ X4 @ X3 )
                                           => ( in @ X4 @ X1 ) )
                                       => ! [X4: $i] :
                                            ~ ( in @ X4 @ X3 ) )
                                   => ~ ! [X4: $i,X5: $i] :
                                          ( ~ ( ~ ( ( in @ X4 @ X2 )
                                                 => ~ ( in @ X5 @ X3 ) )
                                             => ~ ! [X6: $i] :
                                                    ( ( in @ X6 @ X4 )
                                                   => ~ ( in @ X6 @ X3 ) ) )
                                         => ~ ! [X6: $i] :
                                                ( ( in @ X6 @ X2 )
                                               => ( ~ ! [X7: $i] :
                                                        ( ( in @ X7 @ X6 )
                                                       => ( in @ X7 @ X4 ) )
                                                 => ( in @ X5 @ X6 ) ) ) ) ) )
                     => ( ! [X1: $i > $o] :
                            ( ~ ! [X2: $i] :
                                  ( ( X1 @ X2 )
                                 => ~ ! [X3: $i] :
                                        ( ( X1 @ X3 )
                                       => ( X2 = X3 ) ) )
                           => ( X1 @ ( descr @ X1 ) ) )
                       => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                              ( ( in @ X3 @ X1 )
                             => ( ( X2 @ X3 )
                               => ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) ) ) )
                         => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                               => ( in @ X3 @ X1 ) )
                           => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                  ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                 => ( X2 @ X3 ) )
                             => ( ! [X1: $o,X2: $i] :
                                    ( ( in @ X2 @ ( prop2set @ X1 ) )
                                   => X1 )
                               => ( ! [X1: $i] :
                                      ( ( in @ X1 @ emptyset )
                                     => ! [X2: $o] : X2 )
                                 => ( ! [X1: $i] :
                                        ~ ( in @ X1 @ emptyset )
                                   => ( ! [X1: $i] :
                                          ~ ( in @ X1 @ emptyset )
                                     => ( ! [X1: $i > $o] :
                                            ( ~ ! [X2: $i] :
                                                  ( ( X1 @ X2 )
                                                 => ~ ! [X3: $i] :
                                                        ( ( X1 @ X3 )
                                                       => ( X2 = X3 ) ) )
                                           => ~ ! [X2: $i] :
                                                  ~ ( X1 @ X2 ) )
                                       => ( ! [X1: $i,X2: $i] :
                                              ( ! [X3: $i] :
                                                  ( ( in @ X3 @ X1 )
                                                 => ( in @ X3 @ X2 ) )
                                             => ( ! [X3: $i] :
                                                    ( ( in @ X3 @ X2 )
                                                   => ( in @ X3 @ X1 ) )
                                               => ( X1 = X2 ) ) )
                                         => ( ! [X1: $i] :
                                                ( ! [X2: $i] :
                                                    ~ ( in @ X2 @ X1 )
                                               => ( X1 = emptyset ) )
                                           => ( ! [X1: $i] :
                                                  ( ! [X2: $i] :
                                                      ~ ( in @ X2 @ X1 )
                                                 => ( X1 = emptyset ) )
                                             => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                    ( ( in @ X3 @ X1 )
                                                   => ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                      = ( X2 @ X3 ) ) )
                                               => ( ! [X1: $i] :
                                                      ( ( X1 != emptyset )
                                                     => ~ ! [X2: $i] :
                                                            ~ ( in @ X2 @ X1 ) )
                                                 => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                        ( ( in @ X3 @ X1 )
                                                       => ( ( X2 @ X3 )
                                                         => ( ( dsetconstr @ X1 @ X2 )
                                                           != emptyset ) ) )
                                                   => ( ! [X1: $i] :
                                                          ( ~ ! [X2: $i] :
                                                                ~ ( in @ X2 @ X1 )
                                                         => ( X1 != emptyset ) )
                                                     => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) )
                                                       => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                ( ( in @ X3 @ X2 )
                                                               => ( in @ X3 @ ( setadjoin @ X1 @ X2 ) ) )
                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                  ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                                                 => ! [X4: $o] :
                                                                      ( ( ( X3 = X1 )
                                                                       => X4 )
                                                                     => ( ( ( in @ X3 @ X2 )
                                                                         => X4 )
                                                                       => X4 ) ) )
                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                    ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                                                   => ( ( X3 != X1 )
                                                                     => ( in @ X3 @ X2 ) ) )
                                                               => ( ! [X1: $i] :
                                                                      ( ( dsetconstr @ X1
                                                                        @ ^ [X2: $i] : ~ $false )
                                                                      = X1 )
                                                                 => ( ! [X1: $i,X2: $i] :
                                                                        ( ! [X3: $i] :
                                                                            ( ( in @ X3 @ X2 )
                                                                           => ( in @ X3 @ X1 ) )
                                                                       => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                                   => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                                                     => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                              ( ( in @ X2 @ ( powerset @ X1 ) )
                                                                             => ( ( in @ X3 @ X2 )
                                                                               => ( in @ X3 @ X1 ) ) )
                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                ( ( in @ X2 @ X3 )
                                                                               => ( ( in @ X3 @ X1 )
                                                                                 => ( in @ X2 @ ( setunion @ X1 ) ) ) )
                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                  ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                 => ! [X3: $o] :
                                                                                      ( ! [X4: $i] :
                                                                                          ( ( in @ X2 @ X4 )
                                                                                         => ( ( in @ X4 @ X1 )
                                                                                           => X3 ) )
                                                                                     => X3 ) )
                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                    ( ( in @ X2 @ X1 )
                                                                                   => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
                                                                               => ( ! [X1: $i > $o] :
                                                                                      ( ~ ! [X2: $i] :
                                                                                            ( ( X1 @ X2 )
                                                                                           => ~ ! [X3: $i] :
                                                                                                  ( ( X1 @ X3 )
                                                                                                 => ( X2 = X3 ) ) )
                                                                                     => ~ ! [X2: $i] :
                                                                                            ~ ! [X3: $i] :
                                                                                                ( ( X1 @ X3 )
                                                                                                = ( X3 = X2 ) ) )
                                                                                 => ( ! [X1: $i] :
                                                                                        ( ( X1 != emptyset )
                                                                                       => ~ ! [X2: $i] :
                                                                                              ~ ( in @ X2 @ X1 ) )
                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                          ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                         => ( X1 = X2 ) )
                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                            ( ( X1 != X2 )
                                                                                           => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                              ( ( X1 = X2 )
                                                                                             => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                               => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                  ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                 => ( ( X3 != X1 )
                                                                                                   => ( X3 = X2 ) ) )
                                                                                             => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                               => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                                                                        ( ~ ! [X3: $i] :
                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                             => ~ ( X2 @ X3 ) )
                                                                                                       => ( ( dsetconstr @ X1 @ X2 )
                                                                                                         != emptyset ) )
                                                                                                   => ( ! [X1: $i > $o,X2: $i] :
                                                                                                          ( ( in @ X2 @ emptyset )
                                                                                                         => ( X1 @ X2 ) )
                                                                                                     => ( ! [X1: $o] :
                                                                                                            ( X1
                                                                                                           => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                                                                                       => ( ! [X1: $o] :
                                                                                                              ( X1
                                                                                                             => ( set2prop @ ( prop2set @ X1 ) ) )
                                                                                                         => ( ! [X1: $i > $o] :
                                                                                                                ( ~ ! [X2: $i] :
                                                                                                                      ~ ( X1 @ X2 )
                                                                                                               => ( ! [X2: $i,X3: $i] :
                                                                                                                      ( ( X1 @ X2 )
                                                                                                                     => ( ( X1 @ X3 )
                                                                                                                       => ( X2 = X3 ) ) )
                                                                                                                 => ~ ! [X2: $i] :
                                                                                                                        ( ( X1 @ X2 )
                                                                                                                       => ~ ! [X3: $i] :
                                                                                                                              ( ( X1 @ X3 )
                                                                                                                             => ( X2 = X3 ) ) ) ) )
                                                                                                           => ( ! [X1: $i > $o] :
                                                                                                                  ( ~ ! [X2: $i] :
                                                                                                                        ~ ! [X3: $i] :
                                                                                                                            ( ( X1 @ X3 )
                                                                                                                            = ( X3 = X2 ) )
                                                                                                                 => ~ ! [X2: $i] :
                                                                                                                        ( ( X1 @ X2 )
                                                                                                                       => ~ ! [X3: $i] :
                                                                                                                              ( ( X1 @ X3 )
                                                                                                                             => ( X2 = X3 ) ) ) )
                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                    ( ( X1 = X2 )
                                                                                                                   => ! [X3: $i,X4: $i] :
                                                                                                                        ( ( X3 = X4 )
                                                                                                                       => ( ( in @ X3 @ X1 )
                                                                                                                         => ( in @ X4 @ X2 ) ) ) )
                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                      ( ( X1 = X2 )
                                                                                                                     => ! [X3: $i,X4: $i] :
                                                                                                                          ( ( X3 = X4 )
                                                                                                                         => ( ( in @ X3 @ X1 )
                                                                                                                            = ( in @ X4 @ X2 ) ) ) )
                                                                                                                 => ( ! [X1: $i > $o] :
                                                                                                                        ( ~ ! [X2: $i] :
                                                                                                                              ( ( X1 @ X2 )
                                                                                                                             => ~ ! [X3: $i] :
                                                                                                                                    ( ( X1 @ X3 )
                                                                                                                                   => ( X2 = X3 ) ) )
                                                                                                                       => ! [X2: $i,X3: $i] :
                                                                                                                            ( ( X1 @ X2 )
                                                                                                                           => ( ( X1 @ X3 )
                                                                                                                             => ( X2 = X3 ) ) ) )
                                                                                                                   => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                                                          ( ! [X3: $i,X4: $i] :
                                                                                                                              ( ( X3 = X4 )
                                                                                                                             => ( ( X1 @ X3 )
                                                                                                                                = ( X2 @ X4 ) ) )
                                                                                                                         => ( ( ~ ! [X3: $i] :
                                                                                                                                    ( ( X1 @ X3 )
                                                                                                                                   => ~ ! [X4: $i] :
                                                                                                                                          ( ( X1 @ X4 )
                                                                                                                                         => ( X3 = X4 ) ) ) )
                                                                                                                            = ( ~ ! [X3: $i] :
                                                                                                                                    ( ( X2 @ X3 )
                                                                                                                                   => ~ ! [X4: $i] :
                                                                                                                                          ( ( X2 @ X4 )
                                                                                                                                         => ( X3 = X4 ) ) ) ) ) )
                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                            ( ( X1 = X2 )
                                                                                                                           => ! [X3: $i,X4: $i] :
                                                                                                                                ( ( X3 = X4 )
                                                                                                                               => ( ( setadjoin @ X1 @ X3 )
                                                                                                                                  = ( setadjoin @ X2 @ X4 ) ) ) )
                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                              ( ( X1 = X2 )
                                                                                                                             => ( ( powerset @ X1 )
                                                                                                                                = ( powerset @ X2 ) ) )
                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                ( ( X1 = X2 )
                                                                                                                               => ( ( setunion @ X1 )
                                                                                                                                  = ( setunion @ X2 ) ) )
                                                                                                                           => ( ! [X1: $i > $o] :
                                                                                                                                  ( ~ ! [X2: $i] :
                                                                                                                                        ( ( X1 @ X2 )
                                                                                                                                       => ~ ! [X3: $i] :
                                                                                                                                              ( ( X1 @ X3 )
                                                                                                                                             => ( X2 = X3 ) ) )
                                                                                                                                 => ! [X2: $i,X3: $i] :
                                                                                                                                      ( ( X1 @ X2 )
                                                                                                                                     => ( ( X1 @ X3 )
                                                                                                                                       => ( X2 = X3 ) ) ) )
                                                                                                                             => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                                                                    ( ! [X3: $i,X4: $i] :
                                                                                                                                        ( ( X3 = X4 )
                                                                                                                                       => ( ( X1 @ X3 )
                                                                                                                                          = ( X2 @ X4 ) ) )
                                                                                                                                   => ( ~ ! [X3: $i] :
                                                                                                                                            ( ( X1 @ X3 )
                                                                                                                                           => ~ ! [X4: $i] :
                                                                                                                                                  ( ( X1 @ X4 )
                                                                                                                                                 => ( X3 = X4 ) ) )
                                                                                                                                     => ( ~ ! [X3: $i] :
                                                                                                                                              ( ( X2 @ X3 )
                                                                                                                                             => ~ ! [X4: $i] :
                                                                                                                                                    ( ( X2 @ X4 )
                                                                                                                                                   => ( X3 = X4 ) ) )
                                                                                                                                       => ( ( descr @ X1 )
                                                                                                                                          = ( descr @ X2 ) ) ) ) )
                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                      ( ( X1 = X2 )
                                                                                                                                     => ! [X3: $i > $o,X4: $i > $o] :
                                                                                                                                          ( ! [X5: $i] :
                                                                                                                                              ( ( in @ X5 @ X1 )
                                                                                                                                             => ! [X6: $i] :
                                                                                                                                                  ( ( in @ X6 @ X2 )
                                                                                                                                                 => ( ( X5 = X6 )
                                                                                                                                                   => ( ( X3 @ X5 )
                                                                                                                                                      = ( X4 @ X6 ) ) ) ) )
                                                                                                                                         => ( ( dsetconstr @ X1 @ X3 )
                                                                                                                                            = ( dsetconstr @ X2 @ X4 ) ) ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                        ( ! [X3: $i] :
                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                           => ( in @ X3 @ X2 ) )
                                                                                                                                       => ( subset @ X1 @ X2 ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                          ( ( X1 = X2 )
                                                                                                                                         => ( subset @ X2 @ X1 ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                            ( ( X1 = X2 )
                                                                                                                                           => ( subset @ X1 @ X2 ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                              ( ! [X3: $i] :
                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                 => ( in @ X3 @ X2 ) )
                                                                                                                                             => ( subset @ X1 @ X2 ) )
                                                                                                                                         => ( ! [X1: $i] : ( subset @ emptyset @ X1 )
                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                  ( ( subset @ X1 @ X2 )
                                                                                                                                                 => ( ( in @ X3 @ X1 )
                                                                                                                                                   => ( in @ X3 @ X2 ) ) )
                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                    ( ( subset @ X1 @ X2 )
                                                                                                                                                   => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                     => ~ ( in @ X3 @ X1 ) ) )
                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                     => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                       => ~ ( subset @ X1 @ X2 ) ) )
                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                        ( ~ ( subset @ X1 @ X2 )
                                                                                                                                                       => ( X1 != X2 ) )
                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                         => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                           => ( X1 != X2 ) ) )
                                                                                                                                                     => ( ! [X1: $i] : ( subset @ X1 @ X1 )
                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                              ( ( subset @ X1 @ X2 )
                                                                                                                                                             => ( ( subset @ X2 @ X3 )
                                                                                                                                                               => ( subset @ X1 @ X3 ) ) )
                                                                                                                                                         => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) )
                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                  ( ( subset @ X1 @ X3 )
                                                                                                                                                                 => ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                    ( ( subset @ X1 @ X2 )
                                                                                                                                                                   => ( in @ X1 @ ( powerset @ X2 ) ) )
                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                      ( ( subset @ X1 @ X2 )
                                                                                                                                                                     => ( ( subset @ X2 @ X1 )
                                                                                                                                                                       => ( X1 = X2 ) ) )
                                                                                                                                                                 => ( ! [X1: $i] :
                                                                                                                                                                        ( ( subset @ X1 @ emptyset )
                                                                                                                                                                       => ( X1 = emptyset ) )
                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                          ( ( subset @ X2 @ X1 )
                                                                                                                                                                         => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                            ( ( in @ X2 @ ( powerset @ X1 ) )
                                                                                                                                                                           => ( subset @ X2 @ X1 ) )
                                                                                                                                                                       => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                ( ( subset @ X1 @ X2 )
                                                                                                                                                                               => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
                                                                                                                                                                           => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                                                                                                                                                                             => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                     => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                          ( ( in @ X3 @ X2 )
                                                                                                                                                                                         => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                                                                                                                                                                            ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                                                           => ( ( ( in @ X3 @ X1 )
                                                                                                                                                                                               => X4 )
                                                                                                                                                                                             => ( ( ( in @ X3 @ X2 )
                                                                                                                                                                                                 => X4 )
                                                                                                                                                                                               => X4 ) ) )
                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                              ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                                                             => ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                               => ( in @ X3 @ X2 ) ) )
                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                   => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                     => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                      ( ( subset @ X3 @ X1 )
                                                                                                                                                                                                     => ( ( subset @ X3 @ X2 )
                                                                                                                                                                                                       => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                        ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                                                                                       => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                            ( ( subset @ X1 @ X2 )
                                                                                                                                                                                                           => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                                              = X1 ) )
                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                              ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                                                = X2 )
                                                                                                                                                                                                             => ( subset @ X2 @ X1 ) )
                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                                                                                               => ( in @ X3 @ X2 ) )
                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                  ( ! [X3: $i] :
                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                     => ~ ( in @ X3 @ X2 ) )
                                                                                                                                                                                                                 => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                                                    = emptyset ) )
                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                      ( ( subset @ X2 @ X1 )
                                                                                                                                                                                                                     => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                                                        = X2 ) )
                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                        ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                                                          = X1 )
                                                                                                                                                                                                                       => ( subset @ X1 @ X2 ) )
                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                          ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                                                                                                                                                                                          = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                           => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                             => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                              ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                                             => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                                               => ~ ( in @ X3 @ X2 ) )
                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                  ( ( subset @ X1 @ X2 )
                                                                                                                                                                                                                                 => ( ( setminus @ X1 @ X2 )
                                                                                                                                                                                                                                    = emptyset ) )
                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                    ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                                                   => ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                     => ( in @ X3 @ X2 ) ) )
                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                      ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                                                     => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                                       => ~ ( in @ X3 @ X1 ) ) )
                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                        ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                                       => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                          ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                                         => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                              ( ( ( setminus @ X1 @ X2 )
                                                                                                                                                                                                                                                = emptyset )
                                                                                                                                                                                                                                             => ( subset @ X1 @ X2 ) )
                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                                                                                                                                                                               => ! [X4: $o] :
                                                                                                                                                                                                                                                    ( ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                     => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                                                       => X4 ) )
                                                                                                                                                                                                                                                   => ( ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                       => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                                                         => X4 ) )
                                                                                                                                                                                                                                                     => X4 ) ) )
                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                 => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                                                   => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                    ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                   => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                                                     => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                     => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                                                       => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                        ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                       => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                                                         => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                    ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                                                   => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                      ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                                                     => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                       => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                          ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                                                         => ( ( X3 != X1 )
                                                                                                                                                                                                                                                                           => ( X3 = X2 ) ) )
                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                               => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                 => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                   => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                     => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                       => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                         => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                       => ~ ! [X4: $i] :
                                                                                                                                                                                                                                                                                              ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                                             => ! [X5: $i] :
                                                                                                                                                                                                                                                                                                  ( ( in @ X5 @ X2 )
                                                                                                                                                                                                                                                                                                 => ( X3
                                                                                                                                                                                                                                                                                                   != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                                                                                                                                                                                   => ( sP5
                                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                            ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                                                                                                                                                                                           => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                 => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                                                                                                                                                                                       => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                                                                                                                                                                                         => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                           => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                                  ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                                                                                                                                                                                  = X1 )
                                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                                                                    ( ! [X3: $i] :
                                                                                                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                            ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                                                           => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                                                                             => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                                                               => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                                                                                                   => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                           => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                                                                                                     => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                                            ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                           => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                             != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                                                                      ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                                            ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                           => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                             != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                     => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                           => ~ ( X2 @ X3 ) ) )
                                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                       => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                                                                         => ( ! [X4: $i] :
                                                                                                                                                                                                                                                                                                                ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                                                               => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                                                                 => ( X4 = X3 ) ) )
                                                                                                                                                                                                                                                                                                           => ~ ! [X4: $i] :
                                                                                                                                                                                                                                                                                                                  ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                 => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                                   != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                                                                          ( ! [X3: $i] :
                                                                                                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                                  ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                                                                 => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                                                                                   => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                                                                     => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                                                                                                         => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                                 => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                                                                                                           => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                                                  ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                 => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                                   != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                            ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                                                                                                                                                                              = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                                                           => ( X1 = X2 ) )
                                                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                              ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                             => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                                                         => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                                                ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                                                                               => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                                                      ( ( in @ X2
                                                                                                                                                                                                                                                                                                                        @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                                          @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                                                                                                                                                                                     => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                                          @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                                                                                                                       != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                                                                                           => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                                                  ( ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                                                        ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                                                                                                       => ( X1
                                                                                                                                                                                                                                                                                                                         != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                 => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                                    ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                    = X1 )
                                                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                      ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                     => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                        ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                                          = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                       => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                          ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                                            = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                                         => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                                            ( ( X1 = X2 )
                                                                                                                                                                                                                                                                                                                           => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                                                                              = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                                              ( ( X1 = X2 )
                                                                                                                                                                                                                                                                                                                             => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                                                = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                                ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                                                  = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                               => ( ( X3 = X4 )
                                                                                                                                                                                                                                                                                                                                 => ( X2 = X4 ) ) )
                                                                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                                  ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                                                                                    = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                                                                                                                                                                                 => ( X1 = X2 ) )
                                                                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                                    ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                                                      = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                                   => ( X2 = X4 ) )
                                                                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                                      ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                                                        = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                                                     => ( X2 = X4 ) )
                                                                                                                                                                                                                                                                                                                                 => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                                                                        ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                                                                                                       => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                                                                              ( ( in @ X2
                                                                                                                                                                                                                                                                                                                                                @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                                                                  @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                                                                                                      ( X1
                                                                                                                                                                                                                                                                                                                                                      = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                                                                                                                                                                             => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                                                                  @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                                                                                                      ( X1
                                                                                                                                                                                                                                                                                                                                                      = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                                                                                                                                                                               != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                                                          ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                                          = X2 )
                                                                                                                                                                                                                                                                                                                                     => ( sP8
                                                                                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                                              ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                                             => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                                                ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                                               => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                                                  ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                                                 => ( in @ X4 @ X2 ) )
                                                                                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                                                                                       => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                                                                          = X3 ) ) )
                                                                                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                                                                                         => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                                                                            = X4 ) ) )
                                                                                                                                                                                                                                                                                                                                                 => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                                                      ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                                                     => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                                                                                                                                                                                        = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h5,assumption,
    ! [X1: $i,X2: $i,X3: $i] :
      ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
      = ( ( X3 != X1 )
       => ( in @ X3 @ X2 ) ) ),
    introduced(assumption,[]) ).

thf(h6,assumption,
    ~ ( ! [X1: $i,X2: $i] :
          ( ( in @ X2 @ ( powerset @ X1 ) )
          = ( ! [X3: $i] :
                ( ( in @ X3 @ X2 )
               => ( in @ X3 @ X1 ) ) ) )
     => ( ! [X1: $i,X2: $i] :
            ( ( in @ X2 @ ( setunion @ X1 ) )
            = ( ~ ! [X3: $i] :
                    ( ( in @ X2 @ X3 )
                   => ~ ( in @ X3 @ X1 ) ) ) )
       => ( ( in @ emptyset @ omega )
         => ( ! [X1: $i] :
                ( ( in @ X1 @ omega )
               => ( in @ ( setadjoin @ X1 @ X1 ) @ omega ) )
           => ( ! [X1: $i] :
                  ( ~ ( ( in @ emptyset @ X1 )
                     => ~ ! [X2: $i] :
                            ( ~ ( ( in @ X2 @ omega )
                               => ~ ( in @ X2 @ X1 ) )
                           => ( in @ ( setadjoin @ X2 @ X2 ) @ X1 ) ) )
                 => ! [X2: $i] :
                      ( ( in @ X2 @ omega )
                     => ( in @ X2 @ X1 ) ) )
             => ( ! [X1: $i > $i > $o,X2: $i] :
                    ( ! [X3: $i] :
                        ( ( in @ X3 @ X2 )
                       => ~ ! [X4: $i] :
                              ( ( X1 @ X3 @ X4 )
                             => ~ ! [X5: $i] :
                                    ( ( X1 @ X3 @ X5 )
                                   => ( X4 = X5 ) ) ) )
                   => ~ ! [X3: $i] :
                          ~ ! [X4: $i] :
                              ( ( in @ X4 @ X3 )
                              = ( ~ ! [X5: $i] :
                                      ( ( in @ X5 @ X2 )
                                     => ~ ( X1 @ X5 @ X4 ) ) ) ) )
               => ( ! [X1: $i] :
                      ( ~ ! [X2: $i] :
                            ~ ( in @ X2 @ X1 )
                     => ~ ! [X2: $i] :
                            ( ( in @ X2 @ X1 )
                           => ~ ! [X3: $i] :
                                  ( ( in @ X3 @ X2 )
                                 => ~ ( in @ X3 @ X1 ) ) ) )
                 => ( ! [X1: $i] :
                        ~ ! [X2: $i] :
                            ( ~ ( ~ ( ! [X3: $i] :
                                        ( ( in @ X3 @ X2 )
                                       => ! [X4: $i] :
                                            ( ( in @ X4 @ X3 )
                                           => ( in @ X4 @ X1 ) ) )
                                   => ~ ! [X3: $i,X4: $i] :
                                          ( ~ ( ( in @ X3 @ X1 )
                                             => ~ ( in @ X4 @ X1 ) )
                                         => ( ! [X5: $i] :
                                                ( ( in @ X5 @ X2 )
                                               => ( ( in @ X3 @ X5 )
                                                  = ( in @ X4 @ X5 ) ) )
                                           => ( X3 = X4 ) ) ) )
                               => ~ ! [X3: $i,X4: $i] :
                                      ( ~ ( ( in @ X3 @ X2 )
                                         => ~ ( in @ X4 @ X2 ) )
                                     => ( ~ ! [X5: $i] :
                                              ( ( in @ X5 @ X3 )
                                             => ( in @ X5 @ X4 ) )
                                       => ! [X5: $i] :
                                            ( ( in @ X5 @ X4 )
                                           => ( in @ X5 @ X3 ) ) ) ) )
                           => ~ ! [X3: $i] :
                                  ( ~ ( ! [X4: $i] :
                                          ( ( in @ X4 @ X3 )
                                         => ( in @ X4 @ X1 ) )
                                     => ! [X4: $i] :
                                          ~ ( in @ X4 @ X3 ) )
                                 => ~ ! [X4: $i,X5: $i] :
                                        ( ~ ( ~ ( ( in @ X4 @ X2 )
                                               => ~ ( in @ X5 @ X3 ) )
                                           => ~ ! [X6: $i] :
                                                  ( ( in @ X6 @ X4 )
                                                 => ~ ( in @ X6 @ X3 ) ) )
                                       => ~ ! [X6: $i] :
                                              ( ( in @ X6 @ X2 )
                                             => ( ~ ! [X7: $i] :
                                                      ( ( in @ X7 @ X6 )
                                                     => ( in @ X7 @ X4 ) )
                                               => ( in @ X5 @ X6 ) ) ) ) ) )
                   => ( ! [X1: $i > $o] :
                          ( ~ ! [X2: $i] :
                                ( ( X1 @ X2 )
                               => ~ ! [X3: $i] :
                                      ( ( X1 @ X3 )
                                     => ( X2 = X3 ) ) )
                         => ( X1 @ ( descr @ X1 ) ) )
                     => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                            ( ( in @ X3 @ X1 )
                           => ( ( X2 @ X3 )
                             => ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) ) ) )
                       => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                              ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                             => ( in @ X3 @ X1 ) )
                         => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                               => ( X2 @ X3 ) )
                           => ( ! [X1: $o,X2: $i] :
                                  ( ( in @ X2 @ ( prop2set @ X1 ) )
                                 => X1 )
                             => ( ! [X1: $i] :
                                    ( ( in @ X1 @ emptyset )
                                   => ! [X2: $o] : X2 )
                               => ( ! [X1: $i] :
                                      ~ ( in @ X1 @ emptyset )
                                 => ( ! [X1: $i] :
                                        ~ ( in @ X1 @ emptyset )
                                   => ( ! [X1: $i > $o] :
                                          ( ~ ! [X2: $i] :
                                                ( ( X1 @ X2 )
                                               => ~ ! [X3: $i] :
                                                      ( ( X1 @ X3 )
                                                     => ( X2 = X3 ) ) )
                                         => ~ ! [X2: $i] :
                                                ~ ( X1 @ X2 ) )
                                     => ( ! [X1: $i,X2: $i] :
                                            ( ! [X3: $i] :
                                                ( ( in @ X3 @ X1 )
                                               => ( in @ X3 @ X2 ) )
                                           => ( ! [X3: $i] :
                                                  ( ( in @ X3 @ X2 )
                                                 => ( in @ X3 @ X1 ) )
                                             => ( X1 = X2 ) ) )
                                       => ( ! [X1: $i] :
                                              ( ! [X2: $i] :
                                                  ~ ( in @ X2 @ X1 )
                                             => ( X1 = emptyset ) )
                                         => ( ! [X1: $i] :
                                                ( ! [X2: $i] :
                                                    ~ ( in @ X2 @ X1 )
                                               => ( X1 = emptyset ) )
                                           => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                  ( ( in @ X3 @ X1 )
                                                 => ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                    = ( X2 @ X3 ) ) )
                                             => ( ! [X1: $i] :
                                                    ( ( X1 != emptyset )
                                                   => ~ ! [X2: $i] :
                                                          ~ ( in @ X2 @ X1 ) )
                                               => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                      ( ( in @ X3 @ X1 )
                                                     => ( ( X2 @ X3 )
                                                       => ( ( dsetconstr @ X1 @ X2 )
                                                         != emptyset ) ) )
                                                 => ( ! [X1: $i] :
                                                        ( ~ ! [X2: $i] :
                                                              ~ ( in @ X2 @ X1 )
                                                       => ( X1 != emptyset ) )
                                                   => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) )
                                                     => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                              ( ( in @ X3 @ X2 )
                                                             => ( in @ X3 @ ( setadjoin @ X1 @ X2 ) ) )
                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                                               => ! [X4: $o] :
                                                                    ( ( ( X3 = X1 )
                                                                     => X4 )
                                                                   => ( ( ( in @ X3 @ X2 )
                                                                       => X4 )
                                                                     => X4 ) ) )
                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                  ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                                                 => ( ( X3 != X1 )
                                                                   => ( in @ X3 @ X2 ) ) )
                                                             => ( ! [X1: $i] :
                                                                    ( ( dsetconstr @ X1
                                                                      @ ^ [X2: $i] : ~ $false )
                                                                    = X1 )
                                                               => ( ! [X1: $i,X2: $i] :
                                                                      ( ! [X3: $i] :
                                                                          ( ( in @ X3 @ X2 )
                                                                         => ( in @ X3 @ X1 ) )
                                                                     => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                                 => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                                                   => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                            ( ( in @ X2 @ ( powerset @ X1 ) )
                                                                           => ( ( in @ X3 @ X2 )
                                                                             => ( in @ X3 @ X1 ) ) )
                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                              ( ( in @ X2 @ X3 )
                                                                             => ( ( in @ X3 @ X1 )
                                                                               => ( in @ X2 @ ( setunion @ X1 ) ) ) )
                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                               => ! [X3: $o] :
                                                                                    ( ! [X4: $i] :
                                                                                        ( ( in @ X2 @ X4 )
                                                                                       => ( ( in @ X4 @ X1 )
                                                                                         => X3 ) )
                                                                                   => X3 ) )
                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                  ( ( in @ X2 @ X1 )
                                                                                 => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
                                                                             => ( ! [X1: $i > $o] :
                                                                                    ( ~ ! [X2: $i] :
                                                                                          ( ( X1 @ X2 )
                                                                                         => ~ ! [X3: $i] :
                                                                                                ( ( X1 @ X3 )
                                                                                               => ( X2 = X3 ) ) )
                                                                                   => ~ ! [X2: $i] :
                                                                                          ~ ! [X3: $i] :
                                                                                              ( ( X1 @ X3 )
                                                                                              = ( X3 = X2 ) ) )
                                                                               => ( ! [X1: $i] :
                                                                                      ( ( X1 != emptyset )
                                                                                     => ~ ! [X2: $i] :
                                                                                            ~ ( in @ X2 @ X1 ) )
                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                        ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                       => ( X1 = X2 ) )
                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                          ( ( X1 != X2 )
                                                                                         => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                            ( ( X1 = X2 )
                                                                                           => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                              ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                             => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                               => ( ( X3 != X1 )
                                                                                                 => ( X3 = X2 ) ) )
                                                                                           => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                             => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                               => ( ! [X1: $i,X2: $i > $o] :
                                                                                                      ( ~ ! [X3: $i] :
                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                           => ~ ( X2 @ X3 ) )
                                                                                                     => ( ( dsetconstr @ X1 @ X2 )
                                                                                                       != emptyset ) )
                                                                                                 => ( ! [X1: $i > $o,X2: $i] :
                                                                                                        ( ( in @ X2 @ emptyset )
                                                                                                       => ( X1 @ X2 ) )
                                                                                                   => ( ! [X1: $o] :
                                                                                                          ( X1
                                                                                                         => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                                                                                     => ( ! [X1: $o] :
                                                                                                            ( X1
                                                                                                           => ( set2prop @ ( prop2set @ X1 ) ) )
                                                                                                       => ( ! [X1: $i > $o] :
                                                                                                              ( ~ ! [X2: $i] :
                                                                                                                    ~ ( X1 @ X2 )
                                                                                                             => ( ! [X2: $i,X3: $i] :
                                                                                                                    ( ( X1 @ X2 )
                                                                                                                   => ( ( X1 @ X3 )
                                                                                                                     => ( X2 = X3 ) ) )
                                                                                                               => ~ ! [X2: $i] :
                                                                                                                      ( ( X1 @ X2 )
                                                                                                                     => ~ ! [X3: $i] :
                                                                                                                            ( ( X1 @ X3 )
                                                                                                                           => ( X2 = X3 ) ) ) ) )
                                                                                                         => ( ! [X1: $i > $o] :
                                                                                                                ( ~ ! [X2: $i] :
                                                                                                                      ~ ! [X3: $i] :
                                                                                                                          ( ( X1 @ X3 )
                                                                                                                          = ( X3 = X2 ) )
                                                                                                               => ~ ! [X2: $i] :
                                                                                                                      ( ( X1 @ X2 )
                                                                                                                     => ~ ! [X3: $i] :
                                                                                                                            ( ( X1 @ X3 )
                                                                                                                           => ( X2 = X3 ) ) ) )
                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                  ( ( X1 = X2 )
                                                                                                                 => ! [X3: $i,X4: $i] :
                                                                                                                      ( ( X3 = X4 )
                                                                                                                     => ( ( in @ X3 @ X1 )
                                                                                                                       => ( in @ X4 @ X2 ) ) ) )
                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                    ( ( X1 = X2 )
                                                                                                                   => ! [X3: $i,X4: $i] :
                                                                                                                        ( ( X3 = X4 )
                                                                                                                       => ( ( in @ X3 @ X1 )
                                                                                                                          = ( in @ X4 @ X2 ) ) ) )
                                                                                                               => ( ! [X1: $i > $o] :
                                                                                                                      ( ~ ! [X2: $i] :
                                                                                                                            ( ( X1 @ X2 )
                                                                                                                           => ~ ! [X3: $i] :
                                                                                                                                  ( ( X1 @ X3 )
                                                                                                                                 => ( X2 = X3 ) ) )
                                                                                                                     => ! [X2: $i,X3: $i] :
                                                                                                                          ( ( X1 @ X2 )
                                                                                                                         => ( ( X1 @ X3 )
                                                                                                                           => ( X2 = X3 ) ) ) )
                                                                                                                 => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                                                        ( ! [X3: $i,X4: $i] :
                                                                                                                            ( ( X3 = X4 )
                                                                                                                           => ( ( X1 @ X3 )
                                                                                                                              = ( X2 @ X4 ) ) )
                                                                                                                       => ( ( ~ ! [X3: $i] :
                                                                                                                                  ( ( X1 @ X3 )
                                                                                                                                 => ~ ! [X4: $i] :
                                                                                                                                        ( ( X1 @ X4 )
                                                                                                                                       => ( X3 = X4 ) ) ) )
                                                                                                                          = ( ~ ! [X3: $i] :
                                                                                                                                  ( ( X2 @ X3 )
                                                                                                                                 => ~ ! [X4: $i] :
                                                                                                                                        ( ( X2 @ X4 )
                                                                                                                                       => ( X3 = X4 ) ) ) ) ) )
                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                          ( ( X1 = X2 )
                                                                                                                         => ! [X3: $i,X4: $i] :
                                                                                                                              ( ( X3 = X4 )
                                                                                                                             => ( ( setadjoin @ X1 @ X3 )
                                                                                                                                = ( setadjoin @ X2 @ X4 ) ) ) )
                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                            ( ( X1 = X2 )
                                                                                                                           => ( ( powerset @ X1 )
                                                                                                                              = ( powerset @ X2 ) ) )
                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                              ( ( X1 = X2 )
                                                                                                                             => ( ( setunion @ X1 )
                                                                                                                                = ( setunion @ X2 ) ) )
                                                                                                                         => ( ! [X1: $i > $o] :
                                                                                                                                ( ~ ! [X2: $i] :
                                                                                                                                      ( ( X1 @ X2 )
                                                                                                                                     => ~ ! [X3: $i] :
                                                                                                                                            ( ( X1 @ X3 )
                                                                                                                                           => ( X2 = X3 ) ) )
                                                                                                                               => ! [X2: $i,X3: $i] :
                                                                                                                                    ( ( X1 @ X2 )
                                                                                                                                   => ( ( X1 @ X3 )
                                                                                                                                     => ( X2 = X3 ) ) ) )
                                                                                                                           => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                                                                  ( ! [X3: $i,X4: $i] :
                                                                                                                                      ( ( X3 = X4 )
                                                                                                                                     => ( ( X1 @ X3 )
                                                                                                                                        = ( X2 @ X4 ) ) )
                                                                                                                                 => ( ~ ! [X3: $i] :
                                                                                                                                          ( ( X1 @ X3 )
                                                                                                                                         => ~ ! [X4: $i] :
                                                                                                                                                ( ( X1 @ X4 )
                                                                                                                                               => ( X3 = X4 ) ) )
                                                                                                                                   => ( ~ ! [X3: $i] :
                                                                                                                                            ( ( X2 @ X3 )
                                                                                                                                           => ~ ! [X4: $i] :
                                                                                                                                                  ( ( X2 @ X4 )
                                                                                                                                                 => ( X3 = X4 ) ) )
                                                                                                                                     => ( ( descr @ X1 )
                                                                                                                                        = ( descr @ X2 ) ) ) ) )
                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                    ( ( X1 = X2 )
                                                                                                                                   => ! [X3: $i > $o,X4: $i > $o] :
                                                                                                                                        ( ! [X5: $i] :
                                                                                                                                            ( ( in @ X5 @ X1 )
                                                                                                                                           => ! [X6: $i] :
                                                                                                                                                ( ( in @ X6 @ X2 )
                                                                                                                                               => ( ( X5 = X6 )
                                                                                                                                                 => ( ( X3 @ X5 )
                                                                                                                                                    = ( X4 @ X6 ) ) ) ) )
                                                                                                                                       => ( ( dsetconstr @ X1 @ X3 )
                                                                                                                                          = ( dsetconstr @ X2 @ X4 ) ) ) )
                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                      ( ! [X3: $i] :
                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                         => ( in @ X3 @ X2 ) )
                                                                                                                                     => ( subset @ X1 @ X2 ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                        ( ( X1 = X2 )
                                                                                                                                       => ( subset @ X2 @ X1 ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                          ( ( X1 = X2 )
                                                                                                                                         => ( subset @ X1 @ X2 ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                            ( ! [X3: $i] :
                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                               => ( in @ X3 @ X2 ) )
                                                                                                                                           => ( subset @ X1 @ X2 ) )
                                                                                                                                       => ( ! [X1: $i] : ( subset @ emptyset @ X1 )
                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                ( ( subset @ X1 @ X2 )
                                                                                                                                               => ( ( in @ X3 @ X1 )
                                                                                                                                                 => ( in @ X3 @ X2 ) ) )
                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                  ( ( subset @ X1 @ X2 )
                                                                                                                                                 => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                   => ~ ( in @ X3 @ X1 ) ) )
                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                   => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                     => ~ ( subset @ X1 @ X2 ) ) )
                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                      ( ~ ( subset @ X1 @ X2 )
                                                                                                                                                     => ( X1 != X2 ) )
                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                       => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                         => ( X1 != X2 ) ) )
                                                                                                                                                   => ( ! [X1: $i] : ( subset @ X1 @ X1 )
                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                            ( ( subset @ X1 @ X2 )
                                                                                                                                                           => ( ( subset @ X2 @ X3 )
                                                                                                                                                             => ( subset @ X1 @ X3 ) ) )
                                                                                                                                                       => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) )
                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                ( ( subset @ X1 @ X3 )
                                                                                                                                                               => ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                  ( ( subset @ X1 @ X2 )
                                                                                                                                                                 => ( in @ X1 @ ( powerset @ X2 ) ) )
                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                    ( ( subset @ X1 @ X2 )
                                                                                                                                                                   => ( ( subset @ X2 @ X1 )
                                                                                                                                                                     => ( X1 = X2 ) ) )
                                                                                                                                                               => ( ! [X1: $i] :
                                                                                                                                                                      ( ( subset @ X1 @ emptyset )
                                                                                                                                                                     => ( X1 = emptyset ) )
                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                        ( ( subset @ X2 @ X1 )
                                                                                                                                                                       => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                          ( ( in @ X2 @ ( powerset @ X1 ) )
                                                                                                                                                                         => ( subset @ X2 @ X1 ) )
                                                                                                                                                                     => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                              ( ( subset @ X1 @ X2 )
                                                                                                                                                                             => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
                                                                                                                                                                         => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                                                                                                                                                                           => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                   => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                                                                                               => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                        ( ( in @ X3 @ X2 )
                                                                                                                                                                                       => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                                                                                                                                                                          ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                                                         => ( ( ( in @ X3 @ X1 )
                                                                                                                                                                                             => X4 )
                                                                                                                                                                                           => ( ( ( in @ X3 @ X2 )
                                                                                                                                                                                               => X4 )
                                                                                                                                                                                             => X4 ) ) )
                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                            ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                                                           => ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                             => ( in @ X3 @ X2 ) ) )
                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                 => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                   => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                    ( ( subset @ X3 @ X1 )
                                                                                                                                                                                                   => ( ( subset @ X3 @ X2 )
                                                                                                                                                                                                     => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                      ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                                                                                     => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                          ( ( subset @ X1 @ X2 )
                                                                                                                                                                                                         => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                                            = X1 ) )
                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                            ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                                              = X2 )
                                                                                                                                                                                                           => ( subset @ X2 @ X1 ) )
                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                              ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                                                                                             => ( in @ X3 @ X2 ) )
                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                ( ! [X3: $i] :
                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                   => ~ ( in @ X3 @ X2 ) )
                                                                                                                                                                                                               => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                                                  = emptyset ) )
                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                    ( ( subset @ X2 @ X1 )
                                                                                                                                                                                                                   => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                                                      = X2 ) )
                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                      ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                                                        = X1 )
                                                                                                                                                                                                                     => ( subset @ X1 @ X2 ) )
                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                        ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                                                                                                                                                                                        = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                         => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                           => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                            ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                                           => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                              ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                                             => ~ ( in @ X3 @ X2 ) )
                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                ( ( subset @ X1 @ X2 )
                                                                                                                                                                                                                               => ( ( setminus @ X1 @ X2 )
                                                                                                                                                                                                                                  = emptyset ) )
                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                  ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                                                 => ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                   => ( in @ X3 @ X2 ) ) )
                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                    ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                                                   => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                                     => ~ ( in @ X3 @ X1 ) ) )
                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                      ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                                     => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                        ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                                       => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                            ( ( ( setminus @ X1 @ X2 )
                                                                                                                                                                                                                                              = emptyset )
                                                                                                                                                                                                                                           => ( subset @ X1 @ X2 ) )
                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                              ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                                                                                                                                                                             => ! [X4: $o] :
                                                                                                                                                                                                                                                  ( ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                   => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                                                     => X4 ) )
                                                                                                                                                                                                                                                 => ( ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                     => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                                                       => X4 ) )
                                                                                                                                                                                                                                                   => X4 ) ) )
                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                               => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                                                 => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                  ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                 => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                                                   => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                   => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                                                     => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                      ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                     => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                                                       => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                  ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                                                 => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                    ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                                                   => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                     => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                        ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                                                       => ( ( X3 != X1 )
                                                                                                                                                                                                                                                                         => ( X3 = X2 ) ) )
                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                             => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                               => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                 => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                   => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                     => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                       => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                      ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                     => ~ ! [X4: $i] :
                                                                                                                                                                                                                                                                                            ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                                           => ! [X5: $i] :
                                                                                                                                                                                                                                                                                                ( ( in @ X5 @ X2 )
                                                                                                                                                                                                                                                                                               => ( X3
                                                                                                                                                                                                                                                                                                 != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                                                                                                                                                                                 => ( sP5
                                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                          ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                                                                                                                                                                                         => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                               => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                                                                                                                                                                                     => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                                                                                                                                                                                       => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                         => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                                ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                                                                                                                                                                                = X1 )
                                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                                                                  ( ! [X3: $i] :
                                                                                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                          ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                                                         => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                                                                           => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                                                             => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                                                                                                 => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                         => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                                                                                                   => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                                          ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                         => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                           != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                                                                    ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                                          ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                         => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                           != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                   => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                         => ~ ( X2 @ X3 ) ) )
                                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                     => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                                                                       => ( ! [X4: $i] :
                                                                                                                                                                                                                                                                                                              ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                                                             => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                                                               => ( X4 = X3 ) ) )
                                                                                                                                                                                                                                                                                                         => ~ ! [X4: $i] :
                                                                                                                                                                                                                                                                                                                ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                               => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                                 != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                                                                        ( ! [X3: $i] :
                                                                                                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                                ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                                                               => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                                                                                 => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                                                                   => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                                                                                                       => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                               => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                                                                                                         => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                                                ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                               => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                                 != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                          ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                                                                                                                                                                            = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                                                         => ( X1 = X2 ) )
                                                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                            ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                           => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                                                       => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                                              ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                                                                             => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                                                    ( ( in @ X2
                                                                                                                                                                                                                                                                                                                      @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                                        @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                                                                                                                                                                                   => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                                        @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                                                                                                                     != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                                                                                         => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                                                ( ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                                                      ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                                                                                                     => ( X1
                                                                                                                                                                                                                                                                                                                       != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                               => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                                  ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                  = X1 )
                                                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                    ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                   => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                      ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                                        = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                     => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                        ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                                          = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                                       => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                                          ( ( X1 = X2 )
                                                                                                                                                                                                                                                                                                                         => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                                                                            = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                                            ( ( X1 = X2 )
                                                                                                                                                                                                                                                                                                                           => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                                              = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                              ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                                                = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                             => ( ( X3 = X4 )
                                                                                                                                                                                                                                                                                                                               => ( X2 = X4 ) ) )
                                                                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                                ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                                                                                  = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                                                                                                                                                                               => ( X1 = X2 ) )
                                                                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                                  ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                                                    = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                                 => ( X2 = X4 ) )
                                                                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                                    ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                                                      = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                                                   => ( X2 = X4 ) )
                                                                                                                                                                                                                                                                                                                               => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                                                                      ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                                                                                                     => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                                                                            ( ( in @ X2
                                                                                                                                                                                                                                                                                                                                              @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                                                                @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                                                                                                    ( X1
                                                                                                                                                                                                                                                                                                                                                    = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                                                                                                                                                                           => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                                                                @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                                                                                                    ( X1
                                                                                                                                                                                                                                                                                                                                                    = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                                                                                                                                                                             != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                                                        ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                                        = X2 )
                                                                                                                                                                                                                                                                                                                                   => ( sP8
                                                                                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                                            ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                                           => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                                              ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                                             => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                                                ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                                               => ( in @ X4 @ X2 ) )
                                                                                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                                                                                     => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                                                                        = X3 ) ) )
                                                                                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                                                                                       => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                                                                          = X4 ) ) )
                                                                                                                                                                                                                                                                                                                                               => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                                                    ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                                                   => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                                                                                                                                                                                      = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h7,assumption,
    ! [X1: $i,X2: $i] :
      ( ( in @ X2 @ ( powerset @ X1 ) )
      = ( ! [X3: $i] :
            ( ( in @ X3 @ X2 )
           => ( in @ X3 @ X1 ) ) ) ),
    introduced(assumption,[]) ).

thf(h8,assumption,
    ~ ( ! [X1: $i,X2: $i] :
          ( ( in @ X2 @ ( setunion @ X1 ) )
          = ( ~ ! [X3: $i] :
                  ( ( in @ X2 @ X3 )
                 => ~ ( in @ X3 @ X1 ) ) ) )
     => ( ( in @ emptyset @ omega )
       => ( ! [X1: $i] :
              ( ( in @ X1 @ omega )
             => ( in @ ( setadjoin @ X1 @ X1 ) @ omega ) )
         => ( ! [X1: $i] :
                ( ~ ( ( in @ emptyset @ X1 )
                   => ~ ! [X2: $i] :
                          ( ~ ( ( in @ X2 @ omega )
                             => ~ ( in @ X2 @ X1 ) )
                         => ( in @ ( setadjoin @ X2 @ X2 ) @ X1 ) ) )
               => ! [X2: $i] :
                    ( ( in @ X2 @ omega )
                   => ( in @ X2 @ X1 ) ) )
           => ( ! [X1: $i > $i > $o,X2: $i] :
                  ( ! [X3: $i] :
                      ( ( in @ X3 @ X2 )
                     => ~ ! [X4: $i] :
                            ( ( X1 @ X3 @ X4 )
                           => ~ ! [X5: $i] :
                                  ( ( X1 @ X3 @ X5 )
                                 => ( X4 = X5 ) ) ) )
                 => ~ ! [X3: $i] :
                        ~ ! [X4: $i] :
                            ( ( in @ X4 @ X3 )
                            = ( ~ ! [X5: $i] :
                                    ( ( in @ X5 @ X2 )
                                   => ~ ( X1 @ X5 @ X4 ) ) ) ) )
             => ( ! [X1: $i] :
                    ( ~ ! [X2: $i] :
                          ~ ( in @ X2 @ X1 )
                   => ~ ! [X2: $i] :
                          ( ( in @ X2 @ X1 )
                         => ~ ! [X3: $i] :
                                ( ( in @ X3 @ X2 )
                               => ~ ( in @ X3 @ X1 ) ) ) )
               => ( ! [X1: $i] :
                      ~ ! [X2: $i] :
                          ( ~ ( ~ ( ! [X3: $i] :
                                      ( ( in @ X3 @ X2 )
                                     => ! [X4: $i] :
                                          ( ( in @ X4 @ X3 )
                                         => ( in @ X4 @ X1 ) ) )
                                 => ~ ! [X3: $i,X4: $i] :
                                        ( ~ ( ( in @ X3 @ X1 )
                                           => ~ ( in @ X4 @ X1 ) )
                                       => ( ! [X5: $i] :
                                              ( ( in @ X5 @ X2 )
                                             => ( ( in @ X3 @ X5 )
                                                = ( in @ X4 @ X5 ) ) )
                                         => ( X3 = X4 ) ) ) )
                             => ~ ! [X3: $i,X4: $i] :
                                    ( ~ ( ( in @ X3 @ X2 )
                                       => ~ ( in @ X4 @ X2 ) )
                                   => ( ~ ! [X5: $i] :
                                            ( ( in @ X5 @ X3 )
                                           => ( in @ X5 @ X4 ) )
                                     => ! [X5: $i] :
                                          ( ( in @ X5 @ X4 )
                                         => ( in @ X5 @ X3 ) ) ) ) )
                         => ~ ! [X3: $i] :
                                ( ~ ( ! [X4: $i] :
                                        ( ( in @ X4 @ X3 )
                                       => ( in @ X4 @ X1 ) )
                                   => ! [X4: $i] :
                                        ~ ( in @ X4 @ X3 ) )
                               => ~ ! [X4: $i,X5: $i] :
                                      ( ~ ( ~ ( ( in @ X4 @ X2 )
                                             => ~ ( in @ X5 @ X3 ) )
                                         => ~ ! [X6: $i] :
                                                ( ( in @ X6 @ X4 )
                                               => ~ ( in @ X6 @ X3 ) ) )
                                     => ~ ! [X6: $i] :
                                            ( ( in @ X6 @ X2 )
                                           => ( ~ ! [X7: $i] :
                                                    ( ( in @ X7 @ X6 )
                                                   => ( in @ X7 @ X4 ) )
                                             => ( in @ X5 @ X6 ) ) ) ) ) )
                 => ( ! [X1: $i > $o] :
                        ( ~ ! [X2: $i] :
                              ( ( X1 @ X2 )
                             => ~ ! [X3: $i] :
                                    ( ( X1 @ X3 )
                                   => ( X2 = X3 ) ) )
                       => ( X1 @ ( descr @ X1 ) ) )
                   => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                          ( ( in @ X3 @ X1 )
                         => ( ( X2 @ X3 )
                           => ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) ) ) )
                     => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                            ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                           => ( in @ X3 @ X1 ) )
                       => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                              ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                             => ( X2 @ X3 ) )
                         => ( ! [X1: $o,X2: $i] :
                                ( ( in @ X2 @ ( prop2set @ X1 ) )
                               => X1 )
                           => ( ! [X1: $i] :
                                  ( ( in @ X1 @ emptyset )
                                 => ! [X2: $o] : X2 )
                             => ( ! [X1: $i] :
                                    ~ ( in @ X1 @ emptyset )
                               => ( ! [X1: $i] :
                                      ~ ( in @ X1 @ emptyset )
                                 => ( ! [X1: $i > $o] :
                                        ( ~ ! [X2: $i] :
                                              ( ( X1 @ X2 )
                                             => ~ ! [X3: $i] :
                                                    ( ( X1 @ X3 )
                                                   => ( X2 = X3 ) ) )
                                       => ~ ! [X2: $i] :
                                              ~ ( X1 @ X2 ) )
                                   => ( ! [X1: $i,X2: $i] :
                                          ( ! [X3: $i] :
                                              ( ( in @ X3 @ X1 )
                                             => ( in @ X3 @ X2 ) )
                                         => ( ! [X3: $i] :
                                                ( ( in @ X3 @ X2 )
                                               => ( in @ X3 @ X1 ) )
                                           => ( X1 = X2 ) ) )
                                     => ( ! [X1: $i] :
                                            ( ! [X2: $i] :
                                                ~ ( in @ X2 @ X1 )
                                           => ( X1 = emptyset ) )
                                       => ( ! [X1: $i] :
                                              ( ! [X2: $i] :
                                                  ~ ( in @ X2 @ X1 )
                                             => ( X1 = emptyset ) )
                                         => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                ( ( in @ X3 @ X1 )
                                               => ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                  = ( X2 @ X3 ) ) )
                                           => ( ! [X1: $i] :
                                                  ( ( X1 != emptyset )
                                                 => ~ ! [X2: $i] :
                                                        ~ ( in @ X2 @ X1 ) )
                                             => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                    ( ( in @ X3 @ X1 )
                                                   => ( ( X2 @ X3 )
                                                     => ( ( dsetconstr @ X1 @ X2 )
                                                       != emptyset ) ) )
                                               => ( ! [X1: $i] :
                                                      ( ~ ! [X2: $i] :
                                                            ~ ( in @ X2 @ X1 )
                                                     => ( X1 != emptyset ) )
                                                 => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) )
                                                   => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                            ( ( in @ X3 @ X2 )
                                                           => ( in @ X3 @ ( setadjoin @ X1 @ X2 ) ) )
                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                              ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                                             => ! [X4: $o] :
                                                                  ( ( ( X3 = X1 )
                                                                   => X4 )
                                                                 => ( ( ( in @ X3 @ X2 )
                                                                     => X4 )
                                                                   => X4 ) ) )
                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                                               => ( ( X3 != X1 )
                                                                 => ( in @ X3 @ X2 ) ) )
                                                           => ( ! [X1: $i] :
                                                                  ( ( dsetconstr @ X1
                                                                    @ ^ [X2: $i] : ~ $false )
                                                                  = X1 )
                                                             => ( ! [X1: $i,X2: $i] :
                                                                    ( ! [X3: $i] :
                                                                        ( ( in @ X3 @ X2 )
                                                                       => ( in @ X3 @ X1 ) )
                                                                   => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                               => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                                                 => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                          ( ( in @ X2 @ ( powerset @ X1 ) )
                                                                         => ( ( in @ X3 @ X2 )
                                                                           => ( in @ X3 @ X1 ) ) )
                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                            ( ( in @ X2 @ X3 )
                                                                           => ( ( in @ X3 @ X1 )
                                                                             => ( in @ X2 @ ( setunion @ X1 ) ) ) )
                                                                       => ( ! [X1: $i,X2: $i] :
                                                                              ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                             => ! [X3: $o] :
                                                                                  ( ! [X4: $i] :
                                                                                      ( ( in @ X2 @ X4 )
                                                                                     => ( ( in @ X4 @ X1 )
                                                                                       => X3 ) )
                                                                                 => X3 ) )
                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                ( ( in @ X2 @ X1 )
                                                                               => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
                                                                           => ( ! [X1: $i > $o] :
                                                                                  ( ~ ! [X2: $i] :
                                                                                        ( ( X1 @ X2 )
                                                                                       => ~ ! [X3: $i] :
                                                                                              ( ( X1 @ X3 )
                                                                                             => ( X2 = X3 ) ) )
                                                                                 => ~ ! [X2: $i] :
                                                                                        ~ ! [X3: $i] :
                                                                                            ( ( X1 @ X3 )
                                                                                            = ( X3 = X2 ) ) )
                                                                             => ( ! [X1: $i] :
                                                                                    ( ( X1 != emptyset )
                                                                                   => ~ ! [X2: $i] :
                                                                                          ~ ( in @ X2 @ X1 ) )
                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                      ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                     => ( X1 = X2 ) )
                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                        ( ( X1 != X2 )
                                                                                       => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                          ( ( X1 = X2 )
                                                                                         => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                            ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                           => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                              ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                             => ( ( X3 != X1 )
                                                                                               => ( X3 = X2 ) ) )
                                                                                         => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                           => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                             => ( ! [X1: $i,X2: $i > $o] :
                                                                                                    ( ~ ! [X3: $i] :
                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                         => ~ ( X2 @ X3 ) )
                                                                                                   => ( ( dsetconstr @ X1 @ X2 )
                                                                                                     != emptyset ) )
                                                                                               => ( ! [X1: $i > $o,X2: $i] :
                                                                                                      ( ( in @ X2 @ emptyset )
                                                                                                     => ( X1 @ X2 ) )
                                                                                                 => ( ! [X1: $o] :
                                                                                                        ( X1
                                                                                                       => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                                                                                   => ( ! [X1: $o] :
                                                                                                          ( X1
                                                                                                         => ( set2prop @ ( prop2set @ X1 ) ) )
                                                                                                     => ( ! [X1: $i > $o] :
                                                                                                            ( ~ ! [X2: $i] :
                                                                                                                  ~ ( X1 @ X2 )
                                                                                                           => ( ! [X2: $i,X3: $i] :
                                                                                                                  ( ( X1 @ X2 )
                                                                                                                 => ( ( X1 @ X3 )
                                                                                                                   => ( X2 = X3 ) ) )
                                                                                                             => ~ ! [X2: $i] :
                                                                                                                    ( ( X1 @ X2 )
                                                                                                                   => ~ ! [X3: $i] :
                                                                                                                          ( ( X1 @ X3 )
                                                                                                                         => ( X2 = X3 ) ) ) ) )
                                                                                                       => ( ! [X1: $i > $o] :
                                                                                                              ( ~ ! [X2: $i] :
                                                                                                                    ~ ! [X3: $i] :
                                                                                                                        ( ( X1 @ X3 )
                                                                                                                        = ( X3 = X2 ) )
                                                                                                             => ~ ! [X2: $i] :
                                                                                                                    ( ( X1 @ X2 )
                                                                                                                   => ~ ! [X3: $i] :
                                                                                                                          ( ( X1 @ X3 )
                                                                                                                         => ( X2 = X3 ) ) ) )
                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                ( ( X1 = X2 )
                                                                                                               => ! [X3: $i,X4: $i] :
                                                                                                                    ( ( X3 = X4 )
                                                                                                                   => ( ( in @ X3 @ X1 )
                                                                                                                     => ( in @ X4 @ X2 ) ) ) )
                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                  ( ( X1 = X2 )
                                                                                                                 => ! [X3: $i,X4: $i] :
                                                                                                                      ( ( X3 = X4 )
                                                                                                                     => ( ( in @ X3 @ X1 )
                                                                                                                        = ( in @ X4 @ X2 ) ) ) )
                                                                                                             => ( ! [X1: $i > $o] :
                                                                                                                    ( ~ ! [X2: $i] :
                                                                                                                          ( ( X1 @ X2 )
                                                                                                                         => ~ ! [X3: $i] :
                                                                                                                                ( ( X1 @ X3 )
                                                                                                                               => ( X2 = X3 ) ) )
                                                                                                                   => ! [X2: $i,X3: $i] :
                                                                                                                        ( ( X1 @ X2 )
                                                                                                                       => ( ( X1 @ X3 )
                                                                                                                         => ( X2 = X3 ) ) ) )
                                                                                                               => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                                                      ( ! [X3: $i,X4: $i] :
                                                                                                                          ( ( X3 = X4 )
                                                                                                                         => ( ( X1 @ X3 )
                                                                                                                            = ( X2 @ X4 ) ) )
                                                                                                                     => ( ( ~ ! [X3: $i] :
                                                                                                                                ( ( X1 @ X3 )
                                                                                                                               => ~ ! [X4: $i] :
                                                                                                                                      ( ( X1 @ X4 )
                                                                                                                                     => ( X3 = X4 ) ) ) )
                                                                                                                        = ( ~ ! [X3: $i] :
                                                                                                                                ( ( X2 @ X3 )
                                                                                                                               => ~ ! [X4: $i] :
                                                                                                                                      ( ( X2 @ X4 )
                                                                                                                                     => ( X3 = X4 ) ) ) ) ) )
                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                        ( ( X1 = X2 )
                                                                                                                       => ! [X3: $i,X4: $i] :
                                                                                                                            ( ( X3 = X4 )
                                                                                                                           => ( ( setadjoin @ X1 @ X3 )
                                                                                                                              = ( setadjoin @ X2 @ X4 ) ) ) )
                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                          ( ( X1 = X2 )
                                                                                                                         => ( ( powerset @ X1 )
                                                                                                                            = ( powerset @ X2 ) ) )
                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                            ( ( X1 = X2 )
                                                                                                                           => ( ( setunion @ X1 )
                                                                                                                              = ( setunion @ X2 ) ) )
                                                                                                                       => ( ! [X1: $i > $o] :
                                                                                                                              ( ~ ! [X2: $i] :
                                                                                                                                    ( ( X1 @ X2 )
                                                                                                                                   => ~ ! [X3: $i] :
                                                                                                                                          ( ( X1 @ X3 )
                                                                                                                                         => ( X2 = X3 ) ) )
                                                                                                                             => ! [X2: $i,X3: $i] :
                                                                                                                                  ( ( X1 @ X2 )
                                                                                                                                 => ( ( X1 @ X3 )
                                                                                                                                   => ( X2 = X3 ) ) ) )
                                                                                                                         => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                                                                ( ! [X3: $i,X4: $i] :
                                                                                                                                    ( ( X3 = X4 )
                                                                                                                                   => ( ( X1 @ X3 )
                                                                                                                                      = ( X2 @ X4 ) ) )
                                                                                                                               => ( ~ ! [X3: $i] :
                                                                                                                                        ( ( X1 @ X3 )
                                                                                                                                       => ~ ! [X4: $i] :
                                                                                                                                              ( ( X1 @ X4 )
                                                                                                                                             => ( X3 = X4 ) ) )
                                                                                                                                 => ( ~ ! [X3: $i] :
                                                                                                                                          ( ( X2 @ X3 )
                                                                                                                                         => ~ ! [X4: $i] :
                                                                                                                                                ( ( X2 @ X4 )
                                                                                                                                               => ( X3 = X4 ) ) )
                                                                                                                                   => ( ( descr @ X1 )
                                                                                                                                      = ( descr @ X2 ) ) ) ) )
                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                  ( ( X1 = X2 )
                                                                                                                                 => ! [X3: $i > $o,X4: $i > $o] :
                                                                                                                                      ( ! [X5: $i] :
                                                                                                                                          ( ( in @ X5 @ X1 )
                                                                                                                                         => ! [X6: $i] :
                                                                                                                                              ( ( in @ X6 @ X2 )
                                                                                                                                             => ( ( X5 = X6 )
                                                                                                                                               => ( ( X3 @ X5 )
                                                                                                                                                  = ( X4 @ X6 ) ) ) ) )
                                                                                                                                     => ( ( dsetconstr @ X1 @ X3 )
                                                                                                                                        = ( dsetconstr @ X2 @ X4 ) ) ) )
                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                    ( ! [X3: $i] :
                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                       => ( in @ X3 @ X2 ) )
                                                                                                                                   => ( subset @ X1 @ X2 ) )
                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                      ( ( X1 = X2 )
                                                                                                                                     => ( subset @ X2 @ X1 ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                        ( ( X1 = X2 )
                                                                                                                                       => ( subset @ X1 @ X2 ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                          ( ! [X3: $i] :
                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                             => ( in @ X3 @ X2 ) )
                                                                                                                                         => ( subset @ X1 @ X2 ) )
                                                                                                                                     => ( ! [X1: $i] : ( subset @ emptyset @ X1 )
                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                              ( ( subset @ X1 @ X2 )
                                                                                                                                             => ( ( in @ X3 @ X1 )
                                                                                                                                               => ( in @ X3 @ X2 ) ) )
                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                ( ( subset @ X1 @ X2 )
                                                                                                                                               => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                 => ~ ( in @ X3 @ X1 ) ) )
                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                 => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                   => ~ ( subset @ X1 @ X2 ) ) )
                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                    ( ~ ( subset @ X1 @ X2 )
                                                                                                                                                   => ( X1 != X2 ) )
                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                     => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                       => ( X1 != X2 ) ) )
                                                                                                                                                 => ( ! [X1: $i] : ( subset @ X1 @ X1 )
                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                          ( ( subset @ X1 @ X2 )
                                                                                                                                                         => ( ( subset @ X2 @ X3 )
                                                                                                                                                           => ( subset @ X1 @ X3 ) ) )
                                                                                                                                                     => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) )
                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                              ( ( subset @ X1 @ X3 )
                                                                                                                                                             => ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                ( ( subset @ X1 @ X2 )
                                                                                                                                                               => ( in @ X1 @ ( powerset @ X2 ) ) )
                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                  ( ( subset @ X1 @ X2 )
                                                                                                                                                                 => ( ( subset @ X2 @ X1 )
                                                                                                                                                                   => ( X1 = X2 ) ) )
                                                                                                                                                             => ( ! [X1: $i] :
                                                                                                                                                                    ( ( subset @ X1 @ emptyset )
                                                                                                                                                                   => ( X1 = emptyset ) )
                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                      ( ( subset @ X2 @ X1 )
                                                                                                                                                                     => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                        ( ( in @ X2 @ ( powerset @ X1 ) )
                                                                                                                                                                       => ( subset @ X2 @ X1 ) )
                                                                                                                                                                   => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                            ( ( subset @ X1 @ X2 )
                                                                                                                                                                           => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
                                                                                                                                                                       => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                                                                                                                                                                         => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                 => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                                                                                             => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                      ( ( in @ X3 @ X2 )
                                                                                                                                                                                     => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                                                                                                                                                                        ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                                                       => ( ( ( in @ X3 @ X1 )
                                                                                                                                                                                           => X4 )
                                                                                                                                                                                         => ( ( ( in @ X3 @ X2 )
                                                                                                                                                                                             => X4 )
                                                                                                                                                                                           => X4 ) ) )
                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                          ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                                                         => ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                           => ( in @ X3 @ X2 ) ) )
                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                               => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                 => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                  ( ( subset @ X3 @ X1 )
                                                                                                                                                                                                 => ( ( subset @ X3 @ X2 )
                                                                                                                                                                                                   => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                    ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                                                                                   => ( in @ X3 @ X1 ) )
                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                        ( ( subset @ X1 @ X2 )
                                                                                                                                                                                                       => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                                          = X1 ) )
                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                          ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                                            = X2 )
                                                                                                                                                                                                         => ( subset @ X2 @ X1 ) )
                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                            ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                                                                                           => ( in @ X3 @ X2 ) )
                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                              ( ! [X3: $i] :
                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                 => ~ ( in @ X3 @ X2 ) )
                                                                                                                                                                                                             => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                                                = emptyset ) )
                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                  ( ( subset @ X2 @ X1 )
                                                                                                                                                                                                                 => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                                                    = X2 ) )
                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                    ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                                                      = X1 )
                                                                                                                                                                                                                   => ( subset @ X1 @ X2 ) )
                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                      ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                                                                                                                                                                                      = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                       => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                         => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                          ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                                         => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                            ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                                           => ~ ( in @ X3 @ X2 ) )
                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                              ( ( subset @ X1 @ X2 )
                                                                                                                                                                                                                             => ( ( setminus @ X1 @ X2 )
                                                                                                                                                                                                                                = emptyset ) )
                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                                               => ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                 => ( in @ X3 @ X2 ) ) )
                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                  ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                                                 => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                                   => ~ ( in @ X3 @ X1 ) ) )
                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                    ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                                   => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                      ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                                     => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                          ( ( ( setminus @ X1 @ X2 )
                                                                                                                                                                                                                                            = emptyset )
                                                                                                                                                                                                                                         => ( subset @ X1 @ X2 ) )
                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                            ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                                                                                                                                                                           => ! [X4: $o] :
                                                                                                                                                                                                                                                ( ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                 => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                                                   => X4 ) )
                                                                                                                                                                                                                                               => ( ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                   => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                                                     => X4 ) )
                                                                                                                                                                                                                                                 => X4 ) ) )
                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                             => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                                               => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                                               => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                                                 => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                 => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                                                   => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                    ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                   => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                                                     => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                                               => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                  ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                                                 => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                   => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                      ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                                                     => ( ( X3 != X1 )
                                                                                                                                                                                                                                                                       => ( X3 = X2 ) ) )
                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                           => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                             => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                               => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                 => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                   => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                     => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                    ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                   => ~ ! [X4: $i] :
                                                                                                                                                                                                                                                                                          ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                                         => ! [X5: $i] :
                                                                                                                                                                                                                                                                                              ( ( in @ X5 @ X2 )
                                                                                                                                                                                                                                                                                             => ( X3
                                                                                                                                                                                                                                                                                               != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                                                                                                                                                                               => ( sP5
                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                        ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                                                                                                                                                                                       => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                             => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                                                                                                                                                                                   => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                                                                                                                                                                                     => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                       => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                              ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                                                                                                                                                                              = X1 )
                                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                                                                ( ! [X3: $i] :
                                                                                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                        ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                                                       => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                                                                         => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                                                           => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                                                                                               => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                       => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                                                                                                 => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                                        ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                       => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                         != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                                                                  ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                                        ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                       => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                         != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                 => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                       => ~ ( X2 @ X3 ) ) )
                                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                   => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                                                                     => ( ! [X4: $i] :
                                                                                                                                                                                                                                                                                                            ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                                                           => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                                                             => ( X4 = X3 ) ) )
                                                                                                                                                                                                                                                                                                       => ~ ! [X4: $i] :
                                                                                                                                                                                                                                                                                                              ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                             => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                               != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                                                                      ( ! [X3: $i] :
                                                                                                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                              ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                                                             => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                                                                               => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                                                                 => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                                                                                                     => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                             => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                                                                                                       => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                                              ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                             => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                               != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                        ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                                                                                                                                                                          = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                                                       => ( X1 = X2 ) )
                                                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                          ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                         => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                                                     => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                                            ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                                                                           => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                                                  ( ( in @ X2
                                                                                                                                                                                                                                                                                                                    @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                                      @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                                                                                                                                                                                 => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                                      @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                                                                                                                   != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                                                                                       => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                                              ( ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                                                    ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                                                                                                   => ( X1
                                                                                                                                                                                                                                                                                                                     != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                             => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                                ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                = X1 )
                                                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                  ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                 => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                    ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                                      = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                   => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                      ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                                        = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                                     => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                                        ( ( X1 = X2 )
                                                                                                                                                                                                                                                                                                                       => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                                                                          = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                                          ( ( X1 = X2 )
                                                                                                                                                                                                                                                                                                                         => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                                            = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                            ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                                              = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                           => ( ( X3 = X4 )
                                                                                                                                                                                                                                                                                                                             => ( X2 = X4 ) ) )
                                                                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                              ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                                                                                = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                                                                                                                                                                             => ( X1 = X2 ) )
                                                                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                                ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                                                  = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                               => ( X2 = X4 ) )
                                                                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                                  ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                                                    = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                                                 => ( X2 = X4 ) )
                                                                                                                                                                                                                                                                                                                             => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                                                                    ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                                                                                                   => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                                                                          ( ( in @ X2
                                                                                                                                                                                                                                                                                                                                            @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                                                              @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                                                                                                  ( X1
                                                                                                                                                                                                                                                                                                                                                  = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                                                                                                                                                                         => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                                                              @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                                                                                                  ( X1
                                                                                                                                                                                                                                                                                                                                                  = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                                                                                                                                                                           != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                                                      ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                                      = X2 )
                                                                                                                                                                                                                                                                                                                                 => ( sP8
                                                                                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                                          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                                         => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                                            ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                                           => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                                              ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                                             => ( in @ X4 @ X2 ) )
                                                                                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                                                                                   => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                                                                      = X3 ) ) )
                                                                                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                                                                                     => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                                                                        = X4 ) ) )
                                                                                                                                                                                                                                                                                                                                             => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                                                 => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                                                                                                                                                                                    = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h9,assumption,
    ! [X1: $i,X2: $i] :
      ( ( in @ X2 @ ( setunion @ X1 ) )
      = ( ~ ! [X3: $i] :
              ( ( in @ X2 @ X3 )
             => ~ ( in @ X3 @ X1 ) ) ) ),
    introduced(assumption,[]) ).

thf(h10,assumption,
    ~ ( ( in @ emptyset @ omega )
     => ( ! [X1: $i] :
            ( ( in @ X1 @ omega )
           => ( in @ ( setadjoin @ X1 @ X1 ) @ omega ) )
       => ( ! [X1: $i] :
              ( ~ ( ( in @ emptyset @ X1 )
                 => ~ ! [X2: $i] :
                        ( ~ ( ( in @ X2 @ omega )
                           => ~ ( in @ X2 @ X1 ) )
                       => ( in @ ( setadjoin @ X2 @ X2 ) @ X1 ) ) )
             => ! [X2: $i] :
                  ( ( in @ X2 @ omega )
                 => ( in @ X2 @ X1 ) ) )
         => ( ! [X1: $i > $i > $o,X2: $i] :
                ( ! [X3: $i] :
                    ( ( in @ X3 @ X2 )
                   => ~ ! [X4: $i] :
                          ( ( X1 @ X3 @ X4 )
                         => ~ ! [X5: $i] :
                                ( ( X1 @ X3 @ X5 )
                               => ( X4 = X5 ) ) ) )
               => ~ ! [X3: $i] :
                      ~ ! [X4: $i] :
                          ( ( in @ X4 @ X3 )
                          = ( ~ ! [X5: $i] :
                                  ( ( in @ X5 @ X2 )
                                 => ~ ( X1 @ X5 @ X4 ) ) ) ) )
           => ( ! [X1: $i] :
                  ( ~ ! [X2: $i] :
                        ~ ( in @ X2 @ X1 )
                 => ~ ! [X2: $i] :
                        ( ( in @ X2 @ X1 )
                       => ~ ! [X3: $i] :
                              ( ( in @ X3 @ X2 )
                             => ~ ( in @ X3 @ X1 ) ) ) )
             => ( ! [X1: $i] :
                    ~ ! [X2: $i] :
                        ( ~ ( ~ ( ! [X3: $i] :
                                    ( ( in @ X3 @ X2 )
                                   => ! [X4: $i] :
                                        ( ( in @ X4 @ X3 )
                                       => ( in @ X4 @ X1 ) ) )
                               => ~ ! [X3: $i,X4: $i] :
                                      ( ~ ( ( in @ X3 @ X1 )
                                         => ~ ( in @ X4 @ X1 ) )
                                     => ( ! [X5: $i] :
                                            ( ( in @ X5 @ X2 )
                                           => ( ( in @ X3 @ X5 )
                                              = ( in @ X4 @ X5 ) ) )
                                       => ( X3 = X4 ) ) ) )
                           => ~ ! [X3: $i,X4: $i] :
                                  ( ~ ( ( in @ X3 @ X2 )
                                     => ~ ( in @ X4 @ X2 ) )
                                 => ( ~ ! [X5: $i] :
                                          ( ( in @ X5 @ X3 )
                                         => ( in @ X5 @ X4 ) )
                                   => ! [X5: $i] :
                                        ( ( in @ X5 @ X4 )
                                       => ( in @ X5 @ X3 ) ) ) ) )
                       => ~ ! [X3: $i] :
                              ( ~ ( ! [X4: $i] :
                                      ( ( in @ X4 @ X3 )
                                     => ( in @ X4 @ X1 ) )
                                 => ! [X4: $i] :
                                      ~ ( in @ X4 @ X3 ) )
                             => ~ ! [X4: $i,X5: $i] :
                                    ( ~ ( ~ ( ( in @ X4 @ X2 )
                                           => ~ ( in @ X5 @ X3 ) )
                                       => ~ ! [X6: $i] :
                                              ( ( in @ X6 @ X4 )
                                             => ~ ( in @ X6 @ X3 ) ) )
                                   => ~ ! [X6: $i] :
                                          ( ( in @ X6 @ X2 )
                                         => ( ~ ! [X7: $i] :
                                                  ( ( in @ X7 @ X6 )
                                                 => ( in @ X7 @ X4 ) )
                                           => ( in @ X5 @ X6 ) ) ) ) ) )
               => ( ! [X1: $i > $o] :
                      ( ~ ! [X2: $i] :
                            ( ( X1 @ X2 )
                           => ~ ! [X3: $i] :
                                  ( ( X1 @ X3 )
                                 => ( X2 = X3 ) ) )
                     => ( X1 @ ( descr @ X1 ) ) )
                 => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                        ( ( in @ X3 @ X1 )
                       => ( ( X2 @ X3 )
                         => ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) ) ) )
                   => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                          ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                         => ( in @ X3 @ X1 ) )
                     => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                            ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                           => ( X2 @ X3 ) )
                       => ( ! [X1: $o,X2: $i] :
                              ( ( in @ X2 @ ( prop2set @ X1 ) )
                             => X1 )
                         => ( ! [X1: $i] :
                                ( ( in @ X1 @ emptyset )
                               => ! [X2: $o] : X2 )
                           => ( ! [X1: $i] :
                                  ~ ( in @ X1 @ emptyset )
                             => ( ! [X1: $i] :
                                    ~ ( in @ X1 @ emptyset )
                               => ( ! [X1: $i > $o] :
                                      ( ~ ! [X2: $i] :
                                            ( ( X1 @ X2 )
                                           => ~ ! [X3: $i] :
                                                  ( ( X1 @ X3 )
                                                 => ( X2 = X3 ) ) )
                                     => ~ ! [X2: $i] :
                                            ~ ( X1 @ X2 ) )
                                 => ( ! [X1: $i,X2: $i] :
                                        ( ! [X3: $i] :
                                            ( ( in @ X3 @ X1 )
                                           => ( in @ X3 @ X2 ) )
                                       => ( ! [X3: $i] :
                                              ( ( in @ X3 @ X2 )
                                             => ( in @ X3 @ X1 ) )
                                         => ( X1 = X2 ) ) )
                                   => ( ! [X1: $i] :
                                          ( ! [X2: $i] :
                                              ~ ( in @ X2 @ X1 )
                                         => ( X1 = emptyset ) )
                                     => ( ! [X1: $i] :
                                            ( ! [X2: $i] :
                                                ~ ( in @ X2 @ X1 )
                                           => ( X1 = emptyset ) )
                                       => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                              ( ( in @ X3 @ X1 )
                                             => ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                = ( X2 @ X3 ) ) )
                                         => ( ! [X1: $i] :
                                                ( ( X1 != emptyset )
                                               => ~ ! [X2: $i] :
                                                      ~ ( in @ X2 @ X1 ) )
                                           => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                  ( ( in @ X3 @ X1 )
                                                 => ( ( X2 @ X3 )
                                                   => ( ( dsetconstr @ X1 @ X2 )
                                                     != emptyset ) ) )
                                             => ( ! [X1: $i] :
                                                    ( ~ ! [X2: $i] :
                                                          ~ ( in @ X2 @ X1 )
                                                   => ( X1 != emptyset ) )
                                               => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) )
                                                 => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                          ( ( in @ X3 @ X2 )
                                                         => ( in @ X3 @ ( setadjoin @ X1 @ X2 ) ) )
                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                            ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                                           => ! [X4: $o] :
                                                                ( ( ( X3 = X1 )
                                                                 => X4 )
                                                               => ( ( ( in @ X3 @ X2 )
                                                                   => X4 )
                                                                 => X4 ) ) )
                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                              ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                                             => ( ( X3 != X1 )
                                                               => ( in @ X3 @ X2 ) ) )
                                                         => ( ! [X1: $i] :
                                                                ( ( dsetconstr @ X1
                                                                  @ ^ [X2: $i] : ~ $false )
                                                                = X1 )
                                                           => ( ! [X1: $i,X2: $i] :
                                                                  ( ! [X3: $i] :
                                                                      ( ( in @ X3 @ X2 )
                                                                     => ( in @ X3 @ X1 ) )
                                                                 => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                             => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                                               => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                        ( ( in @ X2 @ ( powerset @ X1 ) )
                                                                       => ( ( in @ X3 @ X2 )
                                                                         => ( in @ X3 @ X1 ) ) )
                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                          ( ( in @ X2 @ X3 )
                                                                         => ( ( in @ X3 @ X1 )
                                                                           => ( in @ X2 @ ( setunion @ X1 ) ) ) )
                                                                     => ( ! [X1: $i,X2: $i] :
                                                                            ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                           => ! [X3: $o] :
                                                                                ( ! [X4: $i] :
                                                                                    ( ( in @ X2 @ X4 )
                                                                                   => ( ( in @ X4 @ X1 )
                                                                                     => X3 ) )
                                                                               => X3 ) )
                                                                       => ( ! [X1: $i,X2: $i] :
                                                                              ( ( in @ X2 @ X1 )
                                                                             => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
                                                                         => ( ! [X1: $i > $o] :
                                                                                ( ~ ! [X2: $i] :
                                                                                      ( ( X1 @ X2 )
                                                                                     => ~ ! [X3: $i] :
                                                                                            ( ( X1 @ X3 )
                                                                                           => ( X2 = X3 ) ) )
                                                                               => ~ ! [X2: $i] :
                                                                                      ~ ! [X3: $i] :
                                                                                          ( ( X1 @ X3 )
                                                                                          = ( X3 = X2 ) ) )
                                                                           => ( ! [X1: $i] :
                                                                                  ( ( X1 != emptyset )
                                                                                 => ~ ! [X2: $i] :
                                                                                        ~ ( in @ X2 @ X1 ) )
                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                    ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                   => ( X1 = X2 ) )
                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                      ( ( X1 != X2 )
                                                                                     => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                        ( ( X1 = X2 )
                                                                                       => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                          ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                         => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                            ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                           => ( ( X3 != X1 )
                                                                                             => ( X3 = X2 ) ) )
                                                                                       => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                         => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                           => ( ! [X1: $i,X2: $i > $o] :
                                                                                                  ( ~ ! [X3: $i] :
                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                       => ~ ( X2 @ X3 ) )
                                                                                                 => ( ( dsetconstr @ X1 @ X2 )
                                                                                                   != emptyset ) )
                                                                                             => ( ! [X1: $i > $o,X2: $i] :
                                                                                                    ( ( in @ X2 @ emptyset )
                                                                                                   => ( X1 @ X2 ) )
                                                                                               => ( ! [X1: $o] :
                                                                                                      ( X1
                                                                                                     => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                                                                                 => ( ! [X1: $o] :
                                                                                                        ( X1
                                                                                                       => ( set2prop @ ( prop2set @ X1 ) ) )
                                                                                                   => ( ! [X1: $i > $o] :
                                                                                                          ( ~ ! [X2: $i] :
                                                                                                                ~ ( X1 @ X2 )
                                                                                                         => ( ! [X2: $i,X3: $i] :
                                                                                                                ( ( X1 @ X2 )
                                                                                                               => ( ( X1 @ X3 )
                                                                                                                 => ( X2 = X3 ) ) )
                                                                                                           => ~ ! [X2: $i] :
                                                                                                                  ( ( X1 @ X2 )
                                                                                                                 => ~ ! [X3: $i] :
                                                                                                                        ( ( X1 @ X3 )
                                                                                                                       => ( X2 = X3 ) ) ) ) )
                                                                                                     => ( ! [X1: $i > $o] :
                                                                                                            ( ~ ! [X2: $i] :
                                                                                                                  ~ ! [X3: $i] :
                                                                                                                      ( ( X1 @ X3 )
                                                                                                                      = ( X3 = X2 ) )
                                                                                                           => ~ ! [X2: $i] :
                                                                                                                  ( ( X1 @ X2 )
                                                                                                                 => ~ ! [X3: $i] :
                                                                                                                        ( ( X1 @ X3 )
                                                                                                                       => ( X2 = X3 ) ) ) )
                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                              ( ( X1 = X2 )
                                                                                                             => ! [X3: $i,X4: $i] :
                                                                                                                  ( ( X3 = X4 )
                                                                                                                 => ( ( in @ X3 @ X1 )
                                                                                                                   => ( in @ X4 @ X2 ) ) ) )
                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                ( ( X1 = X2 )
                                                                                                               => ! [X3: $i,X4: $i] :
                                                                                                                    ( ( X3 = X4 )
                                                                                                                   => ( ( in @ X3 @ X1 )
                                                                                                                      = ( in @ X4 @ X2 ) ) ) )
                                                                                                           => ( ! [X1: $i > $o] :
                                                                                                                  ( ~ ! [X2: $i] :
                                                                                                                        ( ( X1 @ X2 )
                                                                                                                       => ~ ! [X3: $i] :
                                                                                                                              ( ( X1 @ X3 )
                                                                                                                             => ( X2 = X3 ) ) )
                                                                                                                 => ! [X2: $i,X3: $i] :
                                                                                                                      ( ( X1 @ X2 )
                                                                                                                     => ( ( X1 @ X3 )
                                                                                                                       => ( X2 = X3 ) ) ) )
                                                                                                             => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                                                    ( ! [X3: $i,X4: $i] :
                                                                                                                        ( ( X3 = X4 )
                                                                                                                       => ( ( X1 @ X3 )
                                                                                                                          = ( X2 @ X4 ) ) )
                                                                                                                   => ( ( ~ ! [X3: $i] :
                                                                                                                              ( ( X1 @ X3 )
                                                                                                                             => ~ ! [X4: $i] :
                                                                                                                                    ( ( X1 @ X4 )
                                                                                                                                   => ( X3 = X4 ) ) ) )
                                                                                                                      = ( ~ ! [X3: $i] :
                                                                                                                              ( ( X2 @ X3 )
                                                                                                                             => ~ ! [X4: $i] :
                                                                                                                                    ( ( X2 @ X4 )
                                                                                                                                   => ( X3 = X4 ) ) ) ) ) )
                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                      ( ( X1 = X2 )
                                                                                                                     => ! [X3: $i,X4: $i] :
                                                                                                                          ( ( X3 = X4 )
                                                                                                                         => ( ( setadjoin @ X1 @ X3 )
                                                                                                                            = ( setadjoin @ X2 @ X4 ) ) ) )
                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                        ( ( X1 = X2 )
                                                                                                                       => ( ( powerset @ X1 )
                                                                                                                          = ( powerset @ X2 ) ) )
                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                          ( ( X1 = X2 )
                                                                                                                         => ( ( setunion @ X1 )
                                                                                                                            = ( setunion @ X2 ) ) )
                                                                                                                     => ( ! [X1: $i > $o] :
                                                                                                                            ( ~ ! [X2: $i] :
                                                                                                                                  ( ( X1 @ X2 )
                                                                                                                                 => ~ ! [X3: $i] :
                                                                                                                                        ( ( X1 @ X3 )
                                                                                                                                       => ( X2 = X3 ) ) )
                                                                                                                           => ! [X2: $i,X3: $i] :
                                                                                                                                ( ( X1 @ X2 )
                                                                                                                               => ( ( X1 @ X3 )
                                                                                                                                 => ( X2 = X3 ) ) ) )
                                                                                                                       => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                                                              ( ! [X3: $i,X4: $i] :
                                                                                                                                  ( ( X3 = X4 )
                                                                                                                                 => ( ( X1 @ X3 )
                                                                                                                                    = ( X2 @ X4 ) ) )
                                                                                                                             => ( ~ ! [X3: $i] :
                                                                                                                                      ( ( X1 @ X3 )
                                                                                                                                     => ~ ! [X4: $i] :
                                                                                                                                            ( ( X1 @ X4 )
                                                                                                                                           => ( X3 = X4 ) ) )
                                                                                                                               => ( ~ ! [X3: $i] :
                                                                                                                                        ( ( X2 @ X3 )
                                                                                                                                       => ~ ! [X4: $i] :
                                                                                                                                              ( ( X2 @ X4 )
                                                                                                                                             => ( X3 = X4 ) ) )
                                                                                                                                 => ( ( descr @ X1 )
                                                                                                                                    = ( descr @ X2 ) ) ) ) )
                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                ( ( X1 = X2 )
                                                                                                                               => ! [X3: $i > $o,X4: $i > $o] :
                                                                                                                                    ( ! [X5: $i] :
                                                                                                                                        ( ( in @ X5 @ X1 )
                                                                                                                                       => ! [X6: $i] :
                                                                                                                                            ( ( in @ X6 @ X2 )
                                                                                                                                           => ( ( X5 = X6 )
                                                                                                                                             => ( ( X3 @ X5 )
                                                                                                                                                = ( X4 @ X6 ) ) ) ) )
                                                                                                                                   => ( ( dsetconstr @ X1 @ X3 )
                                                                                                                                      = ( dsetconstr @ X2 @ X4 ) ) ) )
                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                  ( ! [X3: $i] :
                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                     => ( in @ X3 @ X2 ) )
                                                                                                                                 => ( subset @ X1 @ X2 ) )
                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                    ( ( X1 = X2 )
                                                                                                                                   => ( subset @ X2 @ X1 ) )
                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                      ( ( X1 = X2 )
                                                                                                                                     => ( subset @ X1 @ X2 ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                        ( ! [X3: $i] :
                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                           => ( in @ X3 @ X2 ) )
                                                                                                                                       => ( subset @ X1 @ X2 ) )
                                                                                                                                   => ( ! [X1: $i] : ( subset @ emptyset @ X1 )
                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                            ( ( subset @ X1 @ X2 )
                                                                                                                                           => ( ( in @ X3 @ X1 )
                                                                                                                                             => ( in @ X3 @ X2 ) ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                              ( ( subset @ X1 @ X2 )
                                                                                                                                             => ( ~ ( in @ X3 @ X2 )
                                                                                                                                               => ~ ( in @ X3 @ X1 ) ) )
                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                               => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                 => ~ ( subset @ X1 @ X2 ) ) )
                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                  ( ~ ( subset @ X1 @ X2 )
                                                                                                                                                 => ( X1 != X2 ) )
                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                   => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                     => ( X1 != X2 ) ) )
                                                                                                                                               => ( ! [X1: $i] : ( subset @ X1 @ X1 )
                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                        ( ( subset @ X1 @ X2 )
                                                                                                                                                       => ( ( subset @ X2 @ X3 )
                                                                                                                                                         => ( subset @ X1 @ X3 ) ) )
                                                                                                                                                   => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) )
                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                            ( ( subset @ X1 @ X3 )
                                                                                                                                                           => ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                              ( ( subset @ X1 @ X2 )
                                                                                                                                                             => ( in @ X1 @ ( powerset @ X2 ) ) )
                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                ( ( subset @ X1 @ X2 )
                                                                                                                                                               => ( ( subset @ X2 @ X1 )
                                                                                                                                                                 => ( X1 = X2 ) ) )
                                                                                                                                                           => ( ! [X1: $i] :
                                                                                                                                                                  ( ( subset @ X1 @ emptyset )
                                                                                                                                                                 => ( X1 = emptyset ) )
                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                    ( ( subset @ X2 @ X1 )
                                                                                                                                                                   => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                      ( ( in @ X2 @ ( powerset @ X1 ) )
                                                                                                                                                                     => ( subset @ X2 @ X1 ) )
                                                                                                                                                                 => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                          ( ( subset @ X1 @ X2 )
                                                                                                                                                                         => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
                                                                                                                                                                     => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                                                                                                                                                                       => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                               => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                                                                                           => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                    ( ( in @ X3 @ X2 )
                                                                                                                                                                                   => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                                                                                                                                                                      ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                                                     => ( ( ( in @ X3 @ X1 )
                                                                                                                                                                                         => X4 )
                                                                                                                                                                                       => ( ( ( in @ X3 @ X2 )
                                                                                                                                                                                           => X4 )
                                                                                                                                                                                         => X4 ) ) )
                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                        ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                                                       => ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                         => ( in @ X3 @ X2 ) ) )
                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                             => ( ( in @ X3 @ X2 )
                                                                                                                                                                                               => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                ( ( subset @ X3 @ X1 )
                                                                                                                                                                                               => ( ( subset @ X3 @ X2 )
                                                                                                                                                                                                 => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                  ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                                                                                 => ( in @ X3 @ X1 ) )
                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                      ( ( subset @ X1 @ X2 )
                                                                                                                                                                                                     => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                                        = X1 ) )
                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                        ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                                          = X2 )
                                                                                                                                                                                                       => ( subset @ X2 @ X1 ) )
                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                          ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                                                                                         => ( in @ X3 @ X2 ) )
                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                            ( ! [X3: $i] :
                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                               => ~ ( in @ X3 @ X2 ) )
                                                                                                                                                                                                           => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                                              = emptyset ) )
                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                ( ( subset @ X2 @ X1 )
                                                                                                                                                                                                               => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                                                  = X2 ) )
                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                  ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                                                    = X1 )
                                                                                                                                                                                                                 => ( subset @ X1 @ X2 ) )
                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                    ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                                                                                                                                                                                    = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                     => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                       => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                        ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                                       => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                          ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                                         => ~ ( in @ X3 @ X2 ) )
                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                            ( ( subset @ X1 @ X2 )
                                                                                                                                                                                                                           => ( ( setminus @ X1 @ X2 )
                                                                                                                                                                                                                              = emptyset ) )
                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                              ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                                             => ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                               => ( in @ X3 @ X2 ) ) )
                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                                               => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                                 => ~ ( in @ X3 @ X1 ) ) )
                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                  ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                                 => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                    ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                                   => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                        ( ( ( setminus @ X1 @ X2 )
                                                                                                                                                                                                                                          = emptyset )
                                                                                                                                                                                                                                       => ( subset @ X1 @ X2 ) )
                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                          ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                                                                                                                                                                         => ! [X4: $o] :
                                                                                                                                                                                                                                              ( ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                               => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                                                 => X4 ) )
                                                                                                                                                                                                                                             => ( ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                 => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                                                   => X4 ) )
                                                                                                                                                                                                                                               => X4 ) ) )
                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                           => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                                             => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                              ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                                             => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                                               => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                               => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                                                 => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                  ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                 => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                                                   => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                              ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                                             => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                                               => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                 => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                    ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                                                   => ( ( X3 != X1 )
                                                                                                                                                                                                                                                                     => ( X3 = X2 ) ) )
                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                         => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                           => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                             => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                               => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                 => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                   => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                  ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                 => ~ ! [X4: $i] :
                                                                                                                                                                                                                                                                                        ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                                       => ! [X5: $i] :
                                                                                                                                                                                                                                                                                            ( ( in @ X5 @ X2 )
                                                                                                                                                                                                                                                                                           => ( X3
                                                                                                                                                                                                                                                                                             != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                                                                                                                                                                             => ( sP5
                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                      ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                                                                                                                                                                                     => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                           => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                                                                                                                                                                                 => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                                                                                                                                                                                   => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                     => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                            ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                                                                                                                                                                            = X1 )
                                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                                                              ( ! [X3: $i] :
                                                                                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                      ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                                                     => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                                                                       => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                                                         => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                                                                                             => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                     => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                                                                                               => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                                      ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                     => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                       != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                                                                ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                                      ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                     => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                       != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                               => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                     => ~ ( X2 @ X3 ) ) )
                                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                 => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                                                                   => ( ! [X4: $i] :
                                                                                                                                                                                                                                                                                                          ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                                                         => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                                                           => ( X4 = X3 ) ) )
                                                                                                                                                                                                                                                                                                     => ~ ! [X4: $i] :
                                                                                                                                                                                                                                                                                                            ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                           => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                             != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                                                                    ( ! [X3: $i] :
                                                                                                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                            ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                                                           => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                                                                             => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                                                               => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                                                                                                   => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                           => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                                                                                                     => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                                            ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                           => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                             != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                      ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                                                                                                                                                                        = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                                                     => ( X1 = X2 ) )
                                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                        ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                       => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                                                   => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                                          ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                                                                         => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                                                ( ( in @ X2
                                                                                                                                                                                                                                                                                                                  @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                                    @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                                                                                                                                                                               => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                                    @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                                                                                                                 != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                                                                                     => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                                            ( ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                                                  ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                                                                                                 => ( X1
                                                                                                                                                                                                                                                                                                                   != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                           => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                              ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                              = X1 )
                                                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                               => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                  ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                                    = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                 => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                    ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                                      = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                                   => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                                      ( ( X1 = X2 )
                                                                                                                                                                                                                                                                                                                     => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                                                                        = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                                        ( ( X1 = X2 )
                                                                                                                                                                                                                                                                                                                       => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                                          = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                          ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                                            = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                         => ( ( X3 = X4 )
                                                                                                                                                                                                                                                                                                                           => ( X2 = X4 ) ) )
                                                                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                            ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                                                                              = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                                                                                                                                                                           => ( X1 = X2 ) )
                                                                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                              ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                                                = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                             => ( X2 = X4 ) )
                                                                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                                ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                                                  = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                                               => ( X2 = X4 ) )
                                                                                                                                                                                                                                                                                                                           => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                                                                  ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                                                                                                 => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                                                                        ( ( in @ X2
                                                                                                                                                                                                                                                                                                                                          @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                                                            @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                                                                                                ( X1
                                                                                                                                                                                                                                                                                                                                                = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                                                                                                                                                                       => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                                                            @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                                                                                                ( X1
                                                                                                                                                                                                                                                                                                                                                = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                                                                                                                                                                         != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                                                    ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                                    = X2 )
                                                                                                                                                                                                                                                                                                                               => ( sP8
                                                                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                                        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                                       => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                                          ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                                         => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                                            ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                                           => ( in @ X4 @ X2 ) )
                                                                                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                                                                                 => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                                                                    = X3 ) ) )
                                                                                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                                                                                   => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                                                                      = X4 ) ) )
                                                                                                                                                                                                                                                                                                                                           => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                                                ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                                               => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                                                                                                                                                                                  = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h11,assumption,
    in @ emptyset @ omega,
    introduced(assumption,[]) ).

thf(h12,assumption,
    ~ ( ! [X1: $i] :
          ( ( in @ X1 @ omega )
         => ( in @ ( setadjoin @ X1 @ X1 ) @ omega ) )
     => ( ! [X1: $i] :
            ( ~ ( ( in @ emptyset @ X1 )
               => ~ ! [X2: $i] :
                      ( ~ ( ( in @ X2 @ omega )
                         => ~ ( in @ X2 @ X1 ) )
                     => ( in @ ( setadjoin @ X2 @ X2 ) @ X1 ) ) )
           => ! [X2: $i] :
                ( ( in @ X2 @ omega )
               => ( in @ X2 @ X1 ) ) )
       => ( ! [X1: $i > $i > $o,X2: $i] :
              ( ! [X3: $i] :
                  ( ( in @ X3 @ X2 )
                 => ~ ! [X4: $i] :
                        ( ( X1 @ X3 @ X4 )
                       => ~ ! [X5: $i] :
                              ( ( X1 @ X3 @ X5 )
                             => ( X4 = X5 ) ) ) )
             => ~ ! [X3: $i] :
                    ~ ! [X4: $i] :
                        ( ( in @ X4 @ X3 )
                        = ( ~ ! [X5: $i] :
                                ( ( in @ X5 @ X2 )
                               => ~ ( X1 @ X5 @ X4 ) ) ) ) )
         => ( ! [X1: $i] :
                ( ~ ! [X2: $i] :
                      ~ ( in @ X2 @ X1 )
               => ~ ! [X2: $i] :
                      ( ( in @ X2 @ X1 )
                     => ~ ! [X3: $i] :
                            ( ( in @ X3 @ X2 )
                           => ~ ( in @ X3 @ X1 ) ) ) )
           => ( ! [X1: $i] :
                  ~ ! [X2: $i] :
                      ( ~ ( ~ ( ! [X3: $i] :
                                  ( ( in @ X3 @ X2 )
                                 => ! [X4: $i] :
                                      ( ( in @ X4 @ X3 )
                                     => ( in @ X4 @ X1 ) ) )
                             => ~ ! [X3: $i,X4: $i] :
                                    ( ~ ( ( in @ X3 @ X1 )
                                       => ~ ( in @ X4 @ X1 ) )
                                   => ( ! [X5: $i] :
                                          ( ( in @ X5 @ X2 )
                                         => ( ( in @ X3 @ X5 )
                                            = ( in @ X4 @ X5 ) ) )
                                     => ( X3 = X4 ) ) ) )
                         => ~ ! [X3: $i,X4: $i] :
                                ( ~ ( ( in @ X3 @ X2 )
                                   => ~ ( in @ X4 @ X2 ) )
                               => ( ~ ! [X5: $i] :
                                        ( ( in @ X5 @ X3 )
                                       => ( in @ X5 @ X4 ) )
                                 => ! [X5: $i] :
                                      ( ( in @ X5 @ X4 )
                                     => ( in @ X5 @ X3 ) ) ) ) )
                     => ~ ! [X3: $i] :
                            ( ~ ( ! [X4: $i] :
                                    ( ( in @ X4 @ X3 )
                                   => ( in @ X4 @ X1 ) )
                               => ! [X4: $i] :
                                    ~ ( in @ X4 @ X3 ) )
                           => ~ ! [X4: $i,X5: $i] :
                                  ( ~ ( ~ ( ( in @ X4 @ X2 )
                                         => ~ ( in @ X5 @ X3 ) )
                                     => ~ ! [X6: $i] :
                                            ( ( in @ X6 @ X4 )
                                           => ~ ( in @ X6 @ X3 ) ) )
                                 => ~ ! [X6: $i] :
                                        ( ( in @ X6 @ X2 )
                                       => ( ~ ! [X7: $i] :
                                                ( ( in @ X7 @ X6 )
                                               => ( in @ X7 @ X4 ) )
                                         => ( in @ X5 @ X6 ) ) ) ) ) )
             => ( ! [X1: $i > $o] :
                    ( ~ ! [X2: $i] :
                          ( ( X1 @ X2 )
                         => ~ ! [X3: $i] :
                                ( ( X1 @ X3 )
                               => ( X2 = X3 ) ) )
                   => ( X1 @ ( descr @ X1 ) ) )
               => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                      ( ( in @ X3 @ X1 )
                     => ( ( X2 @ X3 )
                       => ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) ) ) )
                 => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                        ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                       => ( in @ X3 @ X1 ) )
                   => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                          ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                         => ( X2 @ X3 ) )
                     => ( ! [X1: $o,X2: $i] :
                            ( ( in @ X2 @ ( prop2set @ X1 ) )
                           => X1 )
                       => ( ! [X1: $i] :
                              ( ( in @ X1 @ emptyset )
                             => ! [X2: $o] : X2 )
                         => ( ! [X1: $i] :
                                ~ ( in @ X1 @ emptyset )
                           => ( ! [X1: $i] :
                                  ~ ( in @ X1 @ emptyset )
                             => ( ! [X1: $i > $o] :
                                    ( ~ ! [X2: $i] :
                                          ( ( X1 @ X2 )
                                         => ~ ! [X3: $i] :
                                                ( ( X1 @ X3 )
                                               => ( X2 = X3 ) ) )
                                   => ~ ! [X2: $i] :
                                          ~ ( X1 @ X2 ) )
                               => ( ! [X1: $i,X2: $i] :
                                      ( ! [X3: $i] :
                                          ( ( in @ X3 @ X1 )
                                         => ( in @ X3 @ X2 ) )
                                     => ( ! [X3: $i] :
                                            ( ( in @ X3 @ X2 )
                                           => ( in @ X3 @ X1 ) )
                                       => ( X1 = X2 ) ) )
                                 => ( ! [X1: $i] :
                                        ( ! [X2: $i] :
                                            ~ ( in @ X2 @ X1 )
                                       => ( X1 = emptyset ) )
                                   => ( ! [X1: $i] :
                                          ( ! [X2: $i] :
                                              ~ ( in @ X2 @ X1 )
                                         => ( X1 = emptyset ) )
                                     => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                            ( ( in @ X3 @ X1 )
                                           => ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                              = ( X2 @ X3 ) ) )
                                       => ( ! [X1: $i] :
                                              ( ( X1 != emptyset )
                                             => ~ ! [X2: $i] :
                                                    ~ ( in @ X2 @ X1 ) )
                                         => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                ( ( in @ X3 @ X1 )
                                               => ( ( X2 @ X3 )
                                                 => ( ( dsetconstr @ X1 @ X2 )
                                                   != emptyset ) ) )
                                           => ( ! [X1: $i] :
                                                  ( ~ ! [X2: $i] :
                                                        ~ ( in @ X2 @ X1 )
                                                 => ( X1 != emptyset ) )
                                             => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) )
                                               => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                        ( ( in @ X3 @ X2 )
                                                       => ( in @ X3 @ ( setadjoin @ X1 @ X2 ) ) )
                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                          ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                                         => ! [X4: $o] :
                                                              ( ( ( X3 = X1 )
                                                               => X4 )
                                                             => ( ( ( in @ X3 @ X2 )
                                                                 => X4 )
                                                               => X4 ) ) )
                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                            ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                                           => ( ( X3 != X1 )
                                                             => ( in @ X3 @ X2 ) ) )
                                                       => ( ! [X1: $i] :
                                                              ( ( dsetconstr @ X1
                                                                @ ^ [X2: $i] : ~ $false )
                                                              = X1 )
                                                         => ( ! [X1: $i,X2: $i] :
                                                                ( ! [X3: $i] :
                                                                    ( ( in @ X3 @ X2 )
                                                                   => ( in @ X3 @ X1 ) )
                                                               => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                           => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                                             => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                      ( ( in @ X2 @ ( powerset @ X1 ) )
                                                                     => ( ( in @ X3 @ X2 )
                                                                       => ( in @ X3 @ X1 ) ) )
                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                        ( ( in @ X2 @ X3 )
                                                                       => ( ( in @ X3 @ X1 )
                                                                         => ( in @ X2 @ ( setunion @ X1 ) ) ) )
                                                                   => ( ! [X1: $i,X2: $i] :
                                                                          ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                         => ! [X3: $o] :
                                                                              ( ! [X4: $i] :
                                                                                  ( ( in @ X2 @ X4 )
                                                                                 => ( ( in @ X4 @ X1 )
                                                                                   => X3 ) )
                                                                             => X3 ) )
                                                                     => ( ! [X1: $i,X2: $i] :
                                                                            ( ( in @ X2 @ X1 )
                                                                           => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
                                                                       => ( ! [X1: $i > $o] :
                                                                              ( ~ ! [X2: $i] :
                                                                                    ( ( X1 @ X2 )
                                                                                   => ~ ! [X3: $i] :
                                                                                          ( ( X1 @ X3 )
                                                                                         => ( X2 = X3 ) ) )
                                                                             => ~ ! [X2: $i] :
                                                                                    ~ ! [X3: $i] :
                                                                                        ( ( X1 @ X3 )
                                                                                        = ( X3 = X2 ) ) )
                                                                         => ( ! [X1: $i] :
                                                                                ( ( X1 != emptyset )
                                                                               => ~ ! [X2: $i] :
                                                                                      ~ ( in @ X2 @ X1 ) )
                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                  ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                 => ( X1 = X2 ) )
                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                    ( ( X1 != X2 )
                                                                                   => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                      ( ( X1 = X2 )
                                                                                     => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                        ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                       => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                          ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                         => ( ( X3 != X1 )
                                                                                           => ( X3 = X2 ) ) )
                                                                                     => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                       => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                         => ( ! [X1: $i,X2: $i > $o] :
                                                                                                ( ~ ! [X3: $i] :
                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                     => ~ ( X2 @ X3 ) )
                                                                                               => ( ( dsetconstr @ X1 @ X2 )
                                                                                                 != emptyset ) )
                                                                                           => ( ! [X1: $i > $o,X2: $i] :
                                                                                                  ( ( in @ X2 @ emptyset )
                                                                                                 => ( X1 @ X2 ) )
                                                                                             => ( ! [X1: $o] :
                                                                                                    ( X1
                                                                                                   => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                                                                               => ( ! [X1: $o] :
                                                                                                      ( X1
                                                                                                     => ( set2prop @ ( prop2set @ X1 ) ) )
                                                                                                 => ( ! [X1: $i > $o] :
                                                                                                        ( ~ ! [X2: $i] :
                                                                                                              ~ ( X1 @ X2 )
                                                                                                       => ( ! [X2: $i,X3: $i] :
                                                                                                              ( ( X1 @ X2 )
                                                                                                             => ( ( X1 @ X3 )
                                                                                                               => ( X2 = X3 ) ) )
                                                                                                         => ~ ! [X2: $i] :
                                                                                                                ( ( X1 @ X2 )
                                                                                                               => ~ ! [X3: $i] :
                                                                                                                      ( ( X1 @ X3 )
                                                                                                                     => ( X2 = X3 ) ) ) ) )
                                                                                                   => ( ! [X1: $i > $o] :
                                                                                                          ( ~ ! [X2: $i] :
                                                                                                                ~ ! [X3: $i] :
                                                                                                                    ( ( X1 @ X3 )
                                                                                                                    = ( X3 = X2 ) )
                                                                                                         => ~ ! [X2: $i] :
                                                                                                                ( ( X1 @ X2 )
                                                                                                               => ~ ! [X3: $i] :
                                                                                                                      ( ( X1 @ X3 )
                                                                                                                     => ( X2 = X3 ) ) ) )
                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                            ( ( X1 = X2 )
                                                                                                           => ! [X3: $i,X4: $i] :
                                                                                                                ( ( X3 = X4 )
                                                                                                               => ( ( in @ X3 @ X1 )
                                                                                                                 => ( in @ X4 @ X2 ) ) ) )
                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                              ( ( X1 = X2 )
                                                                                                             => ! [X3: $i,X4: $i] :
                                                                                                                  ( ( X3 = X4 )
                                                                                                                 => ( ( in @ X3 @ X1 )
                                                                                                                    = ( in @ X4 @ X2 ) ) ) )
                                                                                                         => ( ! [X1: $i > $o] :
                                                                                                                ( ~ ! [X2: $i] :
                                                                                                                      ( ( X1 @ X2 )
                                                                                                                     => ~ ! [X3: $i] :
                                                                                                                            ( ( X1 @ X3 )
                                                                                                                           => ( X2 = X3 ) ) )
                                                                                                               => ! [X2: $i,X3: $i] :
                                                                                                                    ( ( X1 @ X2 )
                                                                                                                   => ( ( X1 @ X3 )
                                                                                                                     => ( X2 = X3 ) ) ) )
                                                                                                           => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                                                  ( ! [X3: $i,X4: $i] :
                                                                                                                      ( ( X3 = X4 )
                                                                                                                     => ( ( X1 @ X3 )
                                                                                                                        = ( X2 @ X4 ) ) )
                                                                                                                 => ( ( ~ ! [X3: $i] :
                                                                                                                            ( ( X1 @ X3 )
                                                                                                                           => ~ ! [X4: $i] :
                                                                                                                                  ( ( X1 @ X4 )
                                                                                                                                 => ( X3 = X4 ) ) ) )
                                                                                                                    = ( ~ ! [X3: $i] :
                                                                                                                            ( ( X2 @ X3 )
                                                                                                                           => ~ ! [X4: $i] :
                                                                                                                                  ( ( X2 @ X4 )
                                                                                                                                 => ( X3 = X4 ) ) ) ) ) )
                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                    ( ( X1 = X2 )
                                                                                                                   => ! [X3: $i,X4: $i] :
                                                                                                                        ( ( X3 = X4 )
                                                                                                                       => ( ( setadjoin @ X1 @ X3 )
                                                                                                                          = ( setadjoin @ X2 @ X4 ) ) ) )
                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                      ( ( X1 = X2 )
                                                                                                                     => ( ( powerset @ X1 )
                                                                                                                        = ( powerset @ X2 ) ) )
                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                        ( ( X1 = X2 )
                                                                                                                       => ( ( setunion @ X1 )
                                                                                                                          = ( setunion @ X2 ) ) )
                                                                                                                   => ( ! [X1: $i > $o] :
                                                                                                                          ( ~ ! [X2: $i] :
                                                                                                                                ( ( X1 @ X2 )
                                                                                                                               => ~ ! [X3: $i] :
                                                                                                                                      ( ( X1 @ X3 )
                                                                                                                                     => ( X2 = X3 ) ) )
                                                                                                                         => ! [X2: $i,X3: $i] :
                                                                                                                              ( ( X1 @ X2 )
                                                                                                                             => ( ( X1 @ X3 )
                                                                                                                               => ( X2 = X3 ) ) ) )
                                                                                                                     => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                                                            ( ! [X3: $i,X4: $i] :
                                                                                                                                ( ( X3 = X4 )
                                                                                                                               => ( ( X1 @ X3 )
                                                                                                                                  = ( X2 @ X4 ) ) )
                                                                                                                           => ( ~ ! [X3: $i] :
                                                                                                                                    ( ( X1 @ X3 )
                                                                                                                                   => ~ ! [X4: $i] :
                                                                                                                                          ( ( X1 @ X4 )
                                                                                                                                         => ( X3 = X4 ) ) )
                                                                                                                             => ( ~ ! [X3: $i] :
                                                                                                                                      ( ( X2 @ X3 )
                                                                                                                                     => ~ ! [X4: $i] :
                                                                                                                                            ( ( X2 @ X4 )
                                                                                                                                           => ( X3 = X4 ) ) )
                                                                                                                               => ( ( descr @ X1 )
                                                                                                                                  = ( descr @ X2 ) ) ) ) )
                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                              ( ( X1 = X2 )
                                                                                                                             => ! [X3: $i > $o,X4: $i > $o] :
                                                                                                                                  ( ! [X5: $i] :
                                                                                                                                      ( ( in @ X5 @ X1 )
                                                                                                                                     => ! [X6: $i] :
                                                                                                                                          ( ( in @ X6 @ X2 )
                                                                                                                                         => ( ( X5 = X6 )
                                                                                                                                           => ( ( X3 @ X5 )
                                                                                                                                              = ( X4 @ X6 ) ) ) ) )
                                                                                                                                 => ( ( dsetconstr @ X1 @ X3 )
                                                                                                                                    = ( dsetconstr @ X2 @ X4 ) ) ) )
                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                ( ! [X3: $i] :
                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                   => ( in @ X3 @ X2 ) )
                                                                                                                               => ( subset @ X1 @ X2 ) )
                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                  ( ( X1 = X2 )
                                                                                                                                 => ( subset @ X2 @ X1 ) )
                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                    ( ( X1 = X2 )
                                                                                                                                   => ( subset @ X1 @ X2 ) )
                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                      ( ! [X3: $i] :
                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                         => ( in @ X3 @ X2 ) )
                                                                                                                                     => ( subset @ X1 @ X2 ) )
                                                                                                                                 => ( ! [X1: $i] : ( subset @ emptyset @ X1 )
                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                          ( ( subset @ X1 @ X2 )
                                                                                                                                         => ( ( in @ X3 @ X1 )
                                                                                                                                           => ( in @ X3 @ X2 ) ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                            ( ( subset @ X1 @ X2 )
                                                                                                                                           => ( ~ ( in @ X3 @ X2 )
                                                                                                                                             => ~ ( in @ X3 @ X1 ) ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                             => ( ~ ( in @ X3 @ X2 )
                                                                                                                                               => ~ ( subset @ X1 @ X2 ) ) )
                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                ( ~ ( subset @ X1 @ X2 )
                                                                                                                                               => ( X1 != X2 ) )
                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                 => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                   => ( X1 != X2 ) ) )
                                                                                                                                             => ( ! [X1: $i] : ( subset @ X1 @ X1 )
                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                      ( ( subset @ X1 @ X2 )
                                                                                                                                                     => ( ( subset @ X2 @ X3 )
                                                                                                                                                       => ( subset @ X1 @ X3 ) ) )
                                                                                                                                                 => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) )
                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                          ( ( subset @ X1 @ X3 )
                                                                                                                                                         => ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                            ( ( subset @ X1 @ X2 )
                                                                                                                                                           => ( in @ X1 @ ( powerset @ X2 ) ) )
                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                              ( ( subset @ X1 @ X2 )
                                                                                                                                                             => ( ( subset @ X2 @ X1 )
                                                                                                                                                               => ( X1 = X2 ) ) )
                                                                                                                                                         => ( ! [X1: $i] :
                                                                                                                                                                ( ( subset @ X1 @ emptyset )
                                                                                                                                                               => ( X1 = emptyset ) )
                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                  ( ( subset @ X2 @ X1 )
                                                                                                                                                                 => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                    ( ( in @ X2 @ ( powerset @ X1 ) )
                                                                                                                                                                   => ( subset @ X2 @ X1 ) )
                                                                                                                                                               => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                        ( ( subset @ X1 @ X2 )
                                                                                                                                                                       => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
                                                                                                                                                                   => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                                                                                                                                                                     => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                             => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                                                                                         => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                  ( ( in @ X3 @ X2 )
                                                                                                                                                                                 => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                                                                                                                                                                    ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                                                   => ( ( ( in @ X3 @ X1 )
                                                                                                                                                                                       => X4 )
                                                                                                                                                                                     => ( ( ( in @ X3 @ X2 )
                                                                                                                                                                                         => X4 )
                                                                                                                                                                                       => X4 ) ) )
                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                      ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                                                     => ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                       => ( in @ X3 @ X2 ) ) )
                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                           => ( ( in @ X3 @ X2 )
                                                                                                                                                                                             => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                              ( ( subset @ X3 @ X1 )
                                                                                                                                                                                             => ( ( subset @ X3 @ X2 )
                                                                                                                                                                                               => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                                                                               => ( in @ X3 @ X1 ) )
                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                    ( ( subset @ X1 @ X2 )
                                                                                                                                                                                                   => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                                      = X1 ) )
                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                      ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                                        = X2 )
                                                                                                                                                                                                     => ( subset @ X2 @ X1 ) )
                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                        ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                                                                                       => ( in @ X3 @ X2 ) )
                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                          ( ! [X3: $i] :
                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                             => ~ ( in @ X3 @ X2 ) )
                                                                                                                                                                                                         => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                                            = emptyset ) )
                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                              ( ( subset @ X2 @ X1 )
                                                                                                                                                                                                             => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                                                = X2 ) )
                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                                                  = X1 )
                                                                                                                                                                                                               => ( subset @ X1 @ X2 ) )
                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                  ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                                                                                                                                                                                  = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                   => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                     => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                      ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                                     => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                        ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                                       => ~ ( in @ X3 @ X2 ) )
                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                          ( ( subset @ X1 @ X2 )
                                                                                                                                                                                                                         => ( ( setminus @ X1 @ X2 )
                                                                                                                                                                                                                            = emptyset ) )
                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                            ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                                           => ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                             => ( in @ X3 @ X2 ) ) )
                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                              ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                                             => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                               => ~ ( in @ X3 @ X1 ) ) )
                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                               => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                  ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                                 => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                      ( ( ( setminus @ X1 @ X2 )
                                                                                                                                                                                                                                        = emptyset )
                                                                                                                                                                                                                                     => ( subset @ X1 @ X2 ) )
                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                        ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                                                                                                                                                                       => ! [X4: $o] :
                                                                                                                                                                                                                                            ( ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                             => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                                               => X4 ) )
                                                                                                                                                                                                                                           => ( ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                                               => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                                                 => X4 ) )
                                                                                                                                                                                                                                             => X4 ) ) )
                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                         => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                                           => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                            ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                                           => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                                             => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                             => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                                               => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                                               => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                                                 => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                            ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                                           => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                              ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                                             => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                               => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                  ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                                                 => ( ( X3 != X1 )
                                                                                                                                                                                                                                                                   => ( X3 = X2 ) ) )
                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                       => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                         => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                           => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                             => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                               => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                 => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                               => ~ ! [X4: $i] :
                                                                                                                                                                                                                                                                                      ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                                     => ! [X5: $i] :
                                                                                                                                                                                                                                                                                          ( ( in @ X5 @ X2 )
                                                                                                                                                                                                                                                                                         => ( X3
                                                                                                                                                                                                                                                                                           != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                                                                                                                                                                           => ( sP5
                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                    ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                                                                                                                                                                                   => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                         => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                                                                                                                                                                               => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                                                                                                                                                                                 => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                   => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                          ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                                                                                                                                                                          = X1 )
                                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                                                            ( ! [X3: $i] :
                                                                                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                    ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                                                   => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                                                                     => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                                                       => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                                                                                           => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                   => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                                                                                             => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                                    ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                   => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                     != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                                                              ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                                    ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                   => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                     != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                             => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                   => ~ ( X2 @ X3 ) ) )
                                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                               => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                                                                 => ( ! [X4: $i] :
                                                                                                                                                                                                                                                                                                        ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                                                       => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                                                         => ( X4 = X3 ) ) )
                                                                                                                                                                                                                                                                                                   => ~ ! [X4: $i] :
                                                                                                                                                                                                                                                                                                          ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                         => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                           != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                                                                  ( ! [X3: $i] :
                                                                                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                          ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                                                         => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                                                                           => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                                                             => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                                                                                                 => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                         => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                                                                                                   => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                                          ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                         => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                           != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                    ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                                                                                                                                                                      = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                                                   => ( X1 = X2 ) )
                                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                      ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                     => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                                                 => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                                        ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                                                                       => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                                              ( ( in @ X2
                                                                                                                                                                                                                                                                                                                @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                                  @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                                                                                                                                                                             => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                                  @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                                                                                                               != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                                                                                   => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                                          ( ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                                                ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                                                                                               => ( X1
                                                                                                                                                                                                                                                                                                                 != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                         => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                            ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                            = X1 )
                                                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                              ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                             => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                                  = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                               => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                  ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                                    = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                                 => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                                    ( ( X1 = X2 )
                                                                                                                                                                                                                                                                                                                   => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                                                                      = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                                      ( ( X1 = X2 )
                                                                                                                                                                                                                                                                                                                     => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                                        = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                        ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                                          = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                       => ( ( X3 = X4 )
                                                                                                                                                                                                                                                                                                                         => ( X2 = X4 ) ) )
                                                                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                          ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                                                                            = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                                                                                                                                                                         => ( X1 = X2 ) )
                                                                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                            ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                                              = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                           => ( X2 = X4 ) )
                                                                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                              ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                                                = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                                             => ( X2 = X4 ) )
                                                                                                                                                                                                                                                                                                                         => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                                                                ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                                                                                               => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                                                                      ( ( in @ X2
                                                                                                                                                                                                                                                                                                                                        @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                                                          @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                                                                                              ( X1
                                                                                                                                                                                                                                                                                                                                              = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                                                                                                                                                                     => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                                                          @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                                                                                              ( X1
                                                                                                                                                                                                                                                                                                                                              = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                                                                                                                                                                       != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                                                  ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                                  = X2 )
                                                                                                                                                                                                                                                                                                                             => ( sP8
                                                                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                                      ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                                     => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                                        ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                                       => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                                          ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                                         => ( in @ X4 @ X2 ) )
                                                                                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                                                                               => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                                                                  = X3 ) ) )
                                                                                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                                                                                 => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                                                                    = X4 ) ) )
                                                                                                                                                                                                                                                                                                                                         => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                                              ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                                             => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                                                                                                                                                                                = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h13,assumption,
    ! [X1: $i] :
      ( ( in @ X1 @ omega )
     => ( in @ ( setadjoin @ X1 @ X1 ) @ omega ) ),
    introduced(assumption,[]) ).

thf(h14,assumption,
    ~ ( ! [X1: $i] :
          ( ~ ( ( in @ emptyset @ X1 )
             => ~ ! [X2: $i] :
                    ( ~ ( ( in @ X2 @ omega )
                       => ~ ( in @ X2 @ X1 ) )
                   => ( in @ ( setadjoin @ X2 @ X2 ) @ X1 ) ) )
         => ! [X2: $i] :
              ( ( in @ X2 @ omega )
             => ( in @ X2 @ X1 ) ) )
     => ( ! [X1: $i > $i > $o,X2: $i] :
            ( ! [X3: $i] :
                ( ( in @ X3 @ X2 )
               => ~ ! [X4: $i] :
                      ( ( X1 @ X3 @ X4 )
                     => ~ ! [X5: $i] :
                            ( ( X1 @ X3 @ X5 )
                           => ( X4 = X5 ) ) ) )
           => ~ ! [X3: $i] :
                  ~ ! [X4: $i] :
                      ( ( in @ X4 @ X3 )
                      = ( ~ ! [X5: $i] :
                              ( ( in @ X5 @ X2 )
                             => ~ ( X1 @ X5 @ X4 ) ) ) ) )
       => ( ! [X1: $i] :
              ( ~ ! [X2: $i] :
                    ~ ( in @ X2 @ X1 )
             => ~ ! [X2: $i] :
                    ( ( in @ X2 @ X1 )
                   => ~ ! [X3: $i] :
                          ( ( in @ X3 @ X2 )
                         => ~ ( in @ X3 @ X1 ) ) ) )
         => ( ! [X1: $i] :
                ~ ! [X2: $i] :
                    ( ~ ( ~ ( ! [X3: $i] :
                                ( ( in @ X3 @ X2 )
                               => ! [X4: $i] :
                                    ( ( in @ X4 @ X3 )
                                   => ( in @ X4 @ X1 ) ) )
                           => ~ ! [X3: $i,X4: $i] :
                                  ( ~ ( ( in @ X3 @ X1 )
                                     => ~ ( in @ X4 @ X1 ) )
                                 => ( ! [X5: $i] :
                                        ( ( in @ X5 @ X2 )
                                       => ( ( in @ X3 @ X5 )
                                          = ( in @ X4 @ X5 ) ) )
                                   => ( X3 = X4 ) ) ) )
                       => ~ ! [X3: $i,X4: $i] :
                              ( ~ ( ( in @ X3 @ X2 )
                                 => ~ ( in @ X4 @ X2 ) )
                             => ( ~ ! [X5: $i] :
                                      ( ( in @ X5 @ X3 )
                                     => ( in @ X5 @ X4 ) )
                               => ! [X5: $i] :
                                    ( ( in @ X5 @ X4 )
                                   => ( in @ X5 @ X3 ) ) ) ) )
                   => ~ ! [X3: $i] :
                          ( ~ ( ! [X4: $i] :
                                  ( ( in @ X4 @ X3 )
                                 => ( in @ X4 @ X1 ) )
                             => ! [X4: $i] :
                                  ~ ( in @ X4 @ X3 ) )
                         => ~ ! [X4: $i,X5: $i] :
                                ( ~ ( ~ ( ( in @ X4 @ X2 )
                                       => ~ ( in @ X5 @ X3 ) )
                                   => ~ ! [X6: $i] :
                                          ( ( in @ X6 @ X4 )
                                         => ~ ( in @ X6 @ X3 ) ) )
                               => ~ ! [X6: $i] :
                                      ( ( in @ X6 @ X2 )
                                     => ( ~ ! [X7: $i] :
                                              ( ( in @ X7 @ X6 )
                                             => ( in @ X7 @ X4 ) )
                                       => ( in @ X5 @ X6 ) ) ) ) ) )
           => ( ! [X1: $i > $o] :
                  ( ~ ! [X2: $i] :
                        ( ( X1 @ X2 )
                       => ~ ! [X3: $i] :
                              ( ( X1 @ X3 )
                             => ( X2 = X3 ) ) )
                 => ( X1 @ ( descr @ X1 ) ) )
             => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                    ( ( in @ X3 @ X1 )
                   => ( ( X2 @ X3 )
                     => ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) ) ) )
               => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                      ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                     => ( in @ X3 @ X1 ) )
                 => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                        ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                       => ( X2 @ X3 ) )
                   => ( ! [X1: $o,X2: $i] :
                          ( ( in @ X2 @ ( prop2set @ X1 ) )
                         => X1 )
                     => ( ! [X1: $i] :
                            ( ( in @ X1 @ emptyset )
                           => ! [X2: $o] : X2 )
                       => ( ! [X1: $i] :
                              ~ ( in @ X1 @ emptyset )
                         => ( ! [X1: $i] :
                                ~ ( in @ X1 @ emptyset )
                           => ( ! [X1: $i > $o] :
                                  ( ~ ! [X2: $i] :
                                        ( ( X1 @ X2 )
                                       => ~ ! [X3: $i] :
                                              ( ( X1 @ X3 )
                                             => ( X2 = X3 ) ) )
                                 => ~ ! [X2: $i] :
                                        ~ ( X1 @ X2 ) )
                             => ( ! [X1: $i,X2: $i] :
                                    ( ! [X3: $i] :
                                        ( ( in @ X3 @ X1 )
                                       => ( in @ X3 @ X2 ) )
                                   => ( ! [X3: $i] :
                                          ( ( in @ X3 @ X2 )
                                         => ( in @ X3 @ X1 ) )
                                     => ( X1 = X2 ) ) )
                               => ( ! [X1: $i] :
                                      ( ! [X2: $i] :
                                          ~ ( in @ X2 @ X1 )
                                     => ( X1 = emptyset ) )
                                 => ( ! [X1: $i] :
                                        ( ! [X2: $i] :
                                            ~ ( in @ X2 @ X1 )
                                       => ( X1 = emptyset ) )
                                   => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                          ( ( in @ X3 @ X1 )
                                         => ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                            = ( X2 @ X3 ) ) )
                                     => ( ! [X1: $i] :
                                            ( ( X1 != emptyset )
                                           => ~ ! [X2: $i] :
                                                  ~ ( in @ X2 @ X1 ) )
                                       => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                              ( ( in @ X3 @ X1 )
                                             => ( ( X2 @ X3 )
                                               => ( ( dsetconstr @ X1 @ X2 )
                                                 != emptyset ) ) )
                                         => ( ! [X1: $i] :
                                                ( ~ ! [X2: $i] :
                                                      ~ ( in @ X2 @ X1 )
                                               => ( X1 != emptyset ) )
                                           => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) )
                                             => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                      ( ( in @ X3 @ X2 )
                                                     => ( in @ X3 @ ( setadjoin @ X1 @ X2 ) ) )
                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                        ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                                       => ! [X4: $o] :
                                                            ( ( ( X3 = X1 )
                                                             => X4 )
                                                           => ( ( ( in @ X3 @ X2 )
                                                               => X4 )
                                                             => X4 ) ) )
                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                          ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                                         => ( ( X3 != X1 )
                                                           => ( in @ X3 @ X2 ) ) )
                                                     => ( ! [X1: $i] :
                                                            ( ( dsetconstr @ X1
                                                              @ ^ [X2: $i] : ~ $false )
                                                            = X1 )
                                                       => ( ! [X1: $i,X2: $i] :
                                                              ( ! [X3: $i] :
                                                                  ( ( in @ X3 @ X2 )
                                                                 => ( in @ X3 @ X1 ) )
                                                             => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                         => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                                           => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                    ( ( in @ X2 @ ( powerset @ X1 ) )
                                                                   => ( ( in @ X3 @ X2 )
                                                                     => ( in @ X3 @ X1 ) ) )
                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                      ( ( in @ X2 @ X3 )
                                                                     => ( ( in @ X3 @ X1 )
                                                                       => ( in @ X2 @ ( setunion @ X1 ) ) ) )
                                                                 => ( ! [X1: $i,X2: $i] :
                                                                        ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                       => ! [X3: $o] :
                                                                            ( ! [X4: $i] :
                                                                                ( ( in @ X2 @ X4 )
                                                                               => ( ( in @ X4 @ X1 )
                                                                                 => X3 ) )
                                                                           => X3 ) )
                                                                   => ( ! [X1: $i,X2: $i] :
                                                                          ( ( in @ X2 @ X1 )
                                                                         => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
                                                                     => ( ! [X1: $i > $o] :
                                                                            ( ~ ! [X2: $i] :
                                                                                  ( ( X1 @ X2 )
                                                                                 => ~ ! [X3: $i] :
                                                                                        ( ( X1 @ X3 )
                                                                                       => ( X2 = X3 ) ) )
                                                                           => ~ ! [X2: $i] :
                                                                                  ~ ! [X3: $i] :
                                                                                      ( ( X1 @ X3 )
                                                                                      = ( X3 = X2 ) ) )
                                                                       => ( ! [X1: $i] :
                                                                              ( ( X1 != emptyset )
                                                                             => ~ ! [X2: $i] :
                                                                                    ~ ( in @ X2 @ X1 ) )
                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                               => ( X1 = X2 ) )
                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                  ( ( X1 != X2 )
                                                                                 => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                    ( ( X1 = X2 )
                                                                                   => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                      ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                     => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                        ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                       => ( ( X3 != X1 )
                                                                                         => ( X3 = X2 ) ) )
                                                                                   => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                     => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                       => ( ! [X1: $i,X2: $i > $o] :
                                                                                              ( ~ ! [X3: $i] :
                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                   => ~ ( X2 @ X3 ) )
                                                                                             => ( ( dsetconstr @ X1 @ X2 )
                                                                                               != emptyset ) )
                                                                                         => ( ! [X1: $i > $o,X2: $i] :
                                                                                                ( ( in @ X2 @ emptyset )
                                                                                               => ( X1 @ X2 ) )
                                                                                           => ( ! [X1: $o] :
                                                                                                  ( X1
                                                                                                 => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                                                                             => ( ! [X1: $o] :
                                                                                                    ( X1
                                                                                                   => ( set2prop @ ( prop2set @ X1 ) ) )
                                                                                               => ( ! [X1: $i > $o] :
                                                                                                      ( ~ ! [X2: $i] :
                                                                                                            ~ ( X1 @ X2 )
                                                                                                     => ( ! [X2: $i,X3: $i] :
                                                                                                            ( ( X1 @ X2 )
                                                                                                           => ( ( X1 @ X3 )
                                                                                                             => ( X2 = X3 ) ) )
                                                                                                       => ~ ! [X2: $i] :
                                                                                                              ( ( X1 @ X2 )
                                                                                                             => ~ ! [X3: $i] :
                                                                                                                    ( ( X1 @ X3 )
                                                                                                                   => ( X2 = X3 ) ) ) ) )
                                                                                                 => ( ! [X1: $i > $o] :
                                                                                                        ( ~ ! [X2: $i] :
                                                                                                              ~ ! [X3: $i] :
                                                                                                                  ( ( X1 @ X3 )
                                                                                                                  = ( X3 = X2 ) )
                                                                                                       => ~ ! [X2: $i] :
                                                                                                              ( ( X1 @ X2 )
                                                                                                             => ~ ! [X3: $i] :
                                                                                                                    ( ( X1 @ X3 )
                                                                                                                   => ( X2 = X3 ) ) ) )
                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                          ( ( X1 = X2 )
                                                                                                         => ! [X3: $i,X4: $i] :
                                                                                                              ( ( X3 = X4 )
                                                                                                             => ( ( in @ X3 @ X1 )
                                                                                                               => ( in @ X4 @ X2 ) ) ) )
                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                            ( ( X1 = X2 )
                                                                                                           => ! [X3: $i,X4: $i] :
                                                                                                                ( ( X3 = X4 )
                                                                                                               => ( ( in @ X3 @ X1 )
                                                                                                                  = ( in @ X4 @ X2 ) ) ) )
                                                                                                       => ( ! [X1: $i > $o] :
                                                                                                              ( ~ ! [X2: $i] :
                                                                                                                    ( ( X1 @ X2 )
                                                                                                                   => ~ ! [X3: $i] :
                                                                                                                          ( ( X1 @ X3 )
                                                                                                                         => ( X2 = X3 ) ) )
                                                                                                             => ! [X2: $i,X3: $i] :
                                                                                                                  ( ( X1 @ X2 )
                                                                                                                 => ( ( X1 @ X3 )
                                                                                                                   => ( X2 = X3 ) ) ) )
                                                                                                         => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                                                ( ! [X3: $i,X4: $i] :
                                                                                                                    ( ( X3 = X4 )
                                                                                                                   => ( ( X1 @ X3 )
                                                                                                                      = ( X2 @ X4 ) ) )
                                                                                                               => ( ( ~ ! [X3: $i] :
                                                                                                                          ( ( X1 @ X3 )
                                                                                                                         => ~ ! [X4: $i] :
                                                                                                                                ( ( X1 @ X4 )
                                                                                                                               => ( X3 = X4 ) ) ) )
                                                                                                                  = ( ~ ! [X3: $i] :
                                                                                                                          ( ( X2 @ X3 )
                                                                                                                         => ~ ! [X4: $i] :
                                                                                                                                ( ( X2 @ X4 )
                                                                                                                               => ( X3 = X4 ) ) ) ) ) )
                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                  ( ( X1 = X2 )
                                                                                                                 => ! [X3: $i,X4: $i] :
                                                                                                                      ( ( X3 = X4 )
                                                                                                                     => ( ( setadjoin @ X1 @ X3 )
                                                                                                                        = ( setadjoin @ X2 @ X4 ) ) ) )
                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                    ( ( X1 = X2 )
                                                                                                                   => ( ( powerset @ X1 )
                                                                                                                      = ( powerset @ X2 ) ) )
                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                      ( ( X1 = X2 )
                                                                                                                     => ( ( setunion @ X1 )
                                                                                                                        = ( setunion @ X2 ) ) )
                                                                                                                 => ( ! [X1: $i > $o] :
                                                                                                                        ( ~ ! [X2: $i] :
                                                                                                                              ( ( X1 @ X2 )
                                                                                                                             => ~ ! [X3: $i] :
                                                                                                                                    ( ( X1 @ X3 )
                                                                                                                                   => ( X2 = X3 ) ) )
                                                                                                                       => ! [X2: $i,X3: $i] :
                                                                                                                            ( ( X1 @ X2 )
                                                                                                                           => ( ( X1 @ X3 )
                                                                                                                             => ( X2 = X3 ) ) ) )
                                                                                                                   => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                                                          ( ! [X3: $i,X4: $i] :
                                                                                                                              ( ( X3 = X4 )
                                                                                                                             => ( ( X1 @ X3 )
                                                                                                                                = ( X2 @ X4 ) ) )
                                                                                                                         => ( ~ ! [X3: $i] :
                                                                                                                                  ( ( X1 @ X3 )
                                                                                                                                 => ~ ! [X4: $i] :
                                                                                                                                        ( ( X1 @ X4 )
                                                                                                                                       => ( X3 = X4 ) ) )
                                                                                                                           => ( ~ ! [X3: $i] :
                                                                                                                                    ( ( X2 @ X3 )
                                                                                                                                   => ~ ! [X4: $i] :
                                                                                                                                          ( ( X2 @ X4 )
                                                                                                                                         => ( X3 = X4 ) ) )
                                                                                                                             => ( ( descr @ X1 )
                                                                                                                                = ( descr @ X2 ) ) ) ) )
                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                            ( ( X1 = X2 )
                                                                                                                           => ! [X3: $i > $o,X4: $i > $o] :
                                                                                                                                ( ! [X5: $i] :
                                                                                                                                    ( ( in @ X5 @ X1 )
                                                                                                                                   => ! [X6: $i] :
                                                                                                                                        ( ( in @ X6 @ X2 )
                                                                                                                                       => ( ( X5 = X6 )
                                                                                                                                         => ( ( X3 @ X5 )
                                                                                                                                            = ( X4 @ X6 ) ) ) ) )
                                                                                                                               => ( ( dsetconstr @ X1 @ X3 )
                                                                                                                                  = ( dsetconstr @ X2 @ X4 ) ) ) )
                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                              ( ! [X3: $i] :
                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                 => ( in @ X3 @ X2 ) )
                                                                                                                             => ( subset @ X1 @ X2 ) )
                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                ( ( X1 = X2 )
                                                                                                                               => ( subset @ X2 @ X1 ) )
                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                  ( ( X1 = X2 )
                                                                                                                                 => ( subset @ X1 @ X2 ) )
                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                    ( ! [X3: $i] :
                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                       => ( in @ X3 @ X2 ) )
                                                                                                                                   => ( subset @ X1 @ X2 ) )
                                                                                                                               => ( ! [X1: $i] : ( subset @ emptyset @ X1 )
                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                        ( ( subset @ X1 @ X2 )
                                                                                                                                       => ( ( in @ X3 @ X1 )
                                                                                                                                         => ( in @ X3 @ X2 ) ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                          ( ( subset @ X1 @ X2 )
                                                                                                                                         => ( ~ ( in @ X3 @ X2 )
                                                                                                                                           => ~ ( in @ X3 @ X1 ) ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                           => ( ~ ( in @ X3 @ X2 )
                                                                                                                                             => ~ ( subset @ X1 @ X2 ) ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                              ( ~ ( subset @ X1 @ X2 )
                                                                                                                                             => ( X1 != X2 ) )
                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                               => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                 => ( X1 != X2 ) ) )
                                                                                                                                           => ( ! [X1: $i] : ( subset @ X1 @ X1 )
                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                    ( ( subset @ X1 @ X2 )
                                                                                                                                                   => ( ( subset @ X2 @ X3 )
                                                                                                                                                     => ( subset @ X1 @ X3 ) ) )
                                                                                                                                               => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) )
                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                        ( ( subset @ X1 @ X3 )
                                                                                                                                                       => ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                          ( ( subset @ X1 @ X2 )
                                                                                                                                                         => ( in @ X1 @ ( powerset @ X2 ) ) )
                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                            ( ( subset @ X1 @ X2 )
                                                                                                                                                           => ( ( subset @ X2 @ X1 )
                                                                                                                                                             => ( X1 = X2 ) ) )
                                                                                                                                                       => ( ! [X1: $i] :
                                                                                                                                                              ( ( subset @ X1 @ emptyset )
                                                                                                                                                             => ( X1 = emptyset ) )
                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                ( ( subset @ X2 @ X1 )
                                                                                                                                                               => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                  ( ( in @ X2 @ ( powerset @ X1 ) )
                                                                                                                                                                 => ( subset @ X2 @ X1 ) )
                                                                                                                                                             => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                      ( ( subset @ X1 @ X2 )
                                                                                                                                                                     => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
                                                                                                                                                                 => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                                                                                                                                                                   => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                           => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                                                                                       => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                ( ( in @ X3 @ X2 )
                                                                                                                                                                               => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                                                                                                                                                                  ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                                                 => ( ( ( in @ X3 @ X1 )
                                                                                                                                                                                     => X4 )
                                                                                                                                                                                   => ( ( ( in @ X3 @ X2 )
                                                                                                                                                                                       => X4 )
                                                                                                                                                                                     => X4 ) ) )
                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                    ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                                                   => ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                     => ( in @ X3 @ X2 ) ) )
                                                                                                                                                                               => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                         => ( ( in @ X3 @ X2 )
                                                                                                                                                                                           => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                            ( ( subset @ X3 @ X1 )
                                                                                                                                                                                           => ( ( subset @ X3 @ X2 )
                                                                                                                                                                                             => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                              ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                                                                             => ( in @ X3 @ X1 ) )
                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                  ( ( subset @ X1 @ X2 )
                                                                                                                                                                                                 => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                                    = X1 ) )
                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                    ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                                      = X2 )
                                                                                                                                                                                                   => ( subset @ X2 @ X1 ) )
                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                      ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                                                                                     => ( in @ X3 @ X2 ) )
                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                        ( ! [X3: $i] :
                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                           => ~ ( in @ X3 @ X2 ) )
                                                                                                                                                                                                       => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                                          = emptyset ) )
                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                            ( ( subset @ X2 @ X1 )
                                                                                                                                                                                                           => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                                              = X2 ) )
                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                              ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                                                = X1 )
                                                                                                                                                                                                             => ( subset @ X1 @ X2 ) )
                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                                                                                                                                                                                = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                 => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                   => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                    ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                                   => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                      ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                                     => ~ ( in @ X3 @ X2 ) )
                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                        ( ( subset @ X1 @ X2 )
                                                                                                                                                                                                                       => ( ( setminus @ X1 @ X2 )
                                                                                                                                                                                                                          = emptyset ) )
                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                          ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                                         => ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                           => ( in @ X3 @ X2 ) ) )
                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                            ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                                           => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                             => ~ ( in @ X3 @ X1 ) ) )
                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                              ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                             => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                               => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                    ( ( ( setminus @ X1 @ X2 )
                                                                                                                                                                                                                                      = emptyset )
                                                                                                                                                                                                                                   => ( subset @ X1 @ X2 ) )
                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                      ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                                                                                                                                                                     => ! [X4: $o] :
                                                                                                                                                                                                                                          ( ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                           => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                                             => X4 ) )
                                                                                                                                                                                                                                         => ( ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                                             => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                                               => X4 ) )
                                                                                                                                                                                                                                           => X4 ) ) )
                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                       => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                                         => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                          ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                                         => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                                           => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                           => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                                             => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                              ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                                             => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                                               => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                          ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                                         => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                            ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                                           => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                             => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                                               => ( ( X3 != X1 )
                                                                                                                                                                                                                                                                 => ( X3 = X2 ) ) )
                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                     => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                       => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                         => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                           => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                             => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                               => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                              ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                             => ~ ! [X4: $i] :
                                                                                                                                                                                                                                                                                    ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                                   => ! [X5: $i] :
                                                                                                                                                                                                                                                                                        ( ( in @ X5 @ X2 )
                                                                                                                                                                                                                                                                                       => ( X3
                                                                                                                                                                                                                                                                                         != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                                                                                                                                                                         => ( sP5
                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                  ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                                                                                                                                                                                 => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                       => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                                                                                                                                                                             => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                                                                                                                                                                               => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                 => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                        ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                                                                                                                                                                        = X1 )
                                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                                                          ( ! [X3: $i] :
                                                                                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                  ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                                                 => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                                                                   => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                                                     => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                                                                                         => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                 => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                                                                                           => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                                  ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                 => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                   != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                                                            ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                                  ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                 => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                   != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                           => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                 => ~ ( X2 @ X3 ) ) )
                                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                             => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                                                               => ( ! [X4: $i] :
                                                                                                                                                                                                                                                                                                      ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                                                     => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                                                       => ( X4 = X3 ) ) )
                                                                                                                                                                                                                                                                                                 => ~ ! [X4: $i] :
                                                                                                                                                                                                                                                                                                        ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                       => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                         != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                                                                ( ! [X3: $i] :
                                                                                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                        ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                                                       => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                                                                         => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                                                           => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                                                                                               => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                       => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                                                                                                 => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                                        ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                       => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                         != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                  ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                                                                                                                                                                    = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                                                 => ( X1 = X2 ) )
                                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                    ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                   => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                                               => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                                      ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                                                                     => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                                            ( ( in @ X2
                                                                                                                                                                                                                                                                                                              @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                                @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                                                                                                                                                                           => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                                @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                                                                                                             != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                                                                                 => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                                        ( ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                                              ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                                                                                             => ( X1
                                                                                                                                                                                                                                                                                                               != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                       => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                          ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                          = X1 )
                                                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                            ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                           => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                              ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                                = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                             => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                                  = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                               => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                                  ( ( X1 = X2 )
                                                                                                                                                                                                                                                                                                                 => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                                                                    = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                                    ( ( X1 = X2 )
                                                                                                                                                                                                                                                                                                                   => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                                      = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                      ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                                        = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                     => ( ( X3 = X4 )
                                                                                                                                                                                                                                                                                                                       => ( X2 = X4 ) ) )
                                                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                        ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                                                                          = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                                                                                                                                                                       => ( X1 = X2 ) )
                                                                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                          ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                                            = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                         => ( X2 = X4 ) )
                                                                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                            ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                                              = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                                           => ( X2 = X4 ) )
                                                                                                                                                                                                                                                                                                                       => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                                                              ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                                                                                             => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                                                                    ( ( in @ X2
                                                                                                                                                                                                                                                                                                                                      @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                                                        @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                                                                                            ( X1
                                                                                                                                                                                                                                                                                                                                            = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                                                                                                                                                                   => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                                                        @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                                                                                            ( X1
                                                                                                                                                                                                                                                                                                                                            = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                                                                                                                                                                     != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                                                ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                                = X2 )
                                                                                                                                                                                                                                                                                                                           => ( sP8
                                                                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                                    ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                                   => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                                      ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                                     => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                                        ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                                       => ( in @ X4 @ X2 ) )
                                                                                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                                                                             => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                                                                = X3 ) ) )
                                                                                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                                                                               => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                                                                  = X4 ) ) )
                                                                                                                                                                                                                                                                                                                                       => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                                            ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                                           => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                                                                                                                                                                              = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h15,assumption,
    ! [X1: $i] :
      ( ~ ( ( in @ emptyset @ X1 )
         => ~ ! [X2: $i] :
                ( ~ ( ( in @ X2 @ omega )
                   => ~ ( in @ X2 @ X1 ) )
               => ( in @ ( setadjoin @ X2 @ X2 ) @ X1 ) ) )
     => ! [X2: $i] :
          ( ( in @ X2 @ omega )
         => ( in @ X2 @ X1 ) ) ),
    introduced(assumption,[]) ).

thf(h16,assumption,
    ~ ( ! [X1: $i > $i > $o,X2: $i] :
          ( ! [X3: $i] :
              ( ( in @ X3 @ X2 )
             => ~ ! [X4: $i] :
                    ( ( X1 @ X3 @ X4 )
                   => ~ ! [X5: $i] :
                          ( ( X1 @ X3 @ X5 )
                         => ( X4 = X5 ) ) ) )
         => ~ ! [X3: $i] :
                ~ ! [X4: $i] :
                    ( ( in @ X4 @ X3 )
                    = ( ~ ! [X5: $i] :
                            ( ( in @ X5 @ X2 )
                           => ~ ( X1 @ X5 @ X4 ) ) ) ) )
     => ( ! [X1: $i] :
            ( ~ ! [X2: $i] :
                  ~ ( in @ X2 @ X1 )
           => ~ ! [X2: $i] :
                  ( ( in @ X2 @ X1 )
                 => ~ ! [X3: $i] :
                        ( ( in @ X3 @ X2 )
                       => ~ ( in @ X3 @ X1 ) ) ) )
       => ( ! [X1: $i] :
              ~ ! [X2: $i] :
                  ( ~ ( ~ ( ! [X3: $i] :
                              ( ( in @ X3 @ X2 )
                             => ! [X4: $i] :
                                  ( ( in @ X4 @ X3 )
                                 => ( in @ X4 @ X1 ) ) )
                         => ~ ! [X3: $i,X4: $i] :
                                ( ~ ( ( in @ X3 @ X1 )
                                   => ~ ( in @ X4 @ X1 ) )
                               => ( ! [X5: $i] :
                                      ( ( in @ X5 @ X2 )
                                     => ( ( in @ X3 @ X5 )
                                        = ( in @ X4 @ X5 ) ) )
                                 => ( X3 = X4 ) ) ) )
                     => ~ ! [X3: $i,X4: $i] :
                            ( ~ ( ( in @ X3 @ X2 )
                               => ~ ( in @ X4 @ X2 ) )
                           => ( ~ ! [X5: $i] :
                                    ( ( in @ X5 @ X3 )
                                   => ( in @ X5 @ X4 ) )
                             => ! [X5: $i] :
                                  ( ( in @ X5 @ X4 )
                                 => ( in @ X5 @ X3 ) ) ) ) )
                 => ~ ! [X3: $i] :
                        ( ~ ( ! [X4: $i] :
                                ( ( in @ X4 @ X3 )
                               => ( in @ X4 @ X1 ) )
                           => ! [X4: $i] :
                                ~ ( in @ X4 @ X3 ) )
                       => ~ ! [X4: $i,X5: $i] :
                              ( ~ ( ~ ( ( in @ X4 @ X2 )
                                     => ~ ( in @ X5 @ X3 ) )
                                 => ~ ! [X6: $i] :
                                        ( ( in @ X6 @ X4 )
                                       => ~ ( in @ X6 @ X3 ) ) )
                             => ~ ! [X6: $i] :
                                    ( ( in @ X6 @ X2 )
                                   => ( ~ ! [X7: $i] :
                                            ( ( in @ X7 @ X6 )
                                           => ( in @ X7 @ X4 ) )
                                     => ( in @ X5 @ X6 ) ) ) ) ) )
         => ( ! [X1: $i > $o] :
                ( ~ ! [X2: $i] :
                      ( ( X1 @ X2 )
                     => ~ ! [X3: $i] :
                            ( ( X1 @ X3 )
                           => ( X2 = X3 ) ) )
               => ( X1 @ ( descr @ X1 ) ) )
           => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                  ( ( in @ X3 @ X1 )
                 => ( ( X2 @ X3 )
                   => ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) ) ) )
             => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                    ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                   => ( in @ X3 @ X1 ) )
               => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                      ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                     => ( X2 @ X3 ) )
                 => ( ! [X1: $o,X2: $i] :
                        ( ( in @ X2 @ ( prop2set @ X1 ) )
                       => X1 )
                   => ( ! [X1: $i] :
                          ( ( in @ X1 @ emptyset )
                         => ! [X2: $o] : X2 )
                     => ( ! [X1: $i] :
                            ~ ( in @ X1 @ emptyset )
                       => ( ! [X1: $i] :
                              ~ ( in @ X1 @ emptyset )
                         => ( ! [X1: $i > $o] :
                                ( ~ ! [X2: $i] :
                                      ( ( X1 @ X2 )
                                     => ~ ! [X3: $i] :
                                            ( ( X1 @ X3 )
                                           => ( X2 = X3 ) ) )
                               => ~ ! [X2: $i] :
                                      ~ ( X1 @ X2 ) )
                           => ( ! [X1: $i,X2: $i] :
                                  ( ! [X3: $i] :
                                      ( ( in @ X3 @ X1 )
                                     => ( in @ X3 @ X2 ) )
                                 => ( ! [X3: $i] :
                                        ( ( in @ X3 @ X2 )
                                       => ( in @ X3 @ X1 ) )
                                   => ( X1 = X2 ) ) )
                             => ( ! [X1: $i] :
                                    ( ! [X2: $i] :
                                        ~ ( in @ X2 @ X1 )
                                   => ( X1 = emptyset ) )
                               => ( ! [X1: $i] :
                                      ( ! [X2: $i] :
                                          ~ ( in @ X2 @ X1 )
                                     => ( X1 = emptyset ) )
                                 => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                        ( ( in @ X3 @ X1 )
                                       => ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                          = ( X2 @ X3 ) ) )
                                   => ( ! [X1: $i] :
                                          ( ( X1 != emptyset )
                                         => ~ ! [X2: $i] :
                                                ~ ( in @ X2 @ X1 ) )
                                     => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                            ( ( in @ X3 @ X1 )
                                           => ( ( X2 @ X3 )
                                             => ( ( dsetconstr @ X1 @ X2 )
                                               != emptyset ) ) )
                                       => ( ! [X1: $i] :
                                              ( ~ ! [X2: $i] :
                                                    ~ ( in @ X2 @ X1 )
                                             => ( X1 != emptyset ) )
                                         => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) )
                                           => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                    ( ( in @ X3 @ X2 )
                                                   => ( in @ X3 @ ( setadjoin @ X1 @ X2 ) ) )
                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                      ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                                     => ! [X4: $o] :
                                                          ( ( ( X3 = X1 )
                                                           => X4 )
                                                         => ( ( ( in @ X3 @ X2 )
                                                             => X4 )
                                                           => X4 ) ) )
                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                        ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                                       => ( ( X3 != X1 )
                                                         => ( in @ X3 @ X2 ) ) )
                                                   => ( ! [X1: $i] :
                                                          ( ( dsetconstr @ X1
                                                            @ ^ [X2: $i] : ~ $false )
                                                          = X1 )
                                                     => ( ! [X1: $i,X2: $i] :
                                                            ( ! [X3: $i] :
                                                                ( ( in @ X3 @ X2 )
                                                               => ( in @ X3 @ X1 ) )
                                                           => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                       => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                                         => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                  ( ( in @ X2 @ ( powerset @ X1 ) )
                                                                 => ( ( in @ X3 @ X2 )
                                                                   => ( in @ X3 @ X1 ) ) )
                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                    ( ( in @ X2 @ X3 )
                                                                   => ( ( in @ X3 @ X1 )
                                                                     => ( in @ X2 @ ( setunion @ X1 ) ) ) )
                                                               => ( ! [X1: $i,X2: $i] :
                                                                      ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                     => ! [X3: $o] :
                                                                          ( ! [X4: $i] :
                                                                              ( ( in @ X2 @ X4 )
                                                                             => ( ( in @ X4 @ X1 )
                                                                               => X3 ) )
                                                                         => X3 ) )
                                                                 => ( ! [X1: $i,X2: $i] :
                                                                        ( ( in @ X2 @ X1 )
                                                                       => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
                                                                   => ( ! [X1: $i > $o] :
                                                                          ( ~ ! [X2: $i] :
                                                                                ( ( X1 @ X2 )
                                                                               => ~ ! [X3: $i] :
                                                                                      ( ( X1 @ X3 )
                                                                                     => ( X2 = X3 ) ) )
                                                                         => ~ ! [X2: $i] :
                                                                                ~ ! [X3: $i] :
                                                                                    ( ( X1 @ X3 )
                                                                                    = ( X3 = X2 ) ) )
                                                                     => ( ! [X1: $i] :
                                                                            ( ( X1 != emptyset )
                                                                           => ~ ! [X2: $i] :
                                                                                  ~ ( in @ X2 @ X1 ) )
                                                                       => ( ! [X1: $i,X2: $i] :
                                                                              ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                             => ( X1 = X2 ) )
                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                ( ( X1 != X2 )
                                                                               => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                  ( ( X1 = X2 )
                                                                                 => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                    ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                   => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                      ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                     => ( ( X3 != X1 )
                                                                                       => ( X3 = X2 ) ) )
                                                                                 => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                   => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                                                            ( ~ ! [X3: $i] :
                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                 => ~ ( X2 @ X3 ) )
                                                                                           => ( ( dsetconstr @ X1 @ X2 )
                                                                                             != emptyset ) )
                                                                                       => ( ! [X1: $i > $o,X2: $i] :
                                                                                              ( ( in @ X2 @ emptyset )
                                                                                             => ( X1 @ X2 ) )
                                                                                         => ( ! [X1: $o] :
                                                                                                ( X1
                                                                                               => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                                                                           => ( ! [X1: $o] :
                                                                                                  ( X1
                                                                                                 => ( set2prop @ ( prop2set @ X1 ) ) )
                                                                                             => ( ! [X1: $i > $o] :
                                                                                                    ( ~ ! [X2: $i] :
                                                                                                          ~ ( X1 @ X2 )
                                                                                                   => ( ! [X2: $i,X3: $i] :
                                                                                                          ( ( X1 @ X2 )
                                                                                                         => ( ( X1 @ X3 )
                                                                                                           => ( X2 = X3 ) ) )
                                                                                                     => ~ ! [X2: $i] :
                                                                                                            ( ( X1 @ X2 )
                                                                                                           => ~ ! [X3: $i] :
                                                                                                                  ( ( X1 @ X3 )
                                                                                                                 => ( X2 = X3 ) ) ) ) )
                                                                                               => ( ! [X1: $i > $o] :
                                                                                                      ( ~ ! [X2: $i] :
                                                                                                            ~ ! [X3: $i] :
                                                                                                                ( ( X1 @ X3 )
                                                                                                                = ( X3 = X2 ) )
                                                                                                     => ~ ! [X2: $i] :
                                                                                                            ( ( X1 @ X2 )
                                                                                                           => ~ ! [X3: $i] :
                                                                                                                  ( ( X1 @ X3 )
                                                                                                                 => ( X2 = X3 ) ) ) )
                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                        ( ( X1 = X2 )
                                                                                                       => ! [X3: $i,X4: $i] :
                                                                                                            ( ( X3 = X4 )
                                                                                                           => ( ( in @ X3 @ X1 )
                                                                                                             => ( in @ X4 @ X2 ) ) ) )
                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                          ( ( X1 = X2 )
                                                                                                         => ! [X3: $i,X4: $i] :
                                                                                                              ( ( X3 = X4 )
                                                                                                             => ( ( in @ X3 @ X1 )
                                                                                                                = ( in @ X4 @ X2 ) ) ) )
                                                                                                     => ( ! [X1: $i > $o] :
                                                                                                            ( ~ ! [X2: $i] :
                                                                                                                  ( ( X1 @ X2 )
                                                                                                                 => ~ ! [X3: $i] :
                                                                                                                        ( ( X1 @ X3 )
                                                                                                                       => ( X2 = X3 ) ) )
                                                                                                           => ! [X2: $i,X3: $i] :
                                                                                                                ( ( X1 @ X2 )
                                                                                                               => ( ( X1 @ X3 )
                                                                                                                 => ( X2 = X3 ) ) ) )
                                                                                                       => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                                              ( ! [X3: $i,X4: $i] :
                                                                                                                  ( ( X3 = X4 )
                                                                                                                 => ( ( X1 @ X3 )
                                                                                                                    = ( X2 @ X4 ) ) )
                                                                                                             => ( ( ~ ! [X3: $i] :
                                                                                                                        ( ( X1 @ X3 )
                                                                                                                       => ~ ! [X4: $i] :
                                                                                                                              ( ( X1 @ X4 )
                                                                                                                             => ( X3 = X4 ) ) ) )
                                                                                                                = ( ~ ! [X3: $i] :
                                                                                                                        ( ( X2 @ X3 )
                                                                                                                       => ~ ! [X4: $i] :
                                                                                                                              ( ( X2 @ X4 )
                                                                                                                             => ( X3 = X4 ) ) ) ) ) )
                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                ( ( X1 = X2 )
                                                                                                               => ! [X3: $i,X4: $i] :
                                                                                                                    ( ( X3 = X4 )
                                                                                                                   => ( ( setadjoin @ X1 @ X3 )
                                                                                                                      = ( setadjoin @ X2 @ X4 ) ) ) )
                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                  ( ( X1 = X2 )
                                                                                                                 => ( ( powerset @ X1 )
                                                                                                                    = ( powerset @ X2 ) ) )
                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                    ( ( X1 = X2 )
                                                                                                                   => ( ( setunion @ X1 )
                                                                                                                      = ( setunion @ X2 ) ) )
                                                                                                               => ( ! [X1: $i > $o] :
                                                                                                                      ( ~ ! [X2: $i] :
                                                                                                                            ( ( X1 @ X2 )
                                                                                                                           => ~ ! [X3: $i] :
                                                                                                                                  ( ( X1 @ X3 )
                                                                                                                                 => ( X2 = X3 ) ) )
                                                                                                                     => ! [X2: $i,X3: $i] :
                                                                                                                          ( ( X1 @ X2 )
                                                                                                                         => ( ( X1 @ X3 )
                                                                                                                           => ( X2 = X3 ) ) ) )
                                                                                                                 => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                                                        ( ! [X3: $i,X4: $i] :
                                                                                                                            ( ( X3 = X4 )
                                                                                                                           => ( ( X1 @ X3 )
                                                                                                                              = ( X2 @ X4 ) ) )
                                                                                                                       => ( ~ ! [X3: $i] :
                                                                                                                                ( ( X1 @ X3 )
                                                                                                                               => ~ ! [X4: $i] :
                                                                                                                                      ( ( X1 @ X4 )
                                                                                                                                     => ( X3 = X4 ) ) )
                                                                                                                         => ( ~ ! [X3: $i] :
                                                                                                                                  ( ( X2 @ X3 )
                                                                                                                                 => ~ ! [X4: $i] :
                                                                                                                                        ( ( X2 @ X4 )
                                                                                                                                       => ( X3 = X4 ) ) )
                                                                                                                           => ( ( descr @ X1 )
                                                                                                                              = ( descr @ X2 ) ) ) ) )
                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                          ( ( X1 = X2 )
                                                                                                                         => ! [X3: $i > $o,X4: $i > $o] :
                                                                                                                              ( ! [X5: $i] :
                                                                                                                                  ( ( in @ X5 @ X1 )
                                                                                                                                 => ! [X6: $i] :
                                                                                                                                      ( ( in @ X6 @ X2 )
                                                                                                                                     => ( ( X5 = X6 )
                                                                                                                                       => ( ( X3 @ X5 )
                                                                                                                                          = ( X4 @ X6 ) ) ) ) )
                                                                                                                             => ( ( dsetconstr @ X1 @ X3 )
                                                                                                                                = ( dsetconstr @ X2 @ X4 ) ) ) )
                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                            ( ! [X3: $i] :
                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                               => ( in @ X3 @ X2 ) )
                                                                                                                           => ( subset @ X1 @ X2 ) )
                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                              ( ( X1 = X2 )
                                                                                                                             => ( subset @ X2 @ X1 ) )
                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                ( ( X1 = X2 )
                                                                                                                               => ( subset @ X1 @ X2 ) )
                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                  ( ! [X3: $i] :
                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                     => ( in @ X3 @ X2 ) )
                                                                                                                                 => ( subset @ X1 @ X2 ) )
                                                                                                                             => ( ! [X1: $i] : ( subset @ emptyset @ X1 )
                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                      ( ( subset @ X1 @ X2 )
                                                                                                                                     => ( ( in @ X3 @ X1 )
                                                                                                                                       => ( in @ X3 @ X2 ) ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                        ( ( subset @ X1 @ X2 )
                                                                                                                                       => ( ~ ( in @ X3 @ X2 )
                                                                                                                                         => ~ ( in @ X3 @ X1 ) ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                         => ( ~ ( in @ X3 @ X2 )
                                                                                                                                           => ~ ( subset @ X1 @ X2 ) ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                            ( ~ ( subset @ X1 @ X2 )
                                                                                                                                           => ( X1 != X2 ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                             => ( ~ ( in @ X3 @ X2 )
                                                                                                                                               => ( X1 != X2 ) ) )
                                                                                                                                         => ( ! [X1: $i] : ( subset @ X1 @ X1 )
                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                  ( ( subset @ X1 @ X2 )
                                                                                                                                                 => ( ( subset @ X2 @ X3 )
                                                                                                                                                   => ( subset @ X1 @ X3 ) ) )
                                                                                                                                             => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) )
                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                      ( ( subset @ X1 @ X3 )
                                                                                                                                                     => ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                        ( ( subset @ X1 @ X2 )
                                                                                                                                                       => ( in @ X1 @ ( powerset @ X2 ) ) )
                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                          ( ( subset @ X1 @ X2 )
                                                                                                                                                         => ( ( subset @ X2 @ X1 )
                                                                                                                                                           => ( X1 = X2 ) ) )
                                                                                                                                                     => ( ! [X1: $i] :
                                                                                                                                                            ( ( subset @ X1 @ emptyset )
                                                                                                                                                           => ( X1 = emptyset ) )
                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                              ( ( subset @ X2 @ X1 )
                                                                                                                                                             => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                ( ( in @ X2 @ ( powerset @ X1 ) )
                                                                                                                                                               => ( subset @ X2 @ X1 ) )
                                                                                                                                                           => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                    ( ( subset @ X1 @ X2 )
                                                                                                                                                                   => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
                                                                                                                                                               => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                                                                                                                                                                 => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                         => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                                                                                     => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                              ( ( in @ X3 @ X2 )
                                                                                                                                                                             => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                                                                                                                                                                ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                                               => ( ( ( in @ X3 @ X1 )
                                                                                                                                                                                   => X4 )
                                                                                                                                                                                 => ( ( ( in @ X3 @ X2 )
                                                                                                                                                                                     => X4 )
                                                                                                                                                                                   => X4 ) ) )
                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                  ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                                                 => ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                   => ( in @ X3 @ X2 ) ) )
                                                                                                                                                                             => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                                               => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                       => ( ( in @ X3 @ X2 )
                                                                                                                                                                                         => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                          ( ( subset @ X3 @ X1 )
                                                                                                                                                                                         => ( ( subset @ X3 @ X2 )
                                                                                                                                                                                           => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                            ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                                                                           => ( in @ X3 @ X1 ) )
                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                ( ( subset @ X1 @ X2 )
                                                                                                                                                                                               => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                                  = X1 ) )
                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                  ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                                    = X2 )
                                                                                                                                                                                                 => ( subset @ X2 @ X1 ) )
                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                    ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                                                                                   => ( in @ X3 @ X2 ) )
                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                      ( ! [X3: $i] :
                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                         => ~ ( in @ X3 @ X2 ) )
                                                                                                                                                                                                     => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                                        = emptyset ) )
                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                          ( ( subset @ X2 @ X1 )
                                                                                                                                                                                                         => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                                            = X2 ) )
                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                            ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                                              = X1 )
                                                                                                                                                                                                           => ( subset @ X1 @ X2 ) )
                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                              ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                                                                                                                                                                              = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                               => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                 => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                  ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                                 => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                    ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                                   => ~ ( in @ X3 @ X2 ) )
                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                      ( ( subset @ X1 @ X2 )
                                                                                                                                                                                                                     => ( ( setminus @ X1 @ X2 )
                                                                                                                                                                                                                        = emptyset ) )
                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                        ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                                       => ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                         => ( in @ X3 @ X2 ) ) )
                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                          ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                                         => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                           => ~ ( in @ X3 @ X1 ) ) )
                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                            ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                           => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                              ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                             => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                  ( ( ( setminus @ X1 @ X2 )
                                                                                                                                                                                                                                    = emptyset )
                                                                                                                                                                                                                                 => ( subset @ X1 @ X2 ) )
                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                    ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                                                                                                                                                                   => ! [X4: $o] :
                                                                                                                                                                                                                                        ( ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                         => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                                           => X4 ) )
                                                                                                                                                                                                                                       => ( ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                                           => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                                             => X4 ) )
                                                                                                                                                                                                                                         => X4 ) ) )
                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                     => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                                       => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                        ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                                       => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                                         => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                         => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                                           => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                            ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                                           => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                                             => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                        ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                                       => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                          ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                                         => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                           => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                              ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                                             => ( ( X3 != X1 )
                                                                                                                                                                                                                                                               => ( X3 = X2 ) ) )
                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                   => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                     => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                       => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                         => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                           => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                             => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                            ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                           => ~ ! [X4: $i] :
                                                                                                                                                                                                                                                                                  ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                                 => ! [X5: $i] :
                                                                                                                                                                                                                                                                                      ( ( in @ X5 @ X2 )
                                                                                                                                                                                                                                                                                     => ( X3
                                                                                                                                                                                                                                                                                       != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                                                                                                                                                                       => ( sP5
                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                                                                                                                                                                               => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                     => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                                                                                                                                                                           => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                                                                                                                                                                             => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                                                                               => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                      ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                                                                                                                                                                      = X1 )
                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                                                        ( ! [X3: $i] :
                                                                                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                                               => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                                                                 => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                                                   => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                                                                                       => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                               => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                                                                                         => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                                ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                               => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                 != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                                                          ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                                ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                               => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                 != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                         => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                               => ~ ( X2 @ X3 ) ) )
                                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                           => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                                                             => ( ! [X4: $i] :
                                                                                                                                                                                                                                                                                                    ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                                                   => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                                                     => ( X4 = X3 ) ) )
                                                                                                                                                                                                                                                                                               => ~ ! [X4: $i] :
                                                                                                                                                                                                                                                                                                      ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                     => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                       != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                                                              ( ! [X3: $i] :
                                                                                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                      ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                                                     => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                                                                       => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                                                         => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                                                                                             => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                     => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                                                                                               => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                                      ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                     => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                       != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                                                                                                                                                                  = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                                               => ( X1 = X2 ) )
                                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                  ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                 => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                                             => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                                    ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                                                                   => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                                          ( ( in @ X2
                                                                                                                                                                                                                                                                                                            @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                              @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                                                                                                                                                                         => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                              @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                                                                                                           != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                                                                               => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                                      ( ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                                            ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                                                                                           => ( X1
                                                                                                                                                                                                                                                                                                             != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                     => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                        ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                        = X1 )
                                                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                         => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                            ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                              = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                           => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                              ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                                = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                             => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                                ( ( X1 = X2 )
                                                                                                                                                                                                                                                                                                               => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                                                                  = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                                  ( ( X1 = X2 )
                                                                                                                                                                                                                                                                                                                 => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                                    = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                    ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                                      = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                   => ( ( X3 = X4 )
                                                                                                                                                                                                                                                                                                                     => ( X2 = X4 ) ) )
                                                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                      ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                                                                        = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                                                                                                                                                                     => ( X1 = X2 ) )
                                                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                        ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                                          = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                       => ( X2 = X4 ) )
                                                                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                          ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                                            = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                                         => ( X2 = X4 ) )
                                                                                                                                                                                                                                                                                                                     => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                                                            ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                                                                                           => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                                                                  ( ( in @ X2
                                                                                                                                                                                                                                                                                                                                    @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                                                      @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                                                                                          ( X1
                                                                                                                                                                                                                                                                                                                                          = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                                                                                                                                                                 => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                                                      @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                                                                                          ( X1
                                                                                                                                                                                                                                                                                                                                          = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                                                                                                                                                                   != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                                              ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                              = X2 )
                                                                                                                                                                                                                                                                                                                         => ( sP8
                                                                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                                  ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                                 => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                                    ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                                   => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                                      ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                                     => ( in @ X4 @ X2 ) )
                                                                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                                                                           => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                                                              = X3 ) ) )
                                                                                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                                                                             => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                                                                = X4 ) ) )
                                                                                                                                                                                                                                                                                                                                     => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                                          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                                         => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                                                                                                                                                                            = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h17,assumption,
    ! [X1: $i > $i > $o,X2: $i] :
      ( ! [X3: $i] :
          ( ( in @ X3 @ X2 )
         => ~ ! [X4: $i] :
                ( ( X1 @ X3 @ X4 )
               => ~ ! [X5: $i] :
                      ( ( X1 @ X3 @ X5 )
                     => ( X4 = X5 ) ) ) )
     => ~ ! [X3: $i] :
            ~ ! [X4: $i] :
                ( ( in @ X4 @ X3 )
                = ( ~ ! [X5: $i] :
                        ( ( in @ X5 @ X2 )
                       => ~ ( X1 @ X5 @ X4 ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h18,assumption,
    ~ ( ! [X1: $i] :
          ( ~ ! [X2: $i] :
                ~ ( in @ X2 @ X1 )
         => ~ ! [X2: $i] :
                ( ( in @ X2 @ X1 )
               => ~ ! [X3: $i] :
                      ( ( in @ X3 @ X2 )
                     => ~ ( in @ X3 @ X1 ) ) ) )
     => ( ! [X1: $i] :
            ~ ! [X2: $i] :
                ( ~ ( ~ ( ! [X3: $i] :
                            ( ( in @ X3 @ X2 )
                           => ! [X4: $i] :
                                ( ( in @ X4 @ X3 )
                               => ( in @ X4 @ X1 ) ) )
                       => ~ ! [X3: $i,X4: $i] :
                              ( ~ ( ( in @ X3 @ X1 )
                                 => ~ ( in @ X4 @ X1 ) )
                             => ( ! [X5: $i] :
                                    ( ( in @ X5 @ X2 )
                                   => ( ( in @ X3 @ X5 )
                                      = ( in @ X4 @ X5 ) ) )
                               => ( X3 = X4 ) ) ) )
                   => ~ ! [X3: $i,X4: $i] :
                          ( ~ ( ( in @ X3 @ X2 )
                             => ~ ( in @ X4 @ X2 ) )
                         => ( ~ ! [X5: $i] :
                                  ( ( in @ X5 @ X3 )
                                 => ( in @ X5 @ X4 ) )
                           => ! [X5: $i] :
                                ( ( in @ X5 @ X4 )
                               => ( in @ X5 @ X3 ) ) ) ) )
               => ~ ! [X3: $i] :
                      ( ~ ( ! [X4: $i] :
                              ( ( in @ X4 @ X3 )
                             => ( in @ X4 @ X1 ) )
                         => ! [X4: $i] :
                              ~ ( in @ X4 @ X3 ) )
                     => ~ ! [X4: $i,X5: $i] :
                            ( ~ ( ~ ( ( in @ X4 @ X2 )
                                   => ~ ( in @ X5 @ X3 ) )
                               => ~ ! [X6: $i] :
                                      ( ( in @ X6 @ X4 )
                                     => ~ ( in @ X6 @ X3 ) ) )
                           => ~ ! [X6: $i] :
                                  ( ( in @ X6 @ X2 )
                                 => ( ~ ! [X7: $i] :
                                          ( ( in @ X7 @ X6 )
                                         => ( in @ X7 @ X4 ) )
                                   => ( in @ X5 @ X6 ) ) ) ) ) )
       => ( ! [X1: $i > $o] :
              ( ~ ! [X2: $i] :
                    ( ( X1 @ X2 )
                   => ~ ! [X3: $i] :
                          ( ( X1 @ X3 )
                         => ( X2 = X3 ) ) )
             => ( X1 @ ( descr @ X1 ) ) )
         => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                ( ( in @ X3 @ X1 )
               => ( ( X2 @ X3 )
                 => ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) ) ) )
           => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                  ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                 => ( in @ X3 @ X1 ) )
             => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                    ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                   => ( X2 @ X3 ) )
               => ( ! [X1: $o,X2: $i] :
                      ( ( in @ X2 @ ( prop2set @ X1 ) )
                     => X1 )
                 => ( ! [X1: $i] :
                        ( ( in @ X1 @ emptyset )
                       => ! [X2: $o] : X2 )
                   => ( ! [X1: $i] :
                          ~ ( in @ X1 @ emptyset )
                     => ( ! [X1: $i] :
                            ~ ( in @ X1 @ emptyset )
                       => ( ! [X1: $i > $o] :
                              ( ~ ! [X2: $i] :
                                    ( ( X1 @ X2 )
                                   => ~ ! [X3: $i] :
                                          ( ( X1 @ X3 )
                                         => ( X2 = X3 ) ) )
                             => ~ ! [X2: $i] :
                                    ~ ( X1 @ X2 ) )
                         => ( ! [X1: $i,X2: $i] :
                                ( ! [X3: $i] :
                                    ( ( in @ X3 @ X1 )
                                   => ( in @ X3 @ X2 ) )
                               => ( ! [X3: $i] :
                                      ( ( in @ X3 @ X2 )
                                     => ( in @ X3 @ X1 ) )
                                 => ( X1 = X2 ) ) )
                           => ( ! [X1: $i] :
                                  ( ! [X2: $i] :
                                      ~ ( in @ X2 @ X1 )
                                 => ( X1 = emptyset ) )
                             => ( ! [X1: $i] :
                                    ( ! [X2: $i] :
                                        ~ ( in @ X2 @ X1 )
                                   => ( X1 = emptyset ) )
                               => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                      ( ( in @ X3 @ X1 )
                                     => ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                        = ( X2 @ X3 ) ) )
                                 => ( ! [X1: $i] :
                                        ( ( X1 != emptyset )
                                       => ~ ! [X2: $i] :
                                              ~ ( in @ X2 @ X1 ) )
                                   => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                          ( ( in @ X3 @ X1 )
                                         => ( ( X2 @ X3 )
                                           => ( ( dsetconstr @ X1 @ X2 )
                                             != emptyset ) ) )
                                     => ( ! [X1: $i] :
                                            ( ~ ! [X2: $i] :
                                                  ~ ( in @ X2 @ X1 )
                                           => ( X1 != emptyset ) )
                                       => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) )
                                         => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                  ( ( in @ X3 @ X2 )
                                                 => ( in @ X3 @ ( setadjoin @ X1 @ X2 ) ) )
                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                    ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                                   => ! [X4: $o] :
                                                        ( ( ( X3 = X1 )
                                                         => X4 )
                                                       => ( ( ( in @ X3 @ X2 )
                                                           => X4 )
                                                         => X4 ) ) )
                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                      ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                                     => ( ( X3 != X1 )
                                                       => ( in @ X3 @ X2 ) ) )
                                                 => ( ! [X1: $i] :
                                                        ( ( dsetconstr @ X1
                                                          @ ^ [X2: $i] : ~ $false )
                                                        = X1 )
                                                   => ( ! [X1: $i,X2: $i] :
                                                          ( ! [X3: $i] :
                                                              ( ( in @ X3 @ X2 )
                                                             => ( in @ X3 @ X1 ) )
                                                         => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                     => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                                       => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                ( ( in @ X2 @ ( powerset @ X1 ) )
                                                               => ( ( in @ X3 @ X2 )
                                                                 => ( in @ X3 @ X1 ) ) )
                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                  ( ( in @ X2 @ X3 )
                                                                 => ( ( in @ X3 @ X1 )
                                                                   => ( in @ X2 @ ( setunion @ X1 ) ) ) )
                                                             => ( ! [X1: $i,X2: $i] :
                                                                    ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                   => ! [X3: $o] :
                                                                        ( ! [X4: $i] :
                                                                            ( ( in @ X2 @ X4 )
                                                                           => ( ( in @ X4 @ X1 )
                                                                             => X3 ) )
                                                                       => X3 ) )
                                                               => ( ! [X1: $i,X2: $i] :
                                                                      ( ( in @ X2 @ X1 )
                                                                     => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
                                                                 => ( ! [X1: $i > $o] :
                                                                        ( ~ ! [X2: $i] :
                                                                              ( ( X1 @ X2 )
                                                                             => ~ ! [X3: $i] :
                                                                                    ( ( X1 @ X3 )
                                                                                   => ( X2 = X3 ) ) )
                                                                       => ~ ! [X2: $i] :
                                                                              ~ ! [X3: $i] :
                                                                                  ( ( X1 @ X3 )
                                                                                  = ( X3 = X2 ) ) )
                                                                   => ( ! [X1: $i] :
                                                                          ( ( X1 != emptyset )
                                                                         => ~ ! [X2: $i] :
                                                                                ~ ( in @ X2 @ X1 ) )
                                                                     => ( ! [X1: $i,X2: $i] :
                                                                            ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                           => ( X1 = X2 ) )
                                                                       => ( ! [X1: $i,X2: $i] :
                                                                              ( ( X1 != X2 )
                                                                             => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                ( ( X1 = X2 )
                                                                               => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                  ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                 => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                    ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                   => ( ( X3 != X1 )
                                                                                     => ( X3 = X2 ) ) )
                                                                               => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                 => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                                                          ( ~ ! [X3: $i] :
                                                                                                ( ( in @ X3 @ X1 )
                                                                                               => ~ ( X2 @ X3 ) )
                                                                                         => ( ( dsetconstr @ X1 @ X2 )
                                                                                           != emptyset ) )
                                                                                     => ( ! [X1: $i > $o,X2: $i] :
                                                                                            ( ( in @ X2 @ emptyset )
                                                                                           => ( X1 @ X2 ) )
                                                                                       => ( ! [X1: $o] :
                                                                                              ( X1
                                                                                             => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                                                                         => ( ! [X1: $o] :
                                                                                                ( X1
                                                                                               => ( set2prop @ ( prop2set @ X1 ) ) )
                                                                                           => ( ! [X1: $i > $o] :
                                                                                                  ( ~ ! [X2: $i] :
                                                                                                        ~ ( X1 @ X2 )
                                                                                                 => ( ! [X2: $i,X3: $i] :
                                                                                                        ( ( X1 @ X2 )
                                                                                                       => ( ( X1 @ X3 )
                                                                                                         => ( X2 = X3 ) ) )
                                                                                                   => ~ ! [X2: $i] :
                                                                                                          ( ( X1 @ X2 )
                                                                                                         => ~ ! [X3: $i] :
                                                                                                                ( ( X1 @ X3 )
                                                                                                               => ( X2 = X3 ) ) ) ) )
                                                                                             => ( ! [X1: $i > $o] :
                                                                                                    ( ~ ! [X2: $i] :
                                                                                                          ~ ! [X3: $i] :
                                                                                                              ( ( X1 @ X3 )
                                                                                                              = ( X3 = X2 ) )
                                                                                                   => ~ ! [X2: $i] :
                                                                                                          ( ( X1 @ X2 )
                                                                                                         => ~ ! [X3: $i] :
                                                                                                                ( ( X1 @ X3 )
                                                                                                               => ( X2 = X3 ) ) ) )
                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                      ( ( X1 = X2 )
                                                                                                     => ! [X3: $i,X4: $i] :
                                                                                                          ( ( X3 = X4 )
                                                                                                         => ( ( in @ X3 @ X1 )
                                                                                                           => ( in @ X4 @ X2 ) ) ) )
                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                        ( ( X1 = X2 )
                                                                                                       => ! [X3: $i,X4: $i] :
                                                                                                            ( ( X3 = X4 )
                                                                                                           => ( ( in @ X3 @ X1 )
                                                                                                              = ( in @ X4 @ X2 ) ) ) )
                                                                                                   => ( ! [X1: $i > $o] :
                                                                                                          ( ~ ! [X2: $i] :
                                                                                                                ( ( X1 @ X2 )
                                                                                                               => ~ ! [X3: $i] :
                                                                                                                      ( ( X1 @ X3 )
                                                                                                                     => ( X2 = X3 ) ) )
                                                                                                         => ! [X2: $i,X3: $i] :
                                                                                                              ( ( X1 @ X2 )
                                                                                                             => ( ( X1 @ X3 )
                                                                                                               => ( X2 = X3 ) ) ) )
                                                                                                     => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                                            ( ! [X3: $i,X4: $i] :
                                                                                                                ( ( X3 = X4 )
                                                                                                               => ( ( X1 @ X3 )
                                                                                                                  = ( X2 @ X4 ) ) )
                                                                                                           => ( ( ~ ! [X3: $i] :
                                                                                                                      ( ( X1 @ X3 )
                                                                                                                     => ~ ! [X4: $i] :
                                                                                                                            ( ( X1 @ X4 )
                                                                                                                           => ( X3 = X4 ) ) ) )
                                                                                                              = ( ~ ! [X3: $i] :
                                                                                                                      ( ( X2 @ X3 )
                                                                                                                     => ~ ! [X4: $i] :
                                                                                                                            ( ( X2 @ X4 )
                                                                                                                           => ( X3 = X4 ) ) ) ) ) )
                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                              ( ( X1 = X2 )
                                                                                                             => ! [X3: $i,X4: $i] :
                                                                                                                  ( ( X3 = X4 )
                                                                                                                 => ( ( setadjoin @ X1 @ X3 )
                                                                                                                    = ( setadjoin @ X2 @ X4 ) ) ) )
                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                ( ( X1 = X2 )
                                                                                                               => ( ( powerset @ X1 )
                                                                                                                  = ( powerset @ X2 ) ) )
                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                  ( ( X1 = X2 )
                                                                                                                 => ( ( setunion @ X1 )
                                                                                                                    = ( setunion @ X2 ) ) )
                                                                                                             => ( ! [X1: $i > $o] :
                                                                                                                    ( ~ ! [X2: $i] :
                                                                                                                          ( ( X1 @ X2 )
                                                                                                                         => ~ ! [X3: $i] :
                                                                                                                                ( ( X1 @ X3 )
                                                                                                                               => ( X2 = X3 ) ) )
                                                                                                                   => ! [X2: $i,X3: $i] :
                                                                                                                        ( ( X1 @ X2 )
                                                                                                                       => ( ( X1 @ X3 )
                                                                                                                         => ( X2 = X3 ) ) ) )
                                                                                                               => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                                                      ( ! [X3: $i,X4: $i] :
                                                                                                                          ( ( X3 = X4 )
                                                                                                                         => ( ( X1 @ X3 )
                                                                                                                            = ( X2 @ X4 ) ) )
                                                                                                                     => ( ~ ! [X3: $i] :
                                                                                                                              ( ( X1 @ X3 )
                                                                                                                             => ~ ! [X4: $i] :
                                                                                                                                    ( ( X1 @ X4 )
                                                                                                                                   => ( X3 = X4 ) ) )
                                                                                                                       => ( ~ ! [X3: $i] :
                                                                                                                                ( ( X2 @ X3 )
                                                                                                                               => ~ ! [X4: $i] :
                                                                                                                                      ( ( X2 @ X4 )
                                                                                                                                     => ( X3 = X4 ) ) )
                                                                                                                         => ( ( descr @ X1 )
                                                                                                                            = ( descr @ X2 ) ) ) ) )
                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                        ( ( X1 = X2 )
                                                                                                                       => ! [X3: $i > $o,X4: $i > $o] :
                                                                                                                            ( ! [X5: $i] :
                                                                                                                                ( ( in @ X5 @ X1 )
                                                                                                                               => ! [X6: $i] :
                                                                                                                                    ( ( in @ X6 @ X2 )
                                                                                                                                   => ( ( X5 = X6 )
                                                                                                                                     => ( ( X3 @ X5 )
                                                                                                                                        = ( X4 @ X6 ) ) ) ) )
                                                                                                                           => ( ( dsetconstr @ X1 @ X3 )
                                                                                                                              = ( dsetconstr @ X2 @ X4 ) ) ) )
                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                          ( ! [X3: $i] :
                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                             => ( in @ X3 @ X2 ) )
                                                                                                                         => ( subset @ X1 @ X2 ) )
                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                            ( ( X1 = X2 )
                                                                                                                           => ( subset @ X2 @ X1 ) )
                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                              ( ( X1 = X2 )
                                                                                                                             => ( subset @ X1 @ X2 ) )
                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                ( ! [X3: $i] :
                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                   => ( in @ X3 @ X2 ) )
                                                                                                                               => ( subset @ X1 @ X2 ) )
                                                                                                                           => ( ! [X1: $i] : ( subset @ emptyset @ X1 )
                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                    ( ( subset @ X1 @ X2 )
                                                                                                                                   => ( ( in @ X3 @ X1 )
                                                                                                                                     => ( in @ X3 @ X2 ) ) )
                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                      ( ( subset @ X1 @ X2 )
                                                                                                                                     => ( ~ ( in @ X3 @ X2 )
                                                                                                                                       => ~ ( in @ X3 @ X1 ) ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                       => ( ~ ( in @ X3 @ X2 )
                                                                                                                                         => ~ ( subset @ X1 @ X2 ) ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                          ( ~ ( subset @ X1 @ X2 )
                                                                                                                                         => ( X1 != X2 ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                           => ( ~ ( in @ X3 @ X2 )
                                                                                                                                             => ( X1 != X2 ) ) )
                                                                                                                                       => ( ! [X1: $i] : ( subset @ X1 @ X1 )
                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                ( ( subset @ X1 @ X2 )
                                                                                                                                               => ( ( subset @ X2 @ X3 )
                                                                                                                                                 => ( subset @ X1 @ X3 ) ) )
                                                                                                                                           => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) )
                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                    ( ( subset @ X1 @ X3 )
                                                                                                                                                   => ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                      ( ( subset @ X1 @ X2 )
                                                                                                                                                     => ( in @ X1 @ ( powerset @ X2 ) ) )
                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                        ( ( subset @ X1 @ X2 )
                                                                                                                                                       => ( ( subset @ X2 @ X1 )
                                                                                                                                                         => ( X1 = X2 ) ) )
                                                                                                                                                   => ( ! [X1: $i] :
                                                                                                                                                          ( ( subset @ X1 @ emptyset )
                                                                                                                                                         => ( X1 = emptyset ) )
                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                            ( ( subset @ X2 @ X1 )
                                                                                                                                                           => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                              ( ( in @ X2 @ ( powerset @ X1 ) )
                                                                                                                                                             => ( subset @ X2 @ X1 ) )
                                                                                                                                                         => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                  ( ( subset @ X1 @ X2 )
                                                                                                                                                                 => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
                                                                                                                                                             => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                                                                                                                                                               => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                       => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                                                                                   => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                            ( ( in @ X3 @ X2 )
                                                                                                                                                                           => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                                                                                                                                                              ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                                             => ( ( ( in @ X3 @ X1 )
                                                                                                                                                                                 => X4 )
                                                                                                                                                                               => ( ( ( in @ X3 @ X2 )
                                                                                                                                                                                   => X4 )
                                                                                                                                                                                 => X4 ) ) )
                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                                               => ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                 => ( in @ X3 @ X2 ) ) )
                                                                                                                                                                           => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                                             => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                     => ( ( in @ X3 @ X2 )
                                                                                                                                                                                       => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                        ( ( subset @ X3 @ X1 )
                                                                                                                                                                                       => ( ( subset @ X3 @ X2 )
                                                                                                                                                                                         => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                          ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                                                                         => ( in @ X3 @ X1 ) )
                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                              ( ( subset @ X1 @ X2 )
                                                                                                                                                                                             => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                                = X1 ) )
                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                                  = X2 )
                                                                                                                                                                                               => ( subset @ X2 @ X1 ) )
                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                  ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                                                                                 => ( in @ X3 @ X2 ) )
                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                    ( ! [X3: $i] :
                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                       => ~ ( in @ X3 @ X2 ) )
                                                                                                                                                                                                   => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                                      = emptyset ) )
                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                        ( ( subset @ X2 @ X1 )
                                                                                                                                                                                                       => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                                          = X2 ) )
                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                          ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                                            = X1 )
                                                                                                                                                                                                         => ( subset @ X1 @ X2 ) )
                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                            ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                                                                                                                                                                            = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                             => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                               => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                               => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                  ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                                 => ~ ( in @ X3 @ X2 ) )
                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                    ( ( subset @ X1 @ X2 )
                                                                                                                                                                                                                   => ( ( setminus @ X1 @ X2 )
                                                                                                                                                                                                                      = emptyset ) )
                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                      ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                                     => ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                       => ( in @ X3 @ X2 ) ) )
                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                        ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                                       => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                         => ~ ( in @ X3 @ X1 ) ) )
                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                          ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                         => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                            ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                           => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                ( ( ( setminus @ X1 @ X2 )
                                                                                                                                                                                                                                  = emptyset )
                                                                                                                                                                                                                               => ( subset @ X1 @ X2 ) )
                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                  ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                                                                                                                                                                 => ! [X4: $o] :
                                                                                                                                                                                                                                      ( ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                       => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                                         => X4 ) )
                                                                                                                                                                                                                                     => ( ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                                         => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                                           => X4 ) )
                                                                                                                                                                                                                                       => X4 ) ) )
                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                   => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                                     => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                      ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                                     => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                                       => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                       => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                                         => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                          ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                                         => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                                           => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                      ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                                     => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                        ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                                       => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                         => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                            ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                                           => ( ( X3 != X1 )
                                                                                                                                                                                                                                                             => ( X3 = X2 ) ) )
                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                 => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                   => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                     => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                       => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                         => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                           => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                         => ~ ! [X4: $i] :
                                                                                                                                                                                                                                                                                ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                               => ! [X5: $i] :
                                                                                                                                                                                                                                                                                    ( ( in @ X5 @ X2 )
                                                                                                                                                                                                                                                                                   => ( X3
                                                                                                                                                                                                                                                                                     != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                                                                                                                                                                     => ( sP5
                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                              ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                                                                                                                                                                             => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                   => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                                                                                                                                                                         => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                                                                                                                                                                           => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                                                                             => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                    ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                                                                                                                                                                    = X1 )
                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                                                      ( ! [X3: $i] :
                                                                                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                                                                                                                                              ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                                             => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                                                               => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                                                 => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                                                                                     => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                             => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                                                                                       => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                              ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                             => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                                               != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                                                        ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                              ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                             => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                                               != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                       => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                             => ~ ( X2 @ X3 ) ) )
                                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                         => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                                                           => ( ! [X4: $i] :
                                                                                                                                                                                                                                                                                                  ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                                                 => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                                                   => ( X4 = X3 ) ) )
                                                                                                                                                                                                                                                                                             => ~ ! [X4: $i] :
                                                                                                                                                                                                                                                                                                    ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                   => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                     != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                                                            ( ! [X3: $i] :
                                                                                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                    ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                                                   => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                                                                     => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                                                       => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                                                                                           => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                   => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                                                                                             => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                                    ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                   => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                     != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                              ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                                                                                                                                                                = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                                             => ( X1 = X2 ) )
                                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                               => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                                           => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                                  ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                                                                 => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                                        ( ( in @ X2
                                                                                                                                                                                                                                                                                                          @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                            @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                                                                                                                                                                       => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                            @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                                                                                                         != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                                                                             => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                                    ( ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                                          ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                                                                                         => ( X1
                                                                                                                                                                                                                                                                                                           != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                   => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                      ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                      = X1 )
                                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                       => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                          ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                            = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                         => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                            ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                              = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                           => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                              ( ( X1 = X2 )
                                                                                                                                                                                                                                                                                                             => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                                                                = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                                ( ( X1 = X2 )
                                                                                                                                                                                                                                                                                                               => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                                  = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                  ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                                    = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                 => ( ( X3 = X4 )
                                                                                                                                                                                                                                                                                                                   => ( X2 = X4 ) ) )
                                                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                    ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                                                                      = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                                                                                                                                                                   => ( X1 = X2 ) )
                                                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                      ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                                        = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                     => ( X2 = X4 ) )
                                                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                        ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                                          = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                                       => ( X2 = X4 ) )
                                                                                                                                                                                                                                                                                                                   => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                                                          ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                                                                                         => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                                                                ( ( in @ X2
                                                                                                                                                                                                                                                                                                                                  @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                                                    @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                                                                                        ( X1
                                                                                                                                                                                                                                                                                                                                        = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                                                                                                                                                               => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                                                    @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                                                                                        ( X1
                                                                                                                                                                                                                                                                                                                                        = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                                                                                                                                                                 != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                                            ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                            = X2 )
                                                                                                                                                                                                                                                                                                                       => ( sP8
                                                                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                                ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                               => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                                  ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                                 => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                                    ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                                   => ( in @ X4 @ X2 ) )
                                                                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                                                                         => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                                                            = X3 ) ) )
                                                                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                                                                           => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                                                              = X4 ) ) )
                                                                                                                                                                                                                                                                                                                                   => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                                        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                                       => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                                                                                                                                                                          = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h19,assumption,
    ! [X1: $i] :
      ( ~ ! [X2: $i] :
            ~ ( in @ X2 @ X1 )
     => ~ ! [X2: $i] :
            ( ( in @ X2 @ X1 )
           => ~ ! [X3: $i] :
                  ( ( in @ X3 @ X2 )
                 => ~ ( in @ X3 @ X1 ) ) ) ),
    introduced(assumption,[]) ).

thf(h20,assumption,
    ~ ( ! [X1: $i] :
          ~ ! [X2: $i] :
              ( ~ ( ~ ( ! [X3: $i] :
                          ( ( in @ X3 @ X2 )
                         => ! [X4: $i] :
                              ( ( in @ X4 @ X3 )
                             => ( in @ X4 @ X1 ) ) )
                     => ~ ! [X3: $i,X4: $i] :
                            ( ~ ( ( in @ X3 @ X1 )
                               => ~ ( in @ X4 @ X1 ) )
                           => ( ! [X5: $i] :
                                  ( ( in @ X5 @ X2 )
                                 => ( ( in @ X3 @ X5 )
                                    = ( in @ X4 @ X5 ) ) )
                             => ( X3 = X4 ) ) ) )
                 => ~ ! [X3: $i,X4: $i] :
                        ( ~ ( ( in @ X3 @ X2 )
                           => ~ ( in @ X4 @ X2 ) )
                       => ( ~ ! [X5: $i] :
                                ( ( in @ X5 @ X3 )
                               => ( in @ X5 @ X4 ) )
                         => ! [X5: $i] :
                              ( ( in @ X5 @ X4 )
                             => ( in @ X5 @ X3 ) ) ) ) )
             => ~ ! [X3: $i] :
                    ( ~ ( ! [X4: $i] :
                            ( ( in @ X4 @ X3 )
                           => ( in @ X4 @ X1 ) )
                       => ! [X4: $i] :
                            ~ ( in @ X4 @ X3 ) )
                   => ~ ! [X4: $i,X5: $i] :
                          ( ~ ( ~ ( ( in @ X4 @ X2 )
                                 => ~ ( in @ X5 @ X3 ) )
                             => ~ ! [X6: $i] :
                                    ( ( in @ X6 @ X4 )
                                   => ~ ( in @ X6 @ X3 ) ) )
                         => ~ ! [X6: $i] :
                                ( ( in @ X6 @ X2 )
                               => ( ~ ! [X7: $i] :
                                        ( ( in @ X7 @ X6 )
                                       => ( in @ X7 @ X4 ) )
                                 => ( in @ X5 @ X6 ) ) ) ) ) )
     => ( ! [X1: $i > $o] :
            ( ~ ! [X2: $i] :
                  ( ( X1 @ X2 )
                 => ~ ! [X3: $i] :
                        ( ( X1 @ X3 )
                       => ( X2 = X3 ) ) )
           => ( X1 @ ( descr @ X1 ) ) )
       => ( ! [X1: $i,X2: $i > $o,X3: $i] :
              ( ( in @ X3 @ X1 )
             => ( ( X2 @ X3 )
               => ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) ) ) )
         => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
               => ( in @ X3 @ X1 ) )
           => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                  ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                 => ( X2 @ X3 ) )
             => ( ! [X1: $o,X2: $i] :
                    ( ( in @ X2 @ ( prop2set @ X1 ) )
                   => X1 )
               => ( ! [X1: $i] :
                      ( ( in @ X1 @ emptyset )
                     => ! [X2: $o] : X2 )
                 => ( ! [X1: $i] :
                        ~ ( in @ X1 @ emptyset )
                   => ( ! [X1: $i] :
                          ~ ( in @ X1 @ emptyset )
                     => ( ! [X1: $i > $o] :
                            ( ~ ! [X2: $i] :
                                  ( ( X1 @ X2 )
                                 => ~ ! [X3: $i] :
                                        ( ( X1 @ X3 )
                                       => ( X2 = X3 ) ) )
                           => ~ ! [X2: $i] :
                                  ~ ( X1 @ X2 ) )
                       => ( ! [X1: $i,X2: $i] :
                              ( ! [X3: $i] :
                                  ( ( in @ X3 @ X1 )
                                 => ( in @ X3 @ X2 ) )
                             => ( ! [X3: $i] :
                                    ( ( in @ X3 @ X2 )
                                   => ( in @ X3 @ X1 ) )
                               => ( X1 = X2 ) ) )
                         => ( ! [X1: $i] :
                                ( ! [X2: $i] :
                                    ~ ( in @ X2 @ X1 )
                               => ( X1 = emptyset ) )
                           => ( ! [X1: $i] :
                                  ( ! [X2: $i] :
                                      ~ ( in @ X2 @ X1 )
                                 => ( X1 = emptyset ) )
                             => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                    ( ( in @ X3 @ X1 )
                                   => ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                      = ( X2 @ X3 ) ) )
                               => ( ! [X1: $i] :
                                      ( ( X1 != emptyset )
                                     => ~ ! [X2: $i] :
                                            ~ ( in @ X2 @ X1 ) )
                                 => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                        ( ( in @ X3 @ X1 )
                                       => ( ( X2 @ X3 )
                                         => ( ( dsetconstr @ X1 @ X2 )
                                           != emptyset ) ) )
                                   => ( ! [X1: $i] :
                                          ( ~ ! [X2: $i] :
                                                ~ ( in @ X2 @ X1 )
                                         => ( X1 != emptyset ) )
                                     => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) )
                                       => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                ( ( in @ X3 @ X2 )
                                               => ( in @ X3 @ ( setadjoin @ X1 @ X2 ) ) )
                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                  ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                                 => ! [X4: $o] :
                                                      ( ( ( X3 = X1 )
                                                       => X4 )
                                                     => ( ( ( in @ X3 @ X2 )
                                                         => X4 )
                                                       => X4 ) ) )
                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                    ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                                   => ( ( X3 != X1 )
                                                     => ( in @ X3 @ X2 ) ) )
                                               => ( ! [X1: $i] :
                                                      ( ( dsetconstr @ X1
                                                        @ ^ [X2: $i] : ~ $false )
                                                      = X1 )
                                                 => ( ! [X1: $i,X2: $i] :
                                                        ( ! [X3: $i] :
                                                            ( ( in @ X3 @ X2 )
                                                           => ( in @ X3 @ X1 ) )
                                                       => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                   => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                                     => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                              ( ( in @ X2 @ ( powerset @ X1 ) )
                                                             => ( ( in @ X3 @ X2 )
                                                               => ( in @ X3 @ X1 ) ) )
                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                ( ( in @ X2 @ X3 )
                                                               => ( ( in @ X3 @ X1 )
                                                                 => ( in @ X2 @ ( setunion @ X1 ) ) ) )
                                                           => ( ! [X1: $i,X2: $i] :
                                                                  ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                 => ! [X3: $o] :
                                                                      ( ! [X4: $i] :
                                                                          ( ( in @ X2 @ X4 )
                                                                         => ( ( in @ X4 @ X1 )
                                                                           => X3 ) )
                                                                     => X3 ) )
                                                             => ( ! [X1: $i,X2: $i] :
                                                                    ( ( in @ X2 @ X1 )
                                                                   => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
                                                               => ( ! [X1: $i > $o] :
                                                                      ( ~ ! [X2: $i] :
                                                                            ( ( X1 @ X2 )
                                                                           => ~ ! [X3: $i] :
                                                                                  ( ( X1 @ X3 )
                                                                                 => ( X2 = X3 ) ) )
                                                                     => ~ ! [X2: $i] :
                                                                            ~ ! [X3: $i] :
                                                                                ( ( X1 @ X3 )
                                                                                = ( X3 = X2 ) ) )
                                                                 => ( ! [X1: $i] :
                                                                        ( ( X1 != emptyset )
                                                                       => ~ ! [X2: $i] :
                                                                              ~ ( in @ X2 @ X1 ) )
                                                                   => ( ! [X1: $i,X2: $i] :
                                                                          ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                         => ( X1 = X2 ) )
                                                                     => ( ! [X1: $i,X2: $i] :
                                                                            ( ( X1 != X2 )
                                                                           => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                       => ( ! [X1: $i,X2: $i] :
                                                                              ( ( X1 = X2 )
                                                                             => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                               => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                  ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                 => ( ( X3 != X1 )
                                                                                   => ( X3 = X2 ) ) )
                                                                             => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                               => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                                                        ( ~ ! [X3: $i] :
                                                                                              ( ( in @ X3 @ X1 )
                                                                                             => ~ ( X2 @ X3 ) )
                                                                                       => ( ( dsetconstr @ X1 @ X2 )
                                                                                         != emptyset ) )
                                                                                   => ( ! [X1: $i > $o,X2: $i] :
                                                                                          ( ( in @ X2 @ emptyset )
                                                                                         => ( X1 @ X2 ) )
                                                                                     => ( ! [X1: $o] :
                                                                                            ( X1
                                                                                           => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                                                                       => ( ! [X1: $o] :
                                                                                              ( X1
                                                                                             => ( set2prop @ ( prop2set @ X1 ) ) )
                                                                                         => ( ! [X1: $i > $o] :
                                                                                                ( ~ ! [X2: $i] :
                                                                                                      ~ ( X1 @ X2 )
                                                                                               => ( ! [X2: $i,X3: $i] :
                                                                                                      ( ( X1 @ X2 )
                                                                                                     => ( ( X1 @ X3 )
                                                                                                       => ( X2 = X3 ) ) )
                                                                                                 => ~ ! [X2: $i] :
                                                                                                        ( ( X1 @ X2 )
                                                                                                       => ~ ! [X3: $i] :
                                                                                                              ( ( X1 @ X3 )
                                                                                                             => ( X2 = X3 ) ) ) ) )
                                                                                           => ( ! [X1: $i > $o] :
                                                                                                  ( ~ ! [X2: $i] :
                                                                                                        ~ ! [X3: $i] :
                                                                                                            ( ( X1 @ X3 )
                                                                                                            = ( X3 = X2 ) )
                                                                                                 => ~ ! [X2: $i] :
                                                                                                        ( ( X1 @ X2 )
                                                                                                       => ~ ! [X3: $i] :
                                                                                                              ( ( X1 @ X3 )
                                                                                                             => ( X2 = X3 ) ) ) )
                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                    ( ( X1 = X2 )
                                                                                                   => ! [X3: $i,X4: $i] :
                                                                                                        ( ( X3 = X4 )
                                                                                                       => ( ( in @ X3 @ X1 )
                                                                                                         => ( in @ X4 @ X2 ) ) ) )
                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                      ( ( X1 = X2 )
                                                                                                     => ! [X3: $i,X4: $i] :
                                                                                                          ( ( X3 = X4 )
                                                                                                         => ( ( in @ X3 @ X1 )
                                                                                                            = ( in @ X4 @ X2 ) ) ) )
                                                                                                 => ( ! [X1: $i > $o] :
                                                                                                        ( ~ ! [X2: $i] :
                                                                                                              ( ( X1 @ X2 )
                                                                                                             => ~ ! [X3: $i] :
                                                                                                                    ( ( X1 @ X3 )
                                                                                                                   => ( X2 = X3 ) ) )
                                                                                                       => ! [X2: $i,X3: $i] :
                                                                                                            ( ( X1 @ X2 )
                                                                                                           => ( ( X1 @ X3 )
                                                                                                             => ( X2 = X3 ) ) ) )
                                                                                                   => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                                          ( ! [X3: $i,X4: $i] :
                                                                                                              ( ( X3 = X4 )
                                                                                                             => ( ( X1 @ X3 )
                                                                                                                = ( X2 @ X4 ) ) )
                                                                                                         => ( ( ~ ! [X3: $i] :
                                                                                                                    ( ( X1 @ X3 )
                                                                                                                   => ~ ! [X4: $i] :
                                                                                                                          ( ( X1 @ X4 )
                                                                                                                         => ( X3 = X4 ) ) ) )
                                                                                                            = ( ~ ! [X3: $i] :
                                                                                                                    ( ( X2 @ X3 )
                                                                                                                   => ~ ! [X4: $i] :
                                                                                                                          ( ( X2 @ X4 )
                                                                                                                         => ( X3 = X4 ) ) ) ) ) )
                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                            ( ( X1 = X2 )
                                                                                                           => ! [X3: $i,X4: $i] :
                                                                                                                ( ( X3 = X4 )
                                                                                                               => ( ( setadjoin @ X1 @ X3 )
                                                                                                                  = ( setadjoin @ X2 @ X4 ) ) ) )
                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                              ( ( X1 = X2 )
                                                                                                             => ( ( powerset @ X1 )
                                                                                                                = ( powerset @ X2 ) ) )
                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                ( ( X1 = X2 )
                                                                                                               => ( ( setunion @ X1 )
                                                                                                                  = ( setunion @ X2 ) ) )
                                                                                                           => ( ! [X1: $i > $o] :
                                                                                                                  ( ~ ! [X2: $i] :
                                                                                                                        ( ( X1 @ X2 )
                                                                                                                       => ~ ! [X3: $i] :
                                                                                                                              ( ( X1 @ X3 )
                                                                                                                             => ( X2 = X3 ) ) )
                                                                                                                 => ! [X2: $i,X3: $i] :
                                                                                                                      ( ( X1 @ X2 )
                                                                                                                     => ( ( X1 @ X3 )
                                                                                                                       => ( X2 = X3 ) ) ) )
                                                                                                             => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                                                    ( ! [X3: $i,X4: $i] :
                                                                                                                        ( ( X3 = X4 )
                                                                                                                       => ( ( X1 @ X3 )
                                                                                                                          = ( X2 @ X4 ) ) )
                                                                                                                   => ( ~ ! [X3: $i] :
                                                                                                                            ( ( X1 @ X3 )
                                                                                                                           => ~ ! [X4: $i] :
                                                                                                                                  ( ( X1 @ X4 )
                                                                                                                                 => ( X3 = X4 ) ) )
                                                                                                                     => ( ~ ! [X3: $i] :
                                                                                                                              ( ( X2 @ X3 )
                                                                                                                             => ~ ! [X4: $i] :
                                                                                                                                    ( ( X2 @ X4 )
                                                                                                                                   => ( X3 = X4 ) ) )
                                                                                                                       => ( ( descr @ X1 )
                                                                                                                          = ( descr @ X2 ) ) ) ) )
                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                      ( ( X1 = X2 )
                                                                                                                     => ! [X3: $i > $o,X4: $i > $o] :
                                                                                                                          ( ! [X5: $i] :
                                                                                                                              ( ( in @ X5 @ X1 )
                                                                                                                             => ! [X6: $i] :
                                                                                                                                  ( ( in @ X6 @ X2 )
                                                                                                                                 => ( ( X5 = X6 )
                                                                                                                                   => ( ( X3 @ X5 )
                                                                                                                                      = ( X4 @ X6 ) ) ) ) )
                                                                                                                         => ( ( dsetconstr @ X1 @ X3 )
                                                                                                                            = ( dsetconstr @ X2 @ X4 ) ) ) )
                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                        ( ! [X3: $i] :
                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                           => ( in @ X3 @ X2 ) )
                                                                                                                       => ( subset @ X1 @ X2 ) )
                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                          ( ( X1 = X2 )
                                                                                                                         => ( subset @ X2 @ X1 ) )
                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                            ( ( X1 = X2 )
                                                                                                                           => ( subset @ X1 @ X2 ) )
                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                              ( ! [X3: $i] :
                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                 => ( in @ X3 @ X2 ) )
                                                                                                                             => ( subset @ X1 @ X2 ) )
                                                                                                                         => ( ! [X1: $i] : ( subset @ emptyset @ X1 )
                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                  ( ( subset @ X1 @ X2 )
                                                                                                                                 => ( ( in @ X3 @ X1 )
                                                                                                                                   => ( in @ X3 @ X2 ) ) )
                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                    ( ( subset @ X1 @ X2 )
                                                                                                                                   => ( ~ ( in @ X3 @ X2 )
                                                                                                                                     => ~ ( in @ X3 @ X1 ) ) )
                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                     => ( ~ ( in @ X3 @ X2 )
                                                                                                                                       => ~ ( subset @ X1 @ X2 ) ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                        ( ~ ( subset @ X1 @ X2 )
                                                                                                                                       => ( X1 != X2 ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                         => ( ~ ( in @ X3 @ X2 )
                                                                                                                                           => ( X1 != X2 ) ) )
                                                                                                                                     => ( ! [X1: $i] : ( subset @ X1 @ X1 )
                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                              ( ( subset @ X1 @ X2 )
                                                                                                                                             => ( ( subset @ X2 @ X3 )
                                                                                                                                               => ( subset @ X1 @ X3 ) ) )
                                                                                                                                         => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) )
                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                  ( ( subset @ X1 @ X3 )
                                                                                                                                                 => ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                    ( ( subset @ X1 @ X2 )
                                                                                                                                                   => ( in @ X1 @ ( powerset @ X2 ) ) )
                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                      ( ( subset @ X1 @ X2 )
                                                                                                                                                     => ( ( subset @ X2 @ X1 )
                                                                                                                                                       => ( X1 = X2 ) ) )
                                                                                                                                                 => ( ! [X1: $i] :
                                                                                                                                                        ( ( subset @ X1 @ emptyset )
                                                                                                                                                       => ( X1 = emptyset ) )
                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                          ( ( subset @ X2 @ X1 )
                                                                                                                                                         => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                            ( ( in @ X2 @ ( powerset @ X1 ) )
                                                                                                                                                           => ( subset @ X2 @ X1 ) )
                                                                                                                                                       => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                ( ( subset @ X1 @ X2 )
                                                                                                                                                               => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
                                                                                                                                                           => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                                                                                                                                                             => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                     => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                                                                                 => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                          ( ( in @ X3 @ X2 )
                                                                                                                                                                         => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                                                                                                                                                            ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                                           => ( ( ( in @ X3 @ X1 )
                                                                                                                                                                               => X4 )
                                                                                                                                                                             => ( ( ( in @ X3 @ X2 )
                                                                                                                                                                                 => X4 )
                                                                                                                                                                               => X4 ) ) )
                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                              ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                                             => ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                               => ( in @ X3 @ X2 ) ) )
                                                                                                                                                                         => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                                           => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                   => ( ( in @ X3 @ X2 )
                                                                                                                                                                                     => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                      ( ( subset @ X3 @ X1 )
                                                                                                                                                                                     => ( ( subset @ X3 @ X2 )
                                                                                                                                                                                       => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                        ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                                                                       => ( in @ X3 @ X1 ) )
                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                            ( ( subset @ X1 @ X2 )
                                                                                                                                                                                           => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                              = X1 ) )
                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                              ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                                = X2 )
                                                                                                                                                                                             => ( subset @ X2 @ X1 ) )
                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                                                                               => ( in @ X3 @ X2 ) )
                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                  ( ! [X3: $i] :
                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                     => ~ ( in @ X3 @ X2 ) )
                                                                                                                                                                                                 => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                                    = emptyset ) )
                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                      ( ( subset @ X2 @ X1 )
                                                                                                                                                                                                     => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                                        = X2 ) )
                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                        ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                                          = X1 )
                                                                                                                                                                                                       => ( subset @ X1 @ X2 ) )
                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                          ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                                                                                                                                                                          = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                           => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                             => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                              ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                             => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                               => ~ ( in @ X3 @ X2 ) )
                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                  ( ( subset @ X1 @ X2 )
                                                                                                                                                                                                                 => ( ( setminus @ X1 @ X2 )
                                                                                                                                                                                                                    = emptyset ) )
                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                    ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                                   => ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                     => ( in @ X3 @ X2 ) ) )
                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                      ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                                     => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                       => ~ ( in @ X3 @ X1 ) ) )
                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                        ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                       => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                          ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                         => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                              ( ( ( setminus @ X1 @ X2 )
                                                                                                                                                                                                                                = emptyset )
                                                                                                                                                                                                                             => ( subset @ X1 @ X2 ) )
                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                                                                                                                                                               => ! [X4: $o] :
                                                                                                                                                                                                                                    ( ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                     => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                                       => X4 ) )
                                                                                                                                                                                                                                   => ( ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                                       => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                                         => X4 ) )
                                                                                                                                                                                                                                     => X4 ) ) )
                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                 => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                                   => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                    ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                                   => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                                     => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                     => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                                       => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                        ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                                       => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                                         => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                    ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                                   => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                      ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                                     => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                       => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                          ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                                         => ( ( X3 != X1 )
                                                                                                                                                                                                                                                           => ( X3 = X2 ) ) )
                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                               => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                 => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                   => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                     => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                       => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                         => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                       => ~ ! [X4: $i] :
                                                                                                                                                                                                                                                                              ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                             => ! [X5: $i] :
                                                                                                                                                                                                                                                                                  ( ( in @ X5 @ X2 )
                                                                                                                                                                                                                                                                                 => ( X3
                                                                                                                                                                                                                                                                                   != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                                                                                                                                                                   => ( sP5
                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                            ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                                                                                                                                                                           => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                 => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                                                                                                                                                                       => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                                                                                                                                                                         => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                                                                           => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                  ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                                                                                                                                                                  = X1 )
                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                                                    ( ! [X3: $i] :
                                                                                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                                                                                                                                            ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                                           => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                                                             => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                                               => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                                                                                   => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                           => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                                                                                     => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                            ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                           => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                                             != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                                                      ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                            ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                           => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                                             != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                     => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                           => ~ ( X2 @ X3 ) ) )
                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                       => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                                                         => ( ! [X4: $i] :
                                                                                                                                                                                                                                                                                                ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                                               => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                                                 => ( X4 = X3 ) ) )
                                                                                                                                                                                                                                                                                           => ~ ! [X4: $i] :
                                                                                                                                                                                                                                                                                                  ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                 => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                   != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                                                          ( ! [X3: $i] :
                                                                                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                  ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                                                 => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                                                                   => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                                                     => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                                                                                         => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                 => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                                                                                           => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                                  ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                 => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                   != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                            ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                                                                                                                                                              = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                                           => ( X1 = X2 ) )
                                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                              ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                             => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                                         => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                                ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                                                               => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                                      ( ( in @ X2
                                                                                                                                                                                                                                                                                                        @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                          @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                                                                                                                                                                     => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                          @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                                                                                                       != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                                                                           => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                                  ( ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                                        ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                                                                                       => ( X1
                                                                                                                                                                                                                                                                                                         != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                 => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                    ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                    = X1 )
                                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                      ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                     => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                        ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                          = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                       => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                          ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                            = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                         => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                            ( ( X1 = X2 )
                                                                                                                                                                                                                                                                                                           => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                                                              = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                              ( ( X1 = X2 )
                                                                                                                                                                                                                                                                                                             => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                                = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                                  = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                               => ( ( X3 = X4 )
                                                                                                                                                                                                                                                                                                                 => ( X2 = X4 ) ) )
                                                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                  ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                                                                    = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                                                                                                                                                                 => ( X1 = X2 ) )
                                                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                    ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                                      = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                   => ( X2 = X4 ) )
                                                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                      ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                                        = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                                     => ( X2 = X4 ) )
                                                                                                                                                                                                                                                                                                                 => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                                                        ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                                                                                       => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                                                              ( ( in @ X2
                                                                                                                                                                                                                                                                                                                                @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                                                  @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                                                                                      ( X1
                                                                                                                                                                                                                                                                                                                                      = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                                                                                                                                                             => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                                                  @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                                                                                      ( X1
                                                                                                                                                                                                                                                                                                                                      = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                                                                                                                                                               != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                                          ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                          = X2 )
                                                                                                                                                                                                                                                                                                                     => ( sP8
                                                                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                              ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                             => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                                ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                               => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                                  ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                                 => ( in @ X4 @ X2 ) )
                                                                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                                                                       => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                                                          = X3 ) ) )
                                                                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                                                                         => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                                                            = X4 ) ) )
                                                                                                                                                                                                                                                                                                                                 => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                                      ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                                     => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                                                                                                                                                                        = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h21,assumption,
    ! [X1: $i] :
      ~ ! [X2: $i] :
          ( ~ ( ~ ( ! [X3: $i] :
                      ( ( in @ X3 @ X2 )
                     => ! [X4: $i] :
                          ( ( in @ X4 @ X3 )
                         => ( in @ X4 @ X1 ) ) )
                 => ~ ! [X3: $i,X4: $i] :
                        ( ~ ( ( in @ X3 @ X1 )
                           => ~ ( in @ X4 @ X1 ) )
                       => ( ! [X5: $i] :
                              ( ( in @ X5 @ X2 )
                             => ( ( in @ X3 @ X5 )
                                = ( in @ X4 @ X5 ) ) )
                         => ( X3 = X4 ) ) ) )
             => ~ ! [X3: $i,X4: $i] :
                    ( ~ ( ( in @ X3 @ X2 )
                       => ~ ( in @ X4 @ X2 ) )
                   => ( ~ ! [X5: $i] :
                            ( ( in @ X5 @ X3 )
                           => ( in @ X5 @ X4 ) )
                     => ! [X5: $i] :
                          ( ( in @ X5 @ X4 )
                         => ( in @ X5 @ X3 ) ) ) ) )
         => ~ ! [X3: $i] :
                ( ~ ( ! [X4: $i] :
                        ( ( in @ X4 @ X3 )
                       => ( in @ X4 @ X1 ) )
                   => ! [X4: $i] :
                        ~ ( in @ X4 @ X3 ) )
               => ~ ! [X4: $i,X5: $i] :
                      ( ~ ( ~ ( ( in @ X4 @ X2 )
                             => ~ ( in @ X5 @ X3 ) )
                         => ~ ! [X6: $i] :
                                ( ( in @ X6 @ X4 )
                               => ~ ( in @ X6 @ X3 ) ) )
                     => ~ ! [X6: $i] :
                            ( ( in @ X6 @ X2 )
                           => ( ~ ! [X7: $i] :
                                    ( ( in @ X7 @ X6 )
                                   => ( in @ X7 @ X4 ) )
                             => ( in @ X5 @ X6 ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h22,assumption,
    ~ ( ! [X1: $i > $o] :
          ( ~ ! [X2: $i] :
                ( ( X1 @ X2 )
               => ~ ! [X3: $i] :
                      ( ( X1 @ X3 )
                     => ( X2 = X3 ) ) )
         => ( X1 @ ( descr @ X1 ) ) )
     => ( ! [X1: $i,X2: $i > $o,X3: $i] :
            ( ( in @ X3 @ X1 )
           => ( ( X2 @ X3 )
             => ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) ) ) )
       => ( ! [X1: $i,X2: $i > $o,X3: $i] :
              ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
             => ( in @ X3 @ X1 ) )
         => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
               => ( X2 @ X3 ) )
           => ( ! [X1: $o,X2: $i] :
                  ( ( in @ X2 @ ( prop2set @ X1 ) )
                 => X1 )
             => ( ! [X1: $i] :
                    ( ( in @ X1 @ emptyset )
                   => ! [X2: $o] : X2 )
               => ( ! [X1: $i] :
                      ~ ( in @ X1 @ emptyset )
                 => ( ! [X1: $i] :
                        ~ ( in @ X1 @ emptyset )
                   => ( ! [X1: $i > $o] :
                          ( ~ ! [X2: $i] :
                                ( ( X1 @ X2 )
                               => ~ ! [X3: $i] :
                                      ( ( X1 @ X3 )
                                     => ( X2 = X3 ) ) )
                         => ~ ! [X2: $i] :
                                ~ ( X1 @ X2 ) )
                     => ( ! [X1: $i,X2: $i] :
                            ( ! [X3: $i] :
                                ( ( in @ X3 @ X1 )
                               => ( in @ X3 @ X2 ) )
                           => ( ! [X3: $i] :
                                  ( ( in @ X3 @ X2 )
                                 => ( in @ X3 @ X1 ) )
                             => ( X1 = X2 ) ) )
                       => ( ! [X1: $i] :
                              ( ! [X2: $i] :
                                  ~ ( in @ X2 @ X1 )
                             => ( X1 = emptyset ) )
                         => ( ! [X1: $i] :
                                ( ! [X2: $i] :
                                    ~ ( in @ X2 @ X1 )
                               => ( X1 = emptyset ) )
                           => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                  ( ( in @ X3 @ X1 )
                                 => ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                    = ( X2 @ X3 ) ) )
                             => ( ! [X1: $i] :
                                    ( ( X1 != emptyset )
                                   => ~ ! [X2: $i] :
                                          ~ ( in @ X2 @ X1 ) )
                               => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                      ( ( in @ X3 @ X1 )
                                     => ( ( X2 @ X3 )
                                       => ( ( dsetconstr @ X1 @ X2 )
                                         != emptyset ) ) )
                                 => ( ! [X1: $i] :
                                        ( ~ ! [X2: $i] :
                                              ~ ( in @ X2 @ X1 )
                                       => ( X1 != emptyset ) )
                                   => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) )
                                     => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                              ( ( in @ X3 @ X2 )
                                             => ( in @ X3 @ ( setadjoin @ X1 @ X2 ) ) )
                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                               => ! [X4: $o] :
                                                    ( ( ( X3 = X1 )
                                                     => X4 )
                                                   => ( ( ( in @ X3 @ X2 )
                                                       => X4 )
                                                     => X4 ) ) )
                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                  ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                                 => ( ( X3 != X1 )
                                                   => ( in @ X3 @ X2 ) ) )
                                             => ( ! [X1: $i] :
                                                    ( ( dsetconstr @ X1
                                                      @ ^ [X2: $i] : ~ $false )
                                                    = X1 )
                                               => ( ! [X1: $i,X2: $i] :
                                                      ( ! [X3: $i] :
                                                          ( ( in @ X3 @ X2 )
                                                         => ( in @ X3 @ X1 ) )
                                                     => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                 => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                                   => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                            ( ( in @ X2 @ ( powerset @ X1 ) )
                                                           => ( ( in @ X3 @ X2 )
                                                             => ( in @ X3 @ X1 ) ) )
                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                              ( ( in @ X2 @ X3 )
                                                             => ( ( in @ X3 @ X1 )
                                                               => ( in @ X2 @ ( setunion @ X1 ) ) ) )
                                                         => ( ! [X1: $i,X2: $i] :
                                                                ( ( in @ X2 @ ( setunion @ X1 ) )
                                                               => ! [X3: $o] :
                                                                    ( ! [X4: $i] :
                                                                        ( ( in @ X2 @ X4 )
                                                                       => ( ( in @ X4 @ X1 )
                                                                         => X3 ) )
                                                                   => X3 ) )
                                                           => ( ! [X1: $i,X2: $i] :
                                                                  ( ( in @ X2 @ X1 )
                                                                 => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
                                                             => ( ! [X1: $i > $o] :
                                                                    ( ~ ! [X2: $i] :
                                                                          ( ( X1 @ X2 )
                                                                         => ~ ! [X3: $i] :
                                                                                ( ( X1 @ X3 )
                                                                               => ( X2 = X3 ) ) )
                                                                   => ~ ! [X2: $i] :
                                                                          ~ ! [X3: $i] :
                                                                              ( ( X1 @ X3 )
                                                                              = ( X3 = X2 ) ) )
                                                               => ( ! [X1: $i] :
                                                                      ( ( X1 != emptyset )
                                                                     => ~ ! [X2: $i] :
                                                                            ~ ( in @ X2 @ X1 ) )
                                                                 => ( ! [X1: $i,X2: $i] :
                                                                        ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                       => ( X1 = X2 ) )
                                                                   => ( ! [X1: $i,X2: $i] :
                                                                          ( ( X1 != X2 )
                                                                         => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                     => ( ! [X1: $i,X2: $i] :
                                                                            ( ( X1 = X2 )
                                                                           => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                       => ( ! [X1: $i,X2: $i] :
                                                                              ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                             => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                               => ( ( X3 != X1 )
                                                                                 => ( X3 = X2 ) ) )
                                                                           => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                             => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                               => ( ! [X1: $i,X2: $i > $o] :
                                                                                      ( ~ ! [X3: $i] :
                                                                                            ( ( in @ X3 @ X1 )
                                                                                           => ~ ( X2 @ X3 ) )
                                                                                     => ( ( dsetconstr @ X1 @ X2 )
                                                                                       != emptyset ) )
                                                                                 => ( ! [X1: $i > $o,X2: $i] :
                                                                                        ( ( in @ X2 @ emptyset )
                                                                                       => ( X1 @ X2 ) )
                                                                                   => ( ! [X1: $o] :
                                                                                          ( X1
                                                                                         => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                                                                     => ( ! [X1: $o] :
                                                                                            ( X1
                                                                                           => ( set2prop @ ( prop2set @ X1 ) ) )
                                                                                       => ( ! [X1: $i > $o] :
                                                                                              ( ~ ! [X2: $i] :
                                                                                                    ~ ( X1 @ X2 )
                                                                                             => ( ! [X2: $i,X3: $i] :
                                                                                                    ( ( X1 @ X2 )
                                                                                                   => ( ( X1 @ X3 )
                                                                                                     => ( X2 = X3 ) ) )
                                                                                               => ~ ! [X2: $i] :
                                                                                                      ( ( X1 @ X2 )
                                                                                                     => ~ ! [X3: $i] :
                                                                                                            ( ( X1 @ X3 )
                                                                                                           => ( X2 = X3 ) ) ) ) )
                                                                                         => ( ! [X1: $i > $o] :
                                                                                                ( ~ ! [X2: $i] :
                                                                                                      ~ ! [X3: $i] :
                                                                                                          ( ( X1 @ X3 )
                                                                                                          = ( X3 = X2 ) )
                                                                                               => ~ ! [X2: $i] :
                                                                                                      ( ( X1 @ X2 )
                                                                                                     => ~ ! [X3: $i] :
                                                                                                            ( ( X1 @ X3 )
                                                                                                           => ( X2 = X3 ) ) ) )
                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                  ( ( X1 = X2 )
                                                                                                 => ! [X3: $i,X4: $i] :
                                                                                                      ( ( X3 = X4 )
                                                                                                     => ( ( in @ X3 @ X1 )
                                                                                                       => ( in @ X4 @ X2 ) ) ) )
                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                    ( ( X1 = X2 )
                                                                                                   => ! [X3: $i,X4: $i] :
                                                                                                        ( ( X3 = X4 )
                                                                                                       => ( ( in @ X3 @ X1 )
                                                                                                          = ( in @ X4 @ X2 ) ) ) )
                                                                                               => ( ! [X1: $i > $o] :
                                                                                                      ( ~ ! [X2: $i] :
                                                                                                            ( ( X1 @ X2 )
                                                                                                           => ~ ! [X3: $i] :
                                                                                                                  ( ( X1 @ X3 )
                                                                                                                 => ( X2 = X3 ) ) )
                                                                                                     => ! [X2: $i,X3: $i] :
                                                                                                          ( ( X1 @ X2 )
                                                                                                         => ( ( X1 @ X3 )
                                                                                                           => ( X2 = X3 ) ) ) )
                                                                                                 => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                                        ( ! [X3: $i,X4: $i] :
                                                                                                            ( ( X3 = X4 )
                                                                                                           => ( ( X1 @ X3 )
                                                                                                              = ( X2 @ X4 ) ) )
                                                                                                       => ( ( ~ ! [X3: $i] :
                                                                                                                  ( ( X1 @ X3 )
                                                                                                                 => ~ ! [X4: $i] :
                                                                                                                        ( ( X1 @ X4 )
                                                                                                                       => ( X3 = X4 ) ) ) )
                                                                                                          = ( ~ ! [X3: $i] :
                                                                                                                  ( ( X2 @ X3 )
                                                                                                                 => ~ ! [X4: $i] :
                                                                                                                        ( ( X2 @ X4 )
                                                                                                                       => ( X3 = X4 ) ) ) ) ) )
                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                          ( ( X1 = X2 )
                                                                                                         => ! [X3: $i,X4: $i] :
                                                                                                              ( ( X3 = X4 )
                                                                                                             => ( ( setadjoin @ X1 @ X3 )
                                                                                                                = ( setadjoin @ X2 @ X4 ) ) ) )
                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                            ( ( X1 = X2 )
                                                                                                           => ( ( powerset @ X1 )
                                                                                                              = ( powerset @ X2 ) ) )
                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                              ( ( X1 = X2 )
                                                                                                             => ( ( setunion @ X1 )
                                                                                                                = ( setunion @ X2 ) ) )
                                                                                                         => ( ! [X1: $i > $o] :
                                                                                                                ( ~ ! [X2: $i] :
                                                                                                                      ( ( X1 @ X2 )
                                                                                                                     => ~ ! [X3: $i] :
                                                                                                                            ( ( X1 @ X3 )
                                                                                                                           => ( X2 = X3 ) ) )
                                                                                                               => ! [X2: $i,X3: $i] :
                                                                                                                    ( ( X1 @ X2 )
                                                                                                                   => ( ( X1 @ X3 )
                                                                                                                     => ( X2 = X3 ) ) ) )
                                                                                                           => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                                                  ( ! [X3: $i,X4: $i] :
                                                                                                                      ( ( X3 = X4 )
                                                                                                                     => ( ( X1 @ X3 )
                                                                                                                        = ( X2 @ X4 ) ) )
                                                                                                                 => ( ~ ! [X3: $i] :
                                                                                                                          ( ( X1 @ X3 )
                                                                                                                         => ~ ! [X4: $i] :
                                                                                                                                ( ( X1 @ X4 )
                                                                                                                               => ( X3 = X4 ) ) )
                                                                                                                   => ( ~ ! [X3: $i] :
                                                                                                                            ( ( X2 @ X3 )
                                                                                                                           => ~ ! [X4: $i] :
                                                                                                                                  ( ( X2 @ X4 )
                                                                                                                                 => ( X3 = X4 ) ) )
                                                                                                                     => ( ( descr @ X1 )
                                                                                                                        = ( descr @ X2 ) ) ) ) )
                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                    ( ( X1 = X2 )
                                                                                                                   => ! [X3: $i > $o,X4: $i > $o] :
                                                                                                                        ( ! [X5: $i] :
                                                                                                                            ( ( in @ X5 @ X1 )
                                                                                                                           => ! [X6: $i] :
                                                                                                                                ( ( in @ X6 @ X2 )
                                                                                                                               => ( ( X5 = X6 )
                                                                                                                                 => ( ( X3 @ X5 )
                                                                                                                                    = ( X4 @ X6 ) ) ) ) )
                                                                                                                       => ( ( dsetconstr @ X1 @ X3 )
                                                                                                                          = ( dsetconstr @ X2 @ X4 ) ) ) )
                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                      ( ! [X3: $i] :
                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                         => ( in @ X3 @ X2 ) )
                                                                                                                     => ( subset @ X1 @ X2 ) )
                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                        ( ( X1 = X2 )
                                                                                                                       => ( subset @ X2 @ X1 ) )
                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                          ( ( X1 = X2 )
                                                                                                                         => ( subset @ X1 @ X2 ) )
                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                            ( ! [X3: $i] :
                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                               => ( in @ X3 @ X2 ) )
                                                                                                                           => ( subset @ X1 @ X2 ) )
                                                                                                                       => ( ! [X1: $i] : ( subset @ emptyset @ X1 )
                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                ( ( subset @ X1 @ X2 )
                                                                                                                               => ( ( in @ X3 @ X1 )
                                                                                                                                 => ( in @ X3 @ X2 ) ) )
                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                  ( ( subset @ X1 @ X2 )
                                                                                                                                 => ( ~ ( in @ X3 @ X2 )
                                                                                                                                   => ~ ( in @ X3 @ X1 ) ) )
                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                   => ( ~ ( in @ X3 @ X2 )
                                                                                                                                     => ~ ( subset @ X1 @ X2 ) ) )
                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                      ( ~ ( subset @ X1 @ X2 )
                                                                                                                                     => ( X1 != X2 ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                       => ( ~ ( in @ X3 @ X2 )
                                                                                                                                         => ( X1 != X2 ) ) )
                                                                                                                                   => ( ! [X1: $i] : ( subset @ X1 @ X1 )
                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                            ( ( subset @ X1 @ X2 )
                                                                                                                                           => ( ( subset @ X2 @ X3 )
                                                                                                                                             => ( subset @ X1 @ X3 ) ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) )
                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                ( ( subset @ X1 @ X3 )
                                                                                                                                               => ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                  ( ( subset @ X1 @ X2 )
                                                                                                                                                 => ( in @ X1 @ ( powerset @ X2 ) ) )
                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                    ( ( subset @ X1 @ X2 )
                                                                                                                                                   => ( ( subset @ X2 @ X1 )
                                                                                                                                                     => ( X1 = X2 ) ) )
                                                                                                                                               => ( ! [X1: $i] :
                                                                                                                                                      ( ( subset @ X1 @ emptyset )
                                                                                                                                                     => ( X1 = emptyset ) )
                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                        ( ( subset @ X2 @ X1 )
                                                                                                                                                       => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                          ( ( in @ X2 @ ( powerset @ X1 ) )
                                                                                                                                                         => ( subset @ X2 @ X1 ) )
                                                                                                                                                     => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                              ( ( subset @ X1 @ X2 )
                                                                                                                                                             => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
                                                                                                                                                         => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                                                                                                                                                           => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                   => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                                                                               => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                        ( ( in @ X3 @ X2 )
                                                                                                                                                                       => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                                                                                                                                                          ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                                         => ( ( ( in @ X3 @ X1 )
                                                                                                                                                                             => X4 )
                                                                                                                                                                           => ( ( ( in @ X3 @ X2 )
                                                                                                                                                                               => X4 )
                                                                                                                                                                             => X4 ) ) )
                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                            ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                                           => ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                             => ( in @ X3 @ X2 ) ) )
                                                                                                                                                                       => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                                         => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                 => ( ( in @ X3 @ X2 )
                                                                                                                                                                                   => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                    ( ( subset @ X3 @ X1 )
                                                                                                                                                                                   => ( ( subset @ X3 @ X2 )
                                                                                                                                                                                     => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                      ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                                                                     => ( in @ X3 @ X1 ) )
                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                          ( ( subset @ X1 @ X2 )
                                                                                                                                                                                         => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                            = X1 ) )
                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                            ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                              = X2 )
                                                                                                                                                                                           => ( subset @ X2 @ X1 ) )
                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                              ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                                                                             => ( in @ X3 @ X2 ) )
                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                ( ! [X3: $i] :
                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                   => ~ ( in @ X3 @ X2 ) )
                                                                                                                                                                                               => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                                  = emptyset ) )
                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                    ( ( subset @ X2 @ X1 )
                                                                                                                                                                                                   => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                                      = X2 ) )
                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                      ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                                        = X1 )
                                                                                                                                                                                                     => ( subset @ X1 @ X2 ) )
                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                        ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                                                                                                                                                                        = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                         => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                           => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                            ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                           => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                              ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                             => ~ ( in @ X3 @ X2 ) )
                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                ( ( subset @ X1 @ X2 )
                                                                                                                                                                                                               => ( ( setminus @ X1 @ X2 )
                                                                                                                                                                                                                  = emptyset ) )
                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                  ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                                 => ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                   => ( in @ X3 @ X2 ) ) )
                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                    ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                                   => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                     => ~ ( in @ X3 @ X1 ) ) )
                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                      ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                     => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                        ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                       => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                            ( ( ( setminus @ X1 @ X2 )
                                                                                                                                                                                                                              = emptyset )
                                                                                                                                                                                                                           => ( subset @ X1 @ X2 ) )
                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                              ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                                                                                                                                                             => ! [X4: $o] :
                                                                                                                                                                                                                                  ( ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                   => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                                     => X4 ) )
                                                                                                                                                                                                                                 => ( ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                                     => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                                       => X4 ) )
                                                                                                                                                                                                                                   => X4 ) ) )
                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                               => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                                 => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                  ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                                 => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                                   => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                   => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                                     => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                      ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                                     => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                                       => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                  ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                                 => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                    ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                                   => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                     => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                        ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                                       => ( ( X3 != X1 )
                                                                                                                                                                                                                                                         => ( X3 = X2 ) ) )
                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                             => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                               => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                 => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                   => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                     => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                       => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                      ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                     => ~ ! [X4: $i] :
                                                                                                                                                                                                                                                                            ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                           => ! [X5: $i] :
                                                                                                                                                                                                                                                                                ( ( in @ X5 @ X2 )
                                                                                                                                                                                                                                                                               => ( X3
                                                                                                                                                                                                                                                                                 != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                                                                                                                                                                 => ( sP5
                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                          ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                                                                                                                                                                         => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                               => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                                                                                                                                                                     => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                                                                                                                                                                       => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                                                                         => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                                                                                                                                                                = X1 )
                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                                                  ( ! [X3: $i] :
                                                                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                                                                                                                                          ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                                         => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                                                           => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                                             => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                                                                                 => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                         => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                                                                                   => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                          ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                         => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                                           != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                                                    ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                          ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                         => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                                           != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                   => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                         => ~ ( X2 @ X3 ) ) )
                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                     => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                                                       => ( ! [X4: $i] :
                                                                                                                                                                                                                                                                                              ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                                             => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                                               => ( X4 = X3 ) ) )
                                                                                                                                                                                                                                                                                         => ~ ! [X4: $i] :
                                                                                                                                                                                                                                                                                                ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                               => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                 != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                                                        ( ! [X3: $i] :
                                                                                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                                               => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                                                                 => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                                                   => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                                                                                       => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                               => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                                                                                         => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                                ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                               => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                 != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                          ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                                                                                                                                                            = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                                         => ( X1 = X2 ) )
                                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                            ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                           => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                                       => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                              ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                                                             => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                                    ( ( in @ X2
                                                                                                                                                                                                                                                                                                      @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                        @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                                                                                                                                                                   => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                        @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                                                                                                     != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                                                                         => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                                ( ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                                      ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                                                                                     => ( X1
                                                                                                                                                                                                                                                                                                       != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                               => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                  ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                  = X1 )
                                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                    ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                   => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                      ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                        = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                     => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                        ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                          = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                       => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                          ( ( X1 = X2 )
                                                                                                                                                                                                                                                                                                         => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                                                            = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                            ( ( X1 = X2 )
                                                                                                                                                                                                                                                                                                           => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                              = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                              ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                                = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                             => ( ( X3 = X4 )
                                                                                                                                                                                                                                                                                                               => ( X2 = X4 ) ) )
                                                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                                                                  = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                                                                                                                                                               => ( X1 = X2 ) )
                                                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                  ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                                    = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                 => ( X2 = X4 ) )
                                                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                    ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                                      = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                                   => ( X2 = X4 ) )
                                                                                                                                                                                                                                                                                                               => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                                                      ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                                                                                     => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                                                            ( ( in @ X2
                                                                                                                                                                                                                                                                                                                              @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                                                @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                                                                                    ( X1
                                                                                                                                                                                                                                                                                                                                    = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                                                                                                                                                           => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                                                @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                                                                                    ( X1
                                                                                                                                                                                                                                                                                                                                    = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                                                                                                                                                             != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                                        ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                        = X2 )
                                                                                                                                                                                                                                                                                                                   => ( sP8
                                                                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                            ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                           => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                              ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                             => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                                ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                               => ( in @ X4 @ X2 ) )
                                                                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                                                                     => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                                                        = X3 ) ) )
                                                                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                                                                       => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                                                          = X4 ) ) )
                                                                                                                                                                                                                                                                                                                               => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                                    ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                                   => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                                                                                                                                                                      = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h23,assumption,
    ! [X1: $i > $o] :
      ( ~ ! [X2: $i] :
            ( ( X1 @ X2 )
           => ~ ! [X3: $i] :
                  ( ( X1 @ X3 )
                 => ( X2 = X3 ) ) )
     => ( X1 @ ( descr @ X1 ) ) ),
    introduced(assumption,[]) ).

thf(h24,assumption,
    ~ ( ! [X1: $i,X2: $i > $o,X3: $i] :
          ( ( in @ X3 @ X1 )
         => ( ( X2 @ X3 )
           => ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) ) ) )
     => ( ! [X1: $i,X2: $i > $o,X3: $i] :
            ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
           => ( in @ X3 @ X1 ) )
       => ( ! [X1: $i,X2: $i > $o,X3: $i] :
              ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
             => ( X2 @ X3 ) )
         => ( ! [X1: $o,X2: $i] :
                ( ( in @ X2 @ ( prop2set @ X1 ) )
               => X1 )
           => ( ! [X1: $i] :
                  ( ( in @ X1 @ emptyset )
                 => ! [X2: $o] : X2 )
             => ( ! [X1: $i] :
                    ~ ( in @ X1 @ emptyset )
               => ( ! [X1: $i] :
                      ~ ( in @ X1 @ emptyset )
                 => ( ! [X1: $i > $o] :
                        ( ~ ! [X2: $i] :
                              ( ( X1 @ X2 )
                             => ~ ! [X3: $i] :
                                    ( ( X1 @ X3 )
                                   => ( X2 = X3 ) ) )
                       => ~ ! [X2: $i] :
                              ~ ( X1 @ X2 ) )
                   => ( ! [X1: $i,X2: $i] :
                          ( ! [X3: $i] :
                              ( ( in @ X3 @ X1 )
                             => ( in @ X3 @ X2 ) )
                         => ( ! [X3: $i] :
                                ( ( in @ X3 @ X2 )
                               => ( in @ X3 @ X1 ) )
                           => ( X1 = X2 ) ) )
                     => ( ! [X1: $i] :
                            ( ! [X2: $i] :
                                ~ ( in @ X2 @ X1 )
                           => ( X1 = emptyset ) )
                       => ( ! [X1: $i] :
                              ( ! [X2: $i] :
                                  ~ ( in @ X2 @ X1 )
                             => ( X1 = emptyset ) )
                         => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                ( ( in @ X3 @ X1 )
                               => ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                  = ( X2 @ X3 ) ) )
                           => ( ! [X1: $i] :
                                  ( ( X1 != emptyset )
                                 => ~ ! [X2: $i] :
                                        ~ ( in @ X2 @ X1 ) )
                             => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                    ( ( in @ X3 @ X1 )
                                   => ( ( X2 @ X3 )
                                     => ( ( dsetconstr @ X1 @ X2 )
                                       != emptyset ) ) )
                               => ( ! [X1: $i] :
                                      ( ~ ! [X2: $i] :
                                            ~ ( in @ X2 @ X1 )
                                     => ( X1 != emptyset ) )
                                 => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) )
                                   => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                            ( ( in @ X3 @ X2 )
                                           => ( in @ X3 @ ( setadjoin @ X1 @ X2 ) ) )
                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                              ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                             => ! [X4: $o] :
                                                  ( ( ( X3 = X1 )
                                                   => X4 )
                                                 => ( ( ( in @ X3 @ X2 )
                                                     => X4 )
                                                   => X4 ) ) )
                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                               => ( ( X3 != X1 )
                                                 => ( in @ X3 @ X2 ) ) )
                                           => ( ! [X1: $i] :
                                                  ( ( dsetconstr @ X1
                                                    @ ^ [X2: $i] : ~ $false )
                                                  = X1 )
                                             => ( ! [X1: $i,X2: $i] :
                                                    ( ! [X3: $i] :
                                                        ( ( in @ X3 @ X2 )
                                                       => ( in @ X3 @ X1 ) )
                                                   => ( in @ X2 @ ( powerset @ X1 ) ) )
                                               => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                                 => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                          ( ( in @ X2 @ ( powerset @ X1 ) )
                                                         => ( ( in @ X3 @ X2 )
                                                           => ( in @ X3 @ X1 ) ) )
                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                            ( ( in @ X2 @ X3 )
                                                           => ( ( in @ X3 @ X1 )
                                                             => ( in @ X2 @ ( setunion @ X1 ) ) ) )
                                                       => ( ! [X1: $i,X2: $i] :
                                                              ( ( in @ X2 @ ( setunion @ X1 ) )
                                                             => ! [X3: $o] :
                                                                  ( ! [X4: $i] :
                                                                      ( ( in @ X2 @ X4 )
                                                                     => ( ( in @ X4 @ X1 )
                                                                       => X3 ) )
                                                                 => X3 ) )
                                                         => ( ! [X1: $i,X2: $i] :
                                                                ( ( in @ X2 @ X1 )
                                                               => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
                                                           => ( ! [X1: $i > $o] :
                                                                  ( ~ ! [X2: $i] :
                                                                        ( ( X1 @ X2 )
                                                                       => ~ ! [X3: $i] :
                                                                              ( ( X1 @ X3 )
                                                                             => ( X2 = X3 ) ) )
                                                                 => ~ ! [X2: $i] :
                                                                        ~ ! [X3: $i] :
                                                                            ( ( X1 @ X3 )
                                                                            = ( X3 = X2 ) ) )
                                                             => ( ! [X1: $i] :
                                                                    ( ( X1 != emptyset )
                                                                   => ~ ! [X2: $i] :
                                                                          ~ ( in @ X2 @ X1 ) )
                                                               => ( ! [X1: $i,X2: $i] :
                                                                      ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                     => ( X1 = X2 ) )
                                                                 => ( ! [X1: $i,X2: $i] :
                                                                        ( ( X1 != X2 )
                                                                       => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                   => ( ! [X1: $i,X2: $i] :
                                                                          ( ( X1 = X2 )
                                                                         => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                     => ( ! [X1: $i,X2: $i] :
                                                                            ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                           => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                              ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                             => ( ( X3 != X1 )
                                                                               => ( X3 = X2 ) ) )
                                                                         => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                           => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                             => ( ! [X1: $i,X2: $i > $o] :
                                                                                    ( ~ ! [X3: $i] :
                                                                                          ( ( in @ X3 @ X1 )
                                                                                         => ~ ( X2 @ X3 ) )
                                                                                   => ( ( dsetconstr @ X1 @ X2 )
                                                                                     != emptyset ) )
                                                                               => ( ! [X1: $i > $o,X2: $i] :
                                                                                      ( ( in @ X2 @ emptyset )
                                                                                     => ( X1 @ X2 ) )
                                                                                 => ( ! [X1: $o] :
                                                                                        ( X1
                                                                                       => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                                                                   => ( ! [X1: $o] :
                                                                                          ( X1
                                                                                         => ( set2prop @ ( prop2set @ X1 ) ) )
                                                                                     => ( ! [X1: $i > $o] :
                                                                                            ( ~ ! [X2: $i] :
                                                                                                  ~ ( X1 @ X2 )
                                                                                           => ( ! [X2: $i,X3: $i] :
                                                                                                  ( ( X1 @ X2 )
                                                                                                 => ( ( X1 @ X3 )
                                                                                                   => ( X2 = X3 ) ) )
                                                                                             => ~ ! [X2: $i] :
                                                                                                    ( ( X1 @ X2 )
                                                                                                   => ~ ! [X3: $i] :
                                                                                                          ( ( X1 @ X3 )
                                                                                                         => ( X2 = X3 ) ) ) ) )
                                                                                       => ( ! [X1: $i > $o] :
                                                                                              ( ~ ! [X2: $i] :
                                                                                                    ~ ! [X3: $i] :
                                                                                                        ( ( X1 @ X3 )
                                                                                                        = ( X3 = X2 ) )
                                                                                             => ~ ! [X2: $i] :
                                                                                                    ( ( X1 @ X2 )
                                                                                                   => ~ ! [X3: $i] :
                                                                                                          ( ( X1 @ X3 )
                                                                                                         => ( X2 = X3 ) ) ) )
                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                ( ( X1 = X2 )
                                                                                               => ! [X3: $i,X4: $i] :
                                                                                                    ( ( X3 = X4 )
                                                                                                   => ( ( in @ X3 @ X1 )
                                                                                                     => ( in @ X4 @ X2 ) ) ) )
                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                  ( ( X1 = X2 )
                                                                                                 => ! [X3: $i,X4: $i] :
                                                                                                      ( ( X3 = X4 )
                                                                                                     => ( ( in @ X3 @ X1 )
                                                                                                        = ( in @ X4 @ X2 ) ) ) )
                                                                                             => ( ! [X1: $i > $o] :
                                                                                                    ( ~ ! [X2: $i] :
                                                                                                          ( ( X1 @ X2 )
                                                                                                         => ~ ! [X3: $i] :
                                                                                                                ( ( X1 @ X3 )
                                                                                                               => ( X2 = X3 ) ) )
                                                                                                   => ! [X2: $i,X3: $i] :
                                                                                                        ( ( X1 @ X2 )
                                                                                                       => ( ( X1 @ X3 )
                                                                                                         => ( X2 = X3 ) ) ) )
                                                                                               => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                                      ( ! [X3: $i,X4: $i] :
                                                                                                          ( ( X3 = X4 )
                                                                                                         => ( ( X1 @ X3 )
                                                                                                            = ( X2 @ X4 ) ) )
                                                                                                     => ( ( ~ ! [X3: $i] :
                                                                                                                ( ( X1 @ X3 )
                                                                                                               => ~ ! [X4: $i] :
                                                                                                                      ( ( X1 @ X4 )
                                                                                                                     => ( X3 = X4 ) ) ) )
                                                                                                        = ( ~ ! [X3: $i] :
                                                                                                                ( ( X2 @ X3 )
                                                                                                               => ~ ! [X4: $i] :
                                                                                                                      ( ( X2 @ X4 )
                                                                                                                     => ( X3 = X4 ) ) ) ) ) )
                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                        ( ( X1 = X2 )
                                                                                                       => ! [X3: $i,X4: $i] :
                                                                                                            ( ( X3 = X4 )
                                                                                                           => ( ( setadjoin @ X1 @ X3 )
                                                                                                              = ( setadjoin @ X2 @ X4 ) ) ) )
                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                          ( ( X1 = X2 )
                                                                                                         => ( ( powerset @ X1 )
                                                                                                            = ( powerset @ X2 ) ) )
                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                            ( ( X1 = X2 )
                                                                                                           => ( ( setunion @ X1 )
                                                                                                              = ( setunion @ X2 ) ) )
                                                                                                       => ( ! [X1: $i > $o] :
                                                                                                              ( ~ ! [X2: $i] :
                                                                                                                    ( ( X1 @ X2 )
                                                                                                                   => ~ ! [X3: $i] :
                                                                                                                          ( ( X1 @ X3 )
                                                                                                                         => ( X2 = X3 ) ) )
                                                                                                             => ! [X2: $i,X3: $i] :
                                                                                                                  ( ( X1 @ X2 )
                                                                                                                 => ( ( X1 @ X3 )
                                                                                                                   => ( X2 = X3 ) ) ) )
                                                                                                         => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                                                ( ! [X3: $i,X4: $i] :
                                                                                                                    ( ( X3 = X4 )
                                                                                                                   => ( ( X1 @ X3 )
                                                                                                                      = ( X2 @ X4 ) ) )
                                                                                                               => ( ~ ! [X3: $i] :
                                                                                                                        ( ( X1 @ X3 )
                                                                                                                       => ~ ! [X4: $i] :
                                                                                                                              ( ( X1 @ X4 )
                                                                                                                             => ( X3 = X4 ) ) )
                                                                                                                 => ( ~ ! [X3: $i] :
                                                                                                                          ( ( X2 @ X3 )
                                                                                                                         => ~ ! [X4: $i] :
                                                                                                                                ( ( X2 @ X4 )
                                                                                                                               => ( X3 = X4 ) ) )
                                                                                                                   => ( ( descr @ X1 )
                                                                                                                      = ( descr @ X2 ) ) ) ) )
                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                  ( ( X1 = X2 )
                                                                                                                 => ! [X3: $i > $o,X4: $i > $o] :
                                                                                                                      ( ! [X5: $i] :
                                                                                                                          ( ( in @ X5 @ X1 )
                                                                                                                         => ! [X6: $i] :
                                                                                                                              ( ( in @ X6 @ X2 )
                                                                                                                             => ( ( X5 = X6 )
                                                                                                                               => ( ( X3 @ X5 )
                                                                                                                                  = ( X4 @ X6 ) ) ) ) )
                                                                                                                     => ( ( dsetconstr @ X1 @ X3 )
                                                                                                                        = ( dsetconstr @ X2 @ X4 ) ) ) )
                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                    ( ! [X3: $i] :
                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                       => ( in @ X3 @ X2 ) )
                                                                                                                   => ( subset @ X1 @ X2 ) )
                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                      ( ( X1 = X2 )
                                                                                                                     => ( subset @ X2 @ X1 ) )
                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                        ( ( X1 = X2 )
                                                                                                                       => ( subset @ X1 @ X2 ) )
                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                          ( ! [X3: $i] :
                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                             => ( in @ X3 @ X2 ) )
                                                                                                                         => ( subset @ X1 @ X2 ) )
                                                                                                                     => ( ! [X1: $i] : ( subset @ emptyset @ X1 )
                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                              ( ( subset @ X1 @ X2 )
                                                                                                                             => ( ( in @ X3 @ X1 )
                                                                                                                               => ( in @ X3 @ X2 ) ) )
                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                ( ( subset @ X1 @ X2 )
                                                                                                                               => ( ~ ( in @ X3 @ X2 )
                                                                                                                                 => ~ ( in @ X3 @ X1 ) ) )
                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                 => ( ~ ( in @ X3 @ X2 )
                                                                                                                                   => ~ ( subset @ X1 @ X2 ) ) )
                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                    ( ~ ( subset @ X1 @ X2 )
                                                                                                                                   => ( X1 != X2 ) )
                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                     => ( ~ ( in @ X3 @ X2 )
                                                                                                                                       => ( X1 != X2 ) ) )
                                                                                                                                 => ( ! [X1: $i] : ( subset @ X1 @ X1 )
                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                          ( ( subset @ X1 @ X2 )
                                                                                                                                         => ( ( subset @ X2 @ X3 )
                                                                                                                                           => ( subset @ X1 @ X3 ) ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                              ( ( subset @ X1 @ X3 )
                                                                                                                                             => ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                ( ( subset @ X1 @ X2 )
                                                                                                                                               => ( in @ X1 @ ( powerset @ X2 ) ) )
                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                  ( ( subset @ X1 @ X2 )
                                                                                                                                                 => ( ( subset @ X2 @ X1 )
                                                                                                                                                   => ( X1 = X2 ) ) )
                                                                                                                                             => ( ! [X1: $i] :
                                                                                                                                                    ( ( subset @ X1 @ emptyset )
                                                                                                                                                   => ( X1 = emptyset ) )
                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                      ( ( subset @ X2 @ X1 )
                                                                                                                                                     => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                        ( ( in @ X2 @ ( powerset @ X1 ) )
                                                                                                                                                       => ( subset @ X2 @ X1 ) )
                                                                                                                                                   => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                            ( ( subset @ X1 @ X2 )
                                                                                                                                                           => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
                                                                                                                                                       => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                                                                                                                                                         => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                 => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                                                                             => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                      ( ( in @ X3 @ X2 )
                                                                                                                                                                     => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                                                                                                                                                        ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                                       => ( ( ( in @ X3 @ X1 )
                                                                                                                                                                           => X4 )
                                                                                                                                                                         => ( ( ( in @ X3 @ X2 )
                                                                                                                                                                             => X4 )
                                                                                                                                                                           => X4 ) ) )
                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                          ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                                         => ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                           => ( in @ X3 @ X2 ) ) )
                                                                                                                                                                     => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                                       => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                               => ( ( in @ X3 @ X2 )
                                                                                                                                                                                 => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                  ( ( subset @ X3 @ X1 )
                                                                                                                                                                                 => ( ( subset @ X3 @ X2 )
                                                                                                                                                                                   => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                    ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                                                                   => ( in @ X3 @ X1 ) )
                                                                                                                                                                               => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                        ( ( subset @ X1 @ X2 )
                                                                                                                                                                                       => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                          = X1 ) )
                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                          ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                            = X2 )
                                                                                                                                                                                         => ( subset @ X2 @ X1 ) )
                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                            ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                                                                           => ( in @ X3 @ X2 ) )
                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                              ( ! [X3: $i] :
                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                 => ~ ( in @ X3 @ X2 ) )
                                                                                                                                                                                             => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                                = emptyset ) )
                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                  ( ( subset @ X2 @ X1 )
                                                                                                                                                                                                 => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                                    = X2 ) )
                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                    ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                                      = X1 )
                                                                                                                                                                                                   => ( subset @ X1 @ X2 ) )
                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                      ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                                                                                                                                                                      = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                       => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                         => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                          ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                         => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                            ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                           => ~ ( in @ X3 @ X2 ) )
                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                              ( ( subset @ X1 @ X2 )
                                                                                                                                                                                                             => ( ( setminus @ X1 @ X2 )
                                                                                                                                                                                                                = emptyset ) )
                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                               => ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                 => ( in @ X3 @ X2 ) ) )
                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                  ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                                 => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                   => ~ ( in @ X3 @ X1 ) ) )
                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                    ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                   => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                      ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                     => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                          ( ( ( setminus @ X1 @ X2 )
                                                                                                                                                                                                                            = emptyset )
                                                                                                                                                                                                                         => ( subset @ X1 @ X2 ) )
                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                            ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                                                                                                                                                           => ! [X4: $o] :
                                                                                                                                                                                                                                ( ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                 => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                                   => X4 ) )
                                                                                                                                                                                                                               => ( ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                                   => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                                     => X4 ) )
                                                                                                                                                                                                                                 => X4 ) ) )
                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                             => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                               => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                               => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                                 => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                 => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                                   => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                    ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                                   => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                                     => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                               => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                  ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                                 => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                   => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                      ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                                     => ( ( X3 != X1 )
                                                                                                                                                                                                                                                       => ( X3 = X2 ) ) )
                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                           => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                             => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                               => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                 => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                   => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                     => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                    ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                   => ~ ! [X4: $i] :
                                                                                                                                                                                                                                                                          ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                         => ! [X5: $i] :
                                                                                                                                                                                                                                                                              ( ( in @ X5 @ X2 )
                                                                                                                                                                                                                                                                             => ( X3
                                                                                                                                                                                                                                                                               != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                                                                                                                                                               => ( sP5
                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                        ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                                                                                                                                                                       => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                             => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                                                                                                                                                                   => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                                                                                                                                                                     => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                                                                       => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                              ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                                                                                                                                                              = X1 )
                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                                                ( ! [X3: $i] :
                                                                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                                                                                                                                        ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                                       => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                                                         => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                                           => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                                                                               => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                       => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                                                                                 => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                        ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                       => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                                         != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                                                  ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                        ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                       => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                                         != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                 => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                       => ~ ( X2 @ X3 ) ) )
                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                   => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                                                     => ( ! [X4: $i] :
                                                                                                                                                                                                                                                                                            ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                                           => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                                             => ( X4 = X3 ) ) )
                                                                                                                                                                                                                                                                                       => ~ ! [X4: $i] :
                                                                                                                                                                                                                                                                                              ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                             => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                                               != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                                                      ( ! [X3: $i] :
                                                                                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                                                                                                                                              ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                                             => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                                                               => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                                                 => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                                                                                     => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                             => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                                                                                       => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                              ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                             => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                                               != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                        ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                                                                                                                                                          = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                                       => ( X1 = X2 ) )
                                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                          ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                         => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                                     => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                            ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                                                           => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                                  ( ( in @ X2
                                                                                                                                                                                                                                                                                                    @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                      @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                                                                                                                                                                 => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                      @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                                                                                                   != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                                                                       => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                              ( ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                                    ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                                                                                   => ( X1
                                                                                                                                                                                                                                                                                                     != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                             => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                = X1 )
                                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                  ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                 => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                    ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                      = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                   => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                      ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                        = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                     => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                        ( ( X1 = X2 )
                                                                                                                                                                                                                                                                                                       => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                                                          = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                          ( ( X1 = X2 )
                                                                                                                                                                                                                                                                                                         => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                            = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                            ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                              = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                           => ( ( X3 = X4 )
                                                                                                                                                                                                                                                                                                             => ( X2 = X4 ) ) )
                                                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                              ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                                                                = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                                                                                                                                                             => ( X1 = X2 ) )
                                                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                                  = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                               => ( X2 = X4 ) )
                                                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                  ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                                    = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                                 => ( X2 = X4 ) )
                                                                                                                                                                                                                                                                                                             => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                                                    ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                                                                                   => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                                                          ( ( in @ X2
                                                                                                                                                                                                                                                                                                                            @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                                              @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                                                                                  ( X1
                                                                                                                                                                                                                                                                                                                                  = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                                                                                                                                                         => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                                              @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                                                                                  ( X1
                                                                                                                                                                                                                                                                                                                                  = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                                                                                                                                                           != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                                      ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                      = X2 )
                                                                                                                                                                                                                                                                                                                 => ( sP8
                                                                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                         => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                            ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                           => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                              ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                             => ( in @ X4 @ X2 ) )
                                                                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                                                                   => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                                                      = X3 ) ) )
                                                                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                                                                     => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                                                        = X4 ) ) )
                                                                                                                                                                                                                                                                                                                             => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                                  ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                                 => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                                                                                                                                                                    = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h25,assumption,
    ! [X1: $i,X2: $i > $o,X3: $i] :
      ( ( in @ X3 @ X1 )
     => ( ( X2 @ X3 )
       => ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) ) ) ),
    introduced(assumption,[]) ).

thf(h26,assumption,
    ~ ( ! [X1: $i,X2: $i > $o,X3: $i] :
          ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
         => ( in @ X3 @ X1 ) )
     => ( ! [X1: $i,X2: $i > $o,X3: $i] :
            ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
           => ( X2 @ X3 ) )
       => ( ! [X1: $o,X2: $i] :
              ( ( in @ X2 @ ( prop2set @ X1 ) )
             => X1 )
         => ( ! [X1: $i] :
                ( ( in @ X1 @ emptyset )
               => ! [X2: $o] : X2 )
           => ( ! [X1: $i] :
                  ~ ( in @ X1 @ emptyset )
             => ( ! [X1: $i] :
                    ~ ( in @ X1 @ emptyset )
               => ( ! [X1: $i > $o] :
                      ( ~ ! [X2: $i] :
                            ( ( X1 @ X2 )
                           => ~ ! [X3: $i] :
                                  ( ( X1 @ X3 )
                                 => ( X2 = X3 ) ) )
                     => ~ ! [X2: $i] :
                            ~ ( X1 @ X2 ) )
                 => ( ! [X1: $i,X2: $i] :
                        ( ! [X3: $i] :
                            ( ( in @ X3 @ X1 )
                           => ( in @ X3 @ X2 ) )
                       => ( ! [X3: $i] :
                              ( ( in @ X3 @ X2 )
                             => ( in @ X3 @ X1 ) )
                         => ( X1 = X2 ) ) )
                   => ( ! [X1: $i] :
                          ( ! [X2: $i] :
                              ~ ( in @ X2 @ X1 )
                         => ( X1 = emptyset ) )
                     => ( ! [X1: $i] :
                            ( ! [X2: $i] :
                                ~ ( in @ X2 @ X1 )
                           => ( X1 = emptyset ) )
                       => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                              ( ( in @ X3 @ X1 )
                             => ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                = ( X2 @ X3 ) ) )
                         => ( ! [X1: $i] :
                                ( ( X1 != emptyset )
                               => ~ ! [X2: $i] :
                                      ~ ( in @ X2 @ X1 ) )
                           => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                  ( ( in @ X3 @ X1 )
                                 => ( ( X2 @ X3 )
                                   => ( ( dsetconstr @ X1 @ X2 )
                                     != emptyset ) ) )
                             => ( ! [X1: $i] :
                                    ( ~ ! [X2: $i] :
                                          ~ ( in @ X2 @ X1 )
                                   => ( X1 != emptyset ) )
                               => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) )
                                 => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                          ( ( in @ X3 @ X2 )
                                         => ( in @ X3 @ ( setadjoin @ X1 @ X2 ) ) )
                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                            ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                           => ! [X4: $o] :
                                                ( ( ( X3 = X1 )
                                                 => X4 )
                                               => ( ( ( in @ X3 @ X2 )
                                                   => X4 )
                                                 => X4 ) ) )
                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                              ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                             => ( ( X3 != X1 )
                                               => ( in @ X3 @ X2 ) ) )
                                         => ( ! [X1: $i] :
                                                ( ( dsetconstr @ X1
                                                  @ ^ [X2: $i] : ~ $false )
                                                = X1 )
                                           => ( ! [X1: $i,X2: $i] :
                                                  ( ! [X3: $i] :
                                                      ( ( in @ X3 @ X2 )
                                                     => ( in @ X3 @ X1 ) )
                                                 => ( in @ X2 @ ( powerset @ X1 ) ) )
                                             => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                               => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                        ( ( in @ X2 @ ( powerset @ X1 ) )
                                                       => ( ( in @ X3 @ X2 )
                                                         => ( in @ X3 @ X1 ) ) )
                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                          ( ( in @ X2 @ X3 )
                                                         => ( ( in @ X3 @ X1 )
                                                           => ( in @ X2 @ ( setunion @ X1 ) ) ) )
                                                     => ( ! [X1: $i,X2: $i] :
                                                            ( ( in @ X2 @ ( setunion @ X1 ) )
                                                           => ! [X3: $o] :
                                                                ( ! [X4: $i] :
                                                                    ( ( in @ X2 @ X4 )
                                                                   => ( ( in @ X4 @ X1 )
                                                                     => X3 ) )
                                                               => X3 ) )
                                                       => ( ! [X1: $i,X2: $i] :
                                                              ( ( in @ X2 @ X1 )
                                                             => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
                                                         => ( ! [X1: $i > $o] :
                                                                ( ~ ! [X2: $i] :
                                                                      ( ( X1 @ X2 )
                                                                     => ~ ! [X3: $i] :
                                                                            ( ( X1 @ X3 )
                                                                           => ( X2 = X3 ) ) )
                                                               => ~ ! [X2: $i] :
                                                                      ~ ! [X3: $i] :
                                                                          ( ( X1 @ X3 )
                                                                          = ( X3 = X2 ) ) )
                                                           => ( ! [X1: $i] :
                                                                  ( ( X1 != emptyset )
                                                                 => ~ ! [X2: $i] :
                                                                        ~ ( in @ X2 @ X1 ) )
                                                             => ( ! [X1: $i,X2: $i] :
                                                                    ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                   => ( X1 = X2 ) )
                                                               => ( ! [X1: $i,X2: $i] :
                                                                      ( ( X1 != X2 )
                                                                     => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                 => ( ! [X1: $i,X2: $i] :
                                                                        ( ( X1 = X2 )
                                                                       => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                   => ( ! [X1: $i,X2: $i] :
                                                                          ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                         => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                            ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                           => ( ( X3 != X1 )
                                                                             => ( X3 = X2 ) ) )
                                                                       => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                         => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                           => ( ! [X1: $i,X2: $i > $o] :
                                                                                  ( ~ ! [X3: $i] :
                                                                                        ( ( in @ X3 @ X1 )
                                                                                       => ~ ( X2 @ X3 ) )
                                                                                 => ( ( dsetconstr @ X1 @ X2 )
                                                                                   != emptyset ) )
                                                                             => ( ! [X1: $i > $o,X2: $i] :
                                                                                    ( ( in @ X2 @ emptyset )
                                                                                   => ( X1 @ X2 ) )
                                                                               => ( ! [X1: $o] :
                                                                                      ( X1
                                                                                     => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                                                                 => ( ! [X1: $o] :
                                                                                        ( X1
                                                                                       => ( set2prop @ ( prop2set @ X1 ) ) )
                                                                                   => ( ! [X1: $i > $o] :
                                                                                          ( ~ ! [X2: $i] :
                                                                                                ~ ( X1 @ X2 )
                                                                                         => ( ! [X2: $i,X3: $i] :
                                                                                                ( ( X1 @ X2 )
                                                                                               => ( ( X1 @ X3 )
                                                                                                 => ( X2 = X3 ) ) )
                                                                                           => ~ ! [X2: $i] :
                                                                                                  ( ( X1 @ X2 )
                                                                                                 => ~ ! [X3: $i] :
                                                                                                        ( ( X1 @ X3 )
                                                                                                       => ( X2 = X3 ) ) ) ) )
                                                                                     => ( ! [X1: $i > $o] :
                                                                                            ( ~ ! [X2: $i] :
                                                                                                  ~ ! [X3: $i] :
                                                                                                      ( ( X1 @ X3 )
                                                                                                      = ( X3 = X2 ) )
                                                                                           => ~ ! [X2: $i] :
                                                                                                  ( ( X1 @ X2 )
                                                                                                 => ~ ! [X3: $i] :
                                                                                                        ( ( X1 @ X3 )
                                                                                                       => ( X2 = X3 ) ) ) )
                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                              ( ( X1 = X2 )
                                                                                             => ! [X3: $i,X4: $i] :
                                                                                                  ( ( X3 = X4 )
                                                                                                 => ( ( in @ X3 @ X1 )
                                                                                                   => ( in @ X4 @ X2 ) ) ) )
                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                ( ( X1 = X2 )
                                                                                               => ! [X3: $i,X4: $i] :
                                                                                                    ( ( X3 = X4 )
                                                                                                   => ( ( in @ X3 @ X1 )
                                                                                                      = ( in @ X4 @ X2 ) ) ) )
                                                                                           => ( ! [X1: $i > $o] :
                                                                                                  ( ~ ! [X2: $i] :
                                                                                                        ( ( X1 @ X2 )
                                                                                                       => ~ ! [X3: $i] :
                                                                                                              ( ( X1 @ X3 )
                                                                                                             => ( X2 = X3 ) ) )
                                                                                                 => ! [X2: $i,X3: $i] :
                                                                                                      ( ( X1 @ X2 )
                                                                                                     => ( ( X1 @ X3 )
                                                                                                       => ( X2 = X3 ) ) ) )
                                                                                             => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                                    ( ! [X3: $i,X4: $i] :
                                                                                                        ( ( X3 = X4 )
                                                                                                       => ( ( X1 @ X3 )
                                                                                                          = ( X2 @ X4 ) ) )
                                                                                                   => ( ( ~ ! [X3: $i] :
                                                                                                              ( ( X1 @ X3 )
                                                                                                             => ~ ! [X4: $i] :
                                                                                                                    ( ( X1 @ X4 )
                                                                                                                   => ( X3 = X4 ) ) ) )
                                                                                                      = ( ~ ! [X3: $i] :
                                                                                                              ( ( X2 @ X3 )
                                                                                                             => ~ ! [X4: $i] :
                                                                                                                    ( ( X2 @ X4 )
                                                                                                                   => ( X3 = X4 ) ) ) ) ) )
                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                      ( ( X1 = X2 )
                                                                                                     => ! [X3: $i,X4: $i] :
                                                                                                          ( ( X3 = X4 )
                                                                                                         => ( ( setadjoin @ X1 @ X3 )
                                                                                                            = ( setadjoin @ X2 @ X4 ) ) ) )
                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                        ( ( X1 = X2 )
                                                                                                       => ( ( powerset @ X1 )
                                                                                                          = ( powerset @ X2 ) ) )
                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                          ( ( X1 = X2 )
                                                                                                         => ( ( setunion @ X1 )
                                                                                                            = ( setunion @ X2 ) ) )
                                                                                                     => ( ! [X1: $i > $o] :
                                                                                                            ( ~ ! [X2: $i] :
                                                                                                                  ( ( X1 @ X2 )
                                                                                                                 => ~ ! [X3: $i] :
                                                                                                                        ( ( X1 @ X3 )
                                                                                                                       => ( X2 = X3 ) ) )
                                                                                                           => ! [X2: $i,X3: $i] :
                                                                                                                ( ( X1 @ X2 )
                                                                                                               => ( ( X1 @ X3 )
                                                                                                                 => ( X2 = X3 ) ) ) )
                                                                                                       => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                                              ( ! [X3: $i,X4: $i] :
                                                                                                                  ( ( X3 = X4 )
                                                                                                                 => ( ( X1 @ X3 )
                                                                                                                    = ( X2 @ X4 ) ) )
                                                                                                             => ( ~ ! [X3: $i] :
                                                                                                                      ( ( X1 @ X3 )
                                                                                                                     => ~ ! [X4: $i] :
                                                                                                                            ( ( X1 @ X4 )
                                                                                                                           => ( X3 = X4 ) ) )
                                                                                                               => ( ~ ! [X3: $i] :
                                                                                                                        ( ( X2 @ X3 )
                                                                                                                       => ~ ! [X4: $i] :
                                                                                                                              ( ( X2 @ X4 )
                                                                                                                             => ( X3 = X4 ) ) )
                                                                                                                 => ( ( descr @ X1 )
                                                                                                                    = ( descr @ X2 ) ) ) ) )
                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                ( ( X1 = X2 )
                                                                                                               => ! [X3: $i > $o,X4: $i > $o] :
                                                                                                                    ( ! [X5: $i] :
                                                                                                                        ( ( in @ X5 @ X1 )
                                                                                                                       => ! [X6: $i] :
                                                                                                                            ( ( in @ X6 @ X2 )
                                                                                                                           => ( ( X5 = X6 )
                                                                                                                             => ( ( X3 @ X5 )
                                                                                                                                = ( X4 @ X6 ) ) ) ) )
                                                                                                                   => ( ( dsetconstr @ X1 @ X3 )
                                                                                                                      = ( dsetconstr @ X2 @ X4 ) ) ) )
                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                  ( ! [X3: $i] :
                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                     => ( in @ X3 @ X2 ) )
                                                                                                                 => ( subset @ X1 @ X2 ) )
                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                    ( ( X1 = X2 )
                                                                                                                   => ( subset @ X2 @ X1 ) )
                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                      ( ( X1 = X2 )
                                                                                                                     => ( subset @ X1 @ X2 ) )
                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                        ( ! [X3: $i] :
                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                           => ( in @ X3 @ X2 ) )
                                                                                                                       => ( subset @ X1 @ X2 ) )
                                                                                                                   => ( ! [X1: $i] : ( subset @ emptyset @ X1 )
                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                            ( ( subset @ X1 @ X2 )
                                                                                                                           => ( ( in @ X3 @ X1 )
                                                                                                                             => ( in @ X3 @ X2 ) ) )
                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                              ( ( subset @ X1 @ X2 )
                                                                                                                             => ( ~ ( in @ X3 @ X2 )
                                                                                                                               => ~ ( in @ X3 @ X1 ) ) )
                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                               => ( ~ ( in @ X3 @ X2 )
                                                                                                                                 => ~ ( subset @ X1 @ X2 ) ) )
                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                  ( ~ ( subset @ X1 @ X2 )
                                                                                                                                 => ( X1 != X2 ) )
                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                   => ( ~ ( in @ X3 @ X2 )
                                                                                                                                     => ( X1 != X2 ) ) )
                                                                                                                               => ( ! [X1: $i] : ( subset @ X1 @ X1 )
                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                        ( ( subset @ X1 @ X2 )
                                                                                                                                       => ( ( subset @ X2 @ X3 )
                                                                                                                                         => ( subset @ X1 @ X3 ) ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                            ( ( subset @ X1 @ X3 )
                                                                                                                                           => ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                              ( ( subset @ X1 @ X2 )
                                                                                                                                             => ( in @ X1 @ ( powerset @ X2 ) ) )
                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                ( ( subset @ X1 @ X2 )
                                                                                                                                               => ( ( subset @ X2 @ X1 )
                                                                                                                                                 => ( X1 = X2 ) ) )
                                                                                                                                           => ( ! [X1: $i] :
                                                                                                                                                  ( ( subset @ X1 @ emptyset )
                                                                                                                                                 => ( X1 = emptyset ) )
                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                    ( ( subset @ X2 @ X1 )
                                                                                                                                                   => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                      ( ( in @ X2 @ ( powerset @ X1 ) )
                                                                                                                                                     => ( subset @ X2 @ X1 ) )
                                                                                                                                                 => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                          ( ( subset @ X1 @ X2 )
                                                                                                                                                         => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
                                                                                                                                                     => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                                                                                                                                                       => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                               => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                                                                           => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                    ( ( in @ X3 @ X2 )
                                                                                                                                                                   => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                                                                                                                                                      ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                                     => ( ( ( in @ X3 @ X1 )
                                                                                                                                                                         => X4 )
                                                                                                                                                                       => ( ( ( in @ X3 @ X2 )
                                                                                                                                                                           => X4 )
                                                                                                                                                                         => X4 ) ) )
                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                        ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                                       => ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                         => ( in @ X3 @ X2 ) ) )
                                                                                                                                                                   => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                                     => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                             => ( ( in @ X3 @ X2 )
                                                                                                                                                                               => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                ( ( subset @ X3 @ X1 )
                                                                                                                                                                               => ( ( subset @ X3 @ X2 )
                                                                                                                                                                                 => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                  ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                                                                 => ( in @ X3 @ X1 ) )
                                                                                                                                                                             => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                      ( ( subset @ X1 @ X2 )
                                                                                                                                                                                     => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                        = X1 ) )
                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                        ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                          = X2 )
                                                                                                                                                                                       => ( subset @ X2 @ X1 ) )
                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                          ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                                                                         => ( in @ X3 @ X2 ) )
                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                            ( ! [X3: $i] :
                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                               => ~ ( in @ X3 @ X2 ) )
                                                                                                                                                                                           => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                              = emptyset ) )
                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                ( ( subset @ X2 @ X1 )
                                                                                                                                                                                               => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                                  = X2 ) )
                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                  ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                                    = X1 )
                                                                                                                                                                                                 => ( subset @ X1 @ X2 ) )
                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                    ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                                                                                                                                                                    = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                     => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                       => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                        ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                       => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                          ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                         => ~ ( in @ X3 @ X2 ) )
                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                            ( ( subset @ X1 @ X2 )
                                                                                                                                                                                                           => ( ( setminus @ X1 @ X2 )
                                                                                                                                                                                                              = emptyset ) )
                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                              ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                             => ( ( in @ X3 @ X1 )
                                                                                                                                                                                                               => ( in @ X3 @ X2 ) ) )
                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                               => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                 => ~ ( in @ X3 @ X1 ) ) )
                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                  ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                 => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                    ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                   => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                        ( ( ( setminus @ X1 @ X2 )
                                                                                                                                                                                                                          = emptyset )
                                                                                                                                                                                                                       => ( subset @ X1 @ X2 ) )
                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                          ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                                                                                                                                                         => ! [X4: $o] :
                                                                                                                                                                                                                              ( ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                               => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                                 => X4 ) )
                                                                                                                                                                                                                             => ( ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                                 => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                                   => X4 ) )
                                                                                                                                                                                                                               => X4 ) ) )
                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                           => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                             => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                              ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                             => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                               => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                               => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                                 => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                  ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                                 => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                                   => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                              ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                             => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                               => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                 => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                    ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                                   => ( ( X3 != X1 )
                                                                                                                                                                                                                                                     => ( X3 = X2 ) ) )
                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                         => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                           => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                             => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                               => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                 => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                   => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                  ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                 => ~ ! [X4: $i] :
                                                                                                                                                                                                                                                                        ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                       => ! [X5: $i] :
                                                                                                                                                                                                                                                                            ( ( in @ X5 @ X2 )
                                                                                                                                                                                                                                                                           => ( X3
                                                                                                                                                                                                                                                                             != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                                                                                                                                                             => ( sP5
                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                      ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                                                                                                                                                                     => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                           => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                                                                                                                                                                 => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                                                                                                                                                                   => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                                                                     => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                            ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                                                                                                                                                            = X1 )
                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                                              ( ! [X3: $i] :
                                                                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                                                                                                                                      ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                                     => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                                                       => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                                         => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                                                                             => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                     => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                                                                               => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                      ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                     => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                                       != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                                                ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                      ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                     => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                                       != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                                                                                                                                                               => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                     => ~ ( X2 @ X3 ) ) )
                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                 => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                                                   => ( ! [X4: $i] :
                                                                                                                                                                                                                                                                                          ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                                         => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                                           => ( X4 = X3 ) ) )
                                                                                                                                                                                                                                                                                     => ~ ! [X4: $i] :
                                                                                                                                                                                                                                                                                            ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                           => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                                             != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                                                    ( ! [X3: $i] :
                                                                                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                                                                                                                                            ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                                           => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                                                             => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                                               => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                                                                                   => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                           => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                                                                                     => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                            ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                           => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                                             != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                      ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                                                                                                                                                        = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                                     => ( X1 = X2 ) )
                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                        ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                       => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                                   => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                          ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                                                         => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                                ( ( in @ X2
                                                                                                                                                                                                                                                                                                  @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                    @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                                                                                                                                                               => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                    @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                                                                                                 != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                                                                     => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                            ( ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                                  ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                                                                                 => ( X1
                                                                                                                                                                                                                                                                                                   != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                           => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                              ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                              = X1 )
                                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                               => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                  ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                    = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                 => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                    ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                      = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                   => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                      ( ( X1 = X2 )
                                                                                                                                                                                                                                                                                                     => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                                                        = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                        ( ( X1 = X2 )
                                                                                                                                                                                                                                                                                                       => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                          = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                          ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                            = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                         => ( ( X3 = X4 )
                                                                                                                                                                                                                                                                                                           => ( X2 = X4 ) ) )
                                                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                            ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                                                              = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                                                                                                                                                           => ( X1 = X2 ) )
                                                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                              ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                                = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                             => ( X2 = X4 ) )
                                                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                                  = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                               => ( X2 = X4 ) )
                                                                                                                                                                                                                                                                                                           => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                                                  ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                                                                                 => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                                                        ( ( in @ X2
                                                                                                                                                                                                                                                                                                                          @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                                            @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                                                                                ( X1
                                                                                                                                                                                                                                                                                                                                = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                                                                                                                                                       => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                                            @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                                                                                ( X1
                                                                                                                                                                                                                                                                                                                                = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                                                                                                                                                         != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                                    ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                    = X2 )
                                                                                                                                                                                                                                                                                                               => ( sP8
                                                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                       => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                          ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                         => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                            ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                           => ( in @ X4 @ X2 ) )
                                                                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                                                                 => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                                                    = X3 ) ) )
                                                                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                                                                   => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                                                      = X4 ) ) )
                                                                                                                                                                                                                                                                                                                           => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                                ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                               => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                                                                                                                                                                  = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h27,assumption,
    ! [X1: $i,X2: $i > $o,X3: $i] :
      ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
     => ( in @ X3 @ X1 ) ),
    introduced(assumption,[]) ).

thf(h28,assumption,
    ~ ( ! [X1: $i,X2: $i > $o,X3: $i] :
          ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
         => ( X2 @ X3 ) )
     => ( ! [X1: $o,X2: $i] :
            ( ( in @ X2 @ ( prop2set @ X1 ) )
           => X1 )
       => ( ! [X1: $i] :
              ( ( in @ X1 @ emptyset )
             => ! [X2: $o] : X2 )
         => ( ! [X1: $i] :
                ~ ( in @ X1 @ emptyset )
           => ( ! [X1: $i] :
                  ~ ( in @ X1 @ emptyset )
             => ( ! [X1: $i > $o] :
                    ( ~ ! [X2: $i] :
                          ( ( X1 @ X2 )
                         => ~ ! [X3: $i] :
                                ( ( X1 @ X3 )
                               => ( X2 = X3 ) ) )
                   => ~ ! [X2: $i] :
                          ~ ( X1 @ X2 ) )
               => ( ! [X1: $i,X2: $i] :
                      ( ! [X3: $i] :
                          ( ( in @ X3 @ X1 )
                         => ( in @ X3 @ X2 ) )
                     => ( ! [X3: $i] :
                            ( ( in @ X3 @ X2 )
                           => ( in @ X3 @ X1 ) )
                       => ( X1 = X2 ) ) )
                 => ( ! [X1: $i] :
                        ( ! [X2: $i] :
                            ~ ( in @ X2 @ X1 )
                       => ( X1 = emptyset ) )
                   => ( ! [X1: $i] :
                          ( ! [X2: $i] :
                              ~ ( in @ X2 @ X1 )
                         => ( X1 = emptyset ) )
                     => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                            ( ( in @ X3 @ X1 )
                           => ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                              = ( X2 @ X3 ) ) )
                       => ( ! [X1: $i] :
                              ( ( X1 != emptyset )
                             => ~ ! [X2: $i] :
                                    ~ ( in @ X2 @ X1 ) )
                         => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                ( ( in @ X3 @ X1 )
                               => ( ( X2 @ X3 )
                                 => ( ( dsetconstr @ X1 @ X2 )
                                   != emptyset ) ) )
                           => ( ! [X1: $i] :
                                  ( ~ ! [X2: $i] :
                                        ~ ( in @ X2 @ X1 )
                                 => ( X1 != emptyset ) )
                             => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) )
                               => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                        ( ( in @ X3 @ X2 )
                                       => ( in @ X3 @ ( setadjoin @ X1 @ X2 ) ) )
                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                          ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                         => ! [X4: $o] :
                                              ( ( ( X3 = X1 )
                                               => X4 )
                                             => ( ( ( in @ X3 @ X2 )
                                                 => X4 )
                                               => X4 ) ) )
                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                            ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                           => ( ( X3 != X1 )
                                             => ( in @ X3 @ X2 ) ) )
                                       => ( ! [X1: $i] :
                                              ( ( dsetconstr @ X1
                                                @ ^ [X2: $i] : ~ $false )
                                              = X1 )
                                         => ( ! [X1: $i,X2: $i] :
                                                ( ! [X3: $i] :
                                                    ( ( in @ X3 @ X2 )
                                                   => ( in @ X3 @ X1 ) )
                                               => ( in @ X2 @ ( powerset @ X1 ) ) )
                                           => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                             => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                      ( ( in @ X2 @ ( powerset @ X1 ) )
                                                     => ( ( in @ X3 @ X2 )
                                                       => ( in @ X3 @ X1 ) ) )
                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                        ( ( in @ X2 @ X3 )
                                                       => ( ( in @ X3 @ X1 )
                                                         => ( in @ X2 @ ( setunion @ X1 ) ) ) )
                                                   => ( ! [X1: $i,X2: $i] :
                                                          ( ( in @ X2 @ ( setunion @ X1 ) )
                                                         => ! [X3: $o] :
                                                              ( ! [X4: $i] :
                                                                  ( ( in @ X2 @ X4 )
                                                                 => ( ( in @ X4 @ X1 )
                                                                   => X3 ) )
                                                             => X3 ) )
                                                     => ( ! [X1: $i,X2: $i] :
                                                            ( ( in @ X2 @ X1 )
                                                           => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
                                                       => ( ! [X1: $i > $o] :
                                                              ( ~ ! [X2: $i] :
                                                                    ( ( X1 @ X2 )
                                                                   => ~ ! [X3: $i] :
                                                                          ( ( X1 @ X3 )
                                                                         => ( X2 = X3 ) ) )
                                                             => ~ ! [X2: $i] :
                                                                    ~ ! [X3: $i] :
                                                                        ( ( X1 @ X3 )
                                                                        = ( X3 = X2 ) ) )
                                                         => ( ! [X1: $i] :
                                                                ( ( X1 != emptyset )
                                                               => ~ ! [X2: $i] :
                                                                      ~ ( in @ X2 @ X1 ) )
                                                           => ( ! [X1: $i,X2: $i] :
                                                                  ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                 => ( X1 = X2 ) )
                                                             => ( ! [X1: $i,X2: $i] :
                                                                    ( ( X1 != X2 )
                                                                   => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                               => ( ! [X1: $i,X2: $i] :
                                                                      ( ( X1 = X2 )
                                                                     => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                 => ( ! [X1: $i,X2: $i] :
                                                                        ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                       => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                          ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                         => ( ( X3 != X1 )
                                                                           => ( X3 = X2 ) ) )
                                                                     => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                       => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                         => ( ! [X1: $i,X2: $i > $o] :
                                                                                ( ~ ! [X3: $i] :
                                                                                      ( ( in @ X3 @ X1 )
                                                                                     => ~ ( X2 @ X3 ) )
                                                                               => ( ( dsetconstr @ X1 @ X2 )
                                                                                 != emptyset ) )
                                                                           => ( ! [X1: $i > $o,X2: $i] :
                                                                                  ( ( in @ X2 @ emptyset )
                                                                                 => ( X1 @ X2 ) )
                                                                             => ( ! [X1: $o] :
                                                                                    ( X1
                                                                                   => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                                                               => ( ! [X1: $o] :
                                                                                      ( X1
                                                                                     => ( set2prop @ ( prop2set @ X1 ) ) )
                                                                                 => ( ! [X1: $i > $o] :
                                                                                        ( ~ ! [X2: $i] :
                                                                                              ~ ( X1 @ X2 )
                                                                                       => ( ! [X2: $i,X3: $i] :
                                                                                              ( ( X1 @ X2 )
                                                                                             => ( ( X1 @ X3 )
                                                                                               => ( X2 = X3 ) ) )
                                                                                         => ~ ! [X2: $i] :
                                                                                                ( ( X1 @ X2 )
                                                                                               => ~ ! [X3: $i] :
                                                                                                      ( ( X1 @ X3 )
                                                                                                     => ( X2 = X3 ) ) ) ) )
                                                                                   => ( ! [X1: $i > $o] :
                                                                                          ( ~ ! [X2: $i] :
                                                                                                ~ ! [X3: $i] :
                                                                                                    ( ( X1 @ X3 )
                                                                                                    = ( X3 = X2 ) )
                                                                                         => ~ ! [X2: $i] :
                                                                                                ( ( X1 @ X2 )
                                                                                               => ~ ! [X3: $i] :
                                                                                                      ( ( X1 @ X3 )
                                                                                                     => ( X2 = X3 ) ) ) )
                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                            ( ( X1 = X2 )
                                                                                           => ! [X3: $i,X4: $i] :
                                                                                                ( ( X3 = X4 )
                                                                                               => ( ( in @ X3 @ X1 )
                                                                                                 => ( in @ X4 @ X2 ) ) ) )
                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                              ( ( X1 = X2 )
                                                                                             => ! [X3: $i,X4: $i] :
                                                                                                  ( ( X3 = X4 )
                                                                                                 => ( ( in @ X3 @ X1 )
                                                                                                    = ( in @ X4 @ X2 ) ) ) )
                                                                                         => ( ! [X1: $i > $o] :
                                                                                                ( ~ ! [X2: $i] :
                                                                                                      ( ( X1 @ X2 )
                                                                                                     => ~ ! [X3: $i] :
                                                                                                            ( ( X1 @ X3 )
                                                                                                           => ( X2 = X3 ) ) )
                                                                                               => ! [X2: $i,X3: $i] :
                                                                                                    ( ( X1 @ X2 )
                                                                                                   => ( ( X1 @ X3 )
                                                                                                     => ( X2 = X3 ) ) ) )
                                                                                           => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                                  ( ! [X3: $i,X4: $i] :
                                                                                                      ( ( X3 = X4 )
                                                                                                     => ( ( X1 @ X3 )
                                                                                                        = ( X2 @ X4 ) ) )
                                                                                                 => ( ( ~ ! [X3: $i] :
                                                                                                            ( ( X1 @ X3 )
                                                                                                           => ~ ! [X4: $i] :
                                                                                                                  ( ( X1 @ X4 )
                                                                                                                 => ( X3 = X4 ) ) ) )
                                                                                                    = ( ~ ! [X3: $i] :
                                                                                                            ( ( X2 @ X3 )
                                                                                                           => ~ ! [X4: $i] :
                                                                                                                  ( ( X2 @ X4 )
                                                                                                                 => ( X3 = X4 ) ) ) ) ) )
                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                    ( ( X1 = X2 )
                                                                                                   => ! [X3: $i,X4: $i] :
                                                                                                        ( ( X3 = X4 )
                                                                                                       => ( ( setadjoin @ X1 @ X3 )
                                                                                                          = ( setadjoin @ X2 @ X4 ) ) ) )
                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                      ( ( X1 = X2 )
                                                                                                     => ( ( powerset @ X1 )
                                                                                                        = ( powerset @ X2 ) ) )
                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                        ( ( X1 = X2 )
                                                                                                       => ( ( setunion @ X1 )
                                                                                                          = ( setunion @ X2 ) ) )
                                                                                                   => ( ! [X1: $i > $o] :
                                                                                                          ( ~ ! [X2: $i] :
                                                                                                                ( ( X1 @ X2 )
                                                                                                               => ~ ! [X3: $i] :
                                                                                                                      ( ( X1 @ X3 )
                                                                                                                     => ( X2 = X3 ) ) )
                                                                                                         => ! [X2: $i,X3: $i] :
                                                                                                              ( ( X1 @ X2 )
                                                                                                             => ( ( X1 @ X3 )
                                                                                                               => ( X2 = X3 ) ) ) )
                                                                                                     => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                                            ( ! [X3: $i,X4: $i] :
                                                                                                                ( ( X3 = X4 )
                                                                                                               => ( ( X1 @ X3 )
                                                                                                                  = ( X2 @ X4 ) ) )
                                                                                                           => ( ~ ! [X3: $i] :
                                                                                                                    ( ( X1 @ X3 )
                                                                                                                   => ~ ! [X4: $i] :
                                                                                                                          ( ( X1 @ X4 )
                                                                                                                         => ( X3 = X4 ) ) )
                                                                                                             => ( ~ ! [X3: $i] :
                                                                                                                      ( ( X2 @ X3 )
                                                                                                                     => ~ ! [X4: $i] :
                                                                                                                            ( ( X2 @ X4 )
                                                                                                                           => ( X3 = X4 ) ) )
                                                                                                               => ( ( descr @ X1 )
                                                                                                                  = ( descr @ X2 ) ) ) ) )
                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                              ( ( X1 = X2 )
                                                                                                             => ! [X3: $i > $o,X4: $i > $o] :
                                                                                                                  ( ! [X5: $i] :
                                                                                                                      ( ( in @ X5 @ X1 )
                                                                                                                     => ! [X6: $i] :
                                                                                                                          ( ( in @ X6 @ X2 )
                                                                                                                         => ( ( X5 = X6 )
                                                                                                                           => ( ( X3 @ X5 )
                                                                                                                              = ( X4 @ X6 ) ) ) ) )
                                                                                                                 => ( ( dsetconstr @ X1 @ X3 )
                                                                                                                    = ( dsetconstr @ X2 @ X4 ) ) ) )
                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                ( ! [X3: $i] :
                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                   => ( in @ X3 @ X2 ) )
                                                                                                               => ( subset @ X1 @ X2 ) )
                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                  ( ( X1 = X2 )
                                                                                                                 => ( subset @ X2 @ X1 ) )
                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                    ( ( X1 = X2 )
                                                                                                                   => ( subset @ X1 @ X2 ) )
                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                      ( ! [X3: $i] :
                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                         => ( in @ X3 @ X2 ) )
                                                                                                                     => ( subset @ X1 @ X2 ) )
                                                                                                                 => ( ! [X1: $i] : ( subset @ emptyset @ X1 )
                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                          ( ( subset @ X1 @ X2 )
                                                                                                                         => ( ( in @ X3 @ X1 )
                                                                                                                           => ( in @ X3 @ X2 ) ) )
                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                            ( ( subset @ X1 @ X2 )
                                                                                                                           => ( ~ ( in @ X3 @ X2 )
                                                                                                                             => ~ ( in @ X3 @ X1 ) ) )
                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                             => ( ~ ( in @ X3 @ X2 )
                                                                                                                               => ~ ( subset @ X1 @ X2 ) ) )
                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                ( ~ ( subset @ X1 @ X2 )
                                                                                                                               => ( X1 != X2 ) )
                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                 => ( ~ ( in @ X3 @ X2 )
                                                                                                                                   => ( X1 != X2 ) ) )
                                                                                                                             => ( ! [X1: $i] : ( subset @ X1 @ X1 )
                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                      ( ( subset @ X1 @ X2 )
                                                                                                                                     => ( ( subset @ X2 @ X3 )
                                                                                                                                       => ( subset @ X1 @ X3 ) ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                          ( ( subset @ X1 @ X3 )
                                                                                                                                         => ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                            ( ( subset @ X1 @ X2 )
                                                                                                                                           => ( in @ X1 @ ( powerset @ X2 ) ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                              ( ( subset @ X1 @ X2 )
                                                                                                                                             => ( ( subset @ X2 @ X1 )
                                                                                                                                               => ( X1 = X2 ) ) )
                                                                                                                                         => ( ! [X1: $i] :
                                                                                                                                                ( ( subset @ X1 @ emptyset )
                                                                                                                                               => ( X1 = emptyset ) )
                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                  ( ( subset @ X2 @ X1 )
                                                                                                                                                 => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                    ( ( in @ X2 @ ( powerset @ X1 ) )
                                                                                                                                                   => ( subset @ X2 @ X1 ) )
                                                                                                                                               => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                        ( ( subset @ X1 @ X2 )
                                                                                                                                                       => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
                                                                                                                                                   => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                                                                                                                                                     => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                             => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                                                                         => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                  ( ( in @ X3 @ X2 )
                                                                                                                                                                 => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                                                                                                                                                    ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                                   => ( ( ( in @ X3 @ X1 )
                                                                                                                                                                       => X4 )
                                                                                                                                                                     => ( ( ( in @ X3 @ X2 )
                                                                                                                                                                         => X4 )
                                                                                                                                                                       => X4 ) ) )
                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                      ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                                     => ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                       => ( in @ X3 @ X2 ) ) )
                                                                                                                                                                 => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                                   => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                           => ( ( in @ X3 @ X2 )
                                                                                                                                                                             => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                              ( ( subset @ X3 @ X1 )
                                                                                                                                                                             => ( ( subset @ X3 @ X2 )
                                                                                                                                                                               => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                                                               => ( in @ X3 @ X1 ) )
                                                                                                                                                                           => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                    ( ( subset @ X1 @ X2 )
                                                                                                                                                                                   => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                      = X1 ) )
                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                      ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                        = X2 )
                                                                                                                                                                                     => ( subset @ X2 @ X1 ) )
                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                        ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                                                                       => ( in @ X3 @ X2 ) )
                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                          ( ! [X3: $i] :
                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                             => ~ ( in @ X3 @ X2 ) )
                                                                                                                                                                                         => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                            = emptyset ) )
                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                              ( ( subset @ X2 @ X1 )
                                                                                                                                                                                             => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                                = X2 ) )
                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                                  = X1 )
                                                                                                                                                                                               => ( subset @ X1 @ X2 ) )
                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                  ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                                                                                                                                                                  = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                   => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                     => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                      ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                     => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                        ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                       => ~ ( in @ X3 @ X2 ) )
                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                          ( ( subset @ X1 @ X2 )
                                                                                                                                                                                                         => ( ( setminus @ X1 @ X2 )
                                                                                                                                                                                                            = emptyset ) )
                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                            ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                           => ( ( in @ X3 @ X1 )
                                                                                                                                                                                                             => ( in @ X3 @ X2 ) ) )
                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                              ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                             => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                               => ~ ( in @ X3 @ X1 ) ) )
                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                               => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                  ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                 => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                      ( ( ( setminus @ X1 @ X2 )
                                                                                                                                                                                                                        = emptyset )
                                                                                                                                                                                                                     => ( subset @ X1 @ X2 ) )
                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                        ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                                                                                                                                                       => ! [X4: $o] :
                                                                                                                                                                                                                            ( ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                             => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                               => X4 ) )
                                                                                                                                                                                                                           => ( ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                               => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                                 => X4 ) )
                                                                                                                                                                                                                             => X4 ) ) )
                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                         => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                           => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                            ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                           => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                             => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                             => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                               => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                               => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                                 => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                            ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                           => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                              ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                             => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                               => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                  ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                                 => ( ( X3 != X1 )
                                                                                                                                                                                                                                                   => ( X3 = X2 ) ) )
                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                       => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                         => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                           => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                             => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                               => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                 => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                               => ~ ! [X4: $i] :
                                                                                                                                                                                                                                                                      ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                     => ! [X5: $i] :
                                                                                                                                                                                                                                                                          ( ( in @ X5 @ X2 )
                                                                                                                                                                                                                                                                         => ( X3
                                                                                                                                                                                                                                                                           != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                                                                                                                                                           => ( sP5
                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                    ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                                                                                                                                                                   => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                         => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                                                                                                                                                               => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                                                                                                                                                                 => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                                                                   => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                          ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                                                                                                                                                          = X1 )
                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                                            ( ! [X3: $i] :
                                                                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                                                                                                                    ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                                   => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                                                     => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                                       => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                                                                           => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                   => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                                                                             => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                    ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                   => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                                     != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                                              ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                    ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                   => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                                     != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                                                                                                                                                             => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                   => ~ ( X2 @ X3 ) ) )
                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                               => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                                                 => ( ! [X4: $i] :
                                                                                                                                                                                                                                                                                        ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                                       => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                                         => ( X4 = X3 ) ) )
                                                                                                                                                                                                                                                                                   => ~ ! [X4: $i] :
                                                                                                                                                                                                                                                                                          ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                         => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                                           != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                                                  ( ! [X3: $i] :
                                                                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                                                                                                                                          ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                                         => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                                                           => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                                             => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                                                                                 => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                         => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                                                                                   => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                          ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                         => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                                           != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                    ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                                                                                                                                                      = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                                   => ( X1 = X2 ) )
                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                      ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                     => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                                 => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                        ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                                                       => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                              ( ( in @ X2
                                                                                                                                                                                                                                                                                                @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                  @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                                                                                                                                                             => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                  @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                                                                                               != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                                                                   => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                          ( ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                                ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                                                                               => ( X1
                                                                                                                                                                                                                                                                                                 != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                         => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                            ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                            = X1 )
                                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                              ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                             => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                  = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                               => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                  ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                    = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                 => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                    ( ( X1 = X2 )
                                                                                                                                                                                                                                                                                                   => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                                                      = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                      ( ( X1 = X2 )
                                                                                                                                                                                                                                                                                                     => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                        = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                        ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                          = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                       => ( ( X3 = X4 )
                                                                                                                                                                                                                                                                                                         => ( X2 = X4 ) ) )
                                                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                          ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                                                            = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                                                                                                                                                         => ( X1 = X2 ) )
                                                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                            ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                              = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                           => ( X2 = X4 ) )
                                                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                              ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                                = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                             => ( X2 = X4 ) )
                                                                                                                                                                                                                                                                                                         => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                                                ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                                                                               => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                                                      ( ( in @ X2
                                                                                                                                                                                                                                                                                                                        @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                                          @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                                                                              ( X1
                                                                                                                                                                                                                                                                                                                              = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                                                                                                                                                     => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                                          @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                                                                              ( X1
                                                                                                                                                                                                                                                                                                                              = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                                                                                                                                                       != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                                  ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                  = X2 )
                                                                                                                                                                                                                                                                                                             => ( sP8
                                                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                      ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                     => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                        ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                       => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                          ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                         => ( in @ X4 @ X2 ) )
                                                                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                                                               => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                                                  = X3 ) ) )
                                                                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                                                                 => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                                                    = X4 ) ) )
                                                                                                                                                                                                                                                                                                                         => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                              ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                             => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                                                                                                                                                                = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h29,assumption,
    ! [X1: $i,X2: $i > $o,X3: $i] :
      ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
     => ( X2 @ X3 ) ),
    introduced(assumption,[]) ).

thf(h30,assumption,
    ~ ( ! [X1: $o,X2: $i] :
          ( ( in @ X2 @ ( prop2set @ X1 ) )
         => X1 )
     => ( ! [X1: $i] :
            ( ( in @ X1 @ emptyset )
           => ! [X2: $o] : X2 )
       => ( ! [X1: $i] :
              ~ ( in @ X1 @ emptyset )
         => ( ! [X1: $i] :
                ~ ( in @ X1 @ emptyset )
           => ( ! [X1: $i > $o] :
                  ( ~ ! [X2: $i] :
                        ( ( X1 @ X2 )
                       => ~ ! [X3: $i] :
                              ( ( X1 @ X3 )
                             => ( X2 = X3 ) ) )
                 => ~ ! [X2: $i] :
                        ~ ( X1 @ X2 ) )
             => ( ! [X1: $i,X2: $i] :
                    ( ! [X3: $i] :
                        ( ( in @ X3 @ X1 )
                       => ( in @ X3 @ X2 ) )
                   => ( ! [X3: $i] :
                          ( ( in @ X3 @ X2 )
                         => ( in @ X3 @ X1 ) )
                     => ( X1 = X2 ) ) )
               => ( ! [X1: $i] :
                      ( ! [X2: $i] :
                          ~ ( in @ X2 @ X1 )
                     => ( X1 = emptyset ) )
                 => ( ! [X1: $i] :
                        ( ! [X2: $i] :
                            ~ ( in @ X2 @ X1 )
                       => ( X1 = emptyset ) )
                   => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                          ( ( in @ X3 @ X1 )
                         => ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                            = ( X2 @ X3 ) ) )
                     => ( ! [X1: $i] :
                            ( ( X1 != emptyset )
                           => ~ ! [X2: $i] :
                                  ~ ( in @ X2 @ X1 ) )
                       => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                              ( ( in @ X3 @ X1 )
                             => ( ( X2 @ X3 )
                               => ( ( dsetconstr @ X1 @ X2 )
                                 != emptyset ) ) )
                         => ( ! [X1: $i] :
                                ( ~ ! [X2: $i] :
                                      ~ ( in @ X2 @ X1 )
                               => ( X1 != emptyset ) )
                           => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) )
                             => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                      ( ( in @ X3 @ X2 )
                                     => ( in @ X3 @ ( setadjoin @ X1 @ X2 ) ) )
                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                        ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                       => ! [X4: $o] :
                                            ( ( ( X3 = X1 )
                                             => X4 )
                                           => ( ( ( in @ X3 @ X2 )
                                               => X4 )
                                             => X4 ) ) )
                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                          ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                         => ( ( X3 != X1 )
                                           => ( in @ X3 @ X2 ) ) )
                                     => ( ! [X1: $i] :
                                            ( ( dsetconstr @ X1
                                              @ ^ [X2: $i] : ~ $false )
                                            = X1 )
                                       => ( ! [X1: $i,X2: $i] :
                                              ( ! [X3: $i] :
                                                  ( ( in @ X3 @ X2 )
                                                 => ( in @ X3 @ X1 ) )
                                             => ( in @ X2 @ ( powerset @ X1 ) ) )
                                         => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                           => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                    ( ( in @ X2 @ ( powerset @ X1 ) )
                                                   => ( ( in @ X3 @ X2 )
                                                     => ( in @ X3 @ X1 ) ) )
                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                      ( ( in @ X2 @ X3 )
                                                     => ( ( in @ X3 @ X1 )
                                                       => ( in @ X2 @ ( setunion @ X1 ) ) ) )
                                                 => ( ! [X1: $i,X2: $i] :
                                                        ( ( in @ X2 @ ( setunion @ X1 ) )
                                                       => ! [X3: $o] :
                                                            ( ! [X4: $i] :
                                                                ( ( in @ X2 @ X4 )
                                                               => ( ( in @ X4 @ X1 )
                                                                 => X3 ) )
                                                           => X3 ) )
                                                   => ( ! [X1: $i,X2: $i] :
                                                          ( ( in @ X2 @ X1 )
                                                         => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
                                                     => ( ! [X1: $i > $o] :
                                                            ( ~ ! [X2: $i] :
                                                                  ( ( X1 @ X2 )
                                                                 => ~ ! [X3: $i] :
                                                                        ( ( X1 @ X3 )
                                                                       => ( X2 = X3 ) ) )
                                                           => ~ ! [X2: $i] :
                                                                  ~ ! [X3: $i] :
                                                                      ( ( X1 @ X3 )
                                                                      = ( X3 = X2 ) ) )
                                                       => ( ! [X1: $i] :
                                                              ( ( X1 != emptyset )
                                                             => ~ ! [X2: $i] :
                                                                    ~ ( in @ X2 @ X1 ) )
                                                         => ( ! [X1: $i,X2: $i] :
                                                                ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                               => ( X1 = X2 ) )
                                                           => ( ! [X1: $i,X2: $i] :
                                                                  ( ( X1 != X2 )
                                                                 => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                             => ( ! [X1: $i,X2: $i] :
                                                                    ( ( X1 = X2 )
                                                                   => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                               => ( ! [X1: $i,X2: $i] :
                                                                      ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                     => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                        ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                       => ( ( X3 != X1 )
                                                                         => ( X3 = X2 ) ) )
                                                                   => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                     => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                       => ( ! [X1: $i,X2: $i > $o] :
                                                                              ( ~ ! [X3: $i] :
                                                                                    ( ( in @ X3 @ X1 )
                                                                                   => ~ ( X2 @ X3 ) )
                                                                             => ( ( dsetconstr @ X1 @ X2 )
                                                                               != emptyset ) )
                                                                         => ( ! [X1: $i > $o,X2: $i] :
                                                                                ( ( in @ X2 @ emptyset )
                                                                               => ( X1 @ X2 ) )
                                                                           => ( ! [X1: $o] :
                                                                                  ( X1
                                                                                 => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                                                             => ( ! [X1: $o] :
                                                                                    ( X1
                                                                                   => ( set2prop @ ( prop2set @ X1 ) ) )
                                                                               => ( ! [X1: $i > $o] :
                                                                                      ( ~ ! [X2: $i] :
                                                                                            ~ ( X1 @ X2 )
                                                                                     => ( ! [X2: $i,X3: $i] :
                                                                                            ( ( X1 @ X2 )
                                                                                           => ( ( X1 @ X3 )
                                                                                             => ( X2 = X3 ) ) )
                                                                                       => ~ ! [X2: $i] :
                                                                                              ( ( X1 @ X2 )
                                                                                             => ~ ! [X3: $i] :
                                                                                                    ( ( X1 @ X3 )
                                                                                                   => ( X2 = X3 ) ) ) ) )
                                                                                 => ( ! [X1: $i > $o] :
                                                                                        ( ~ ! [X2: $i] :
                                                                                              ~ ! [X3: $i] :
                                                                                                  ( ( X1 @ X3 )
                                                                                                  = ( X3 = X2 ) )
                                                                                       => ~ ! [X2: $i] :
                                                                                              ( ( X1 @ X2 )
                                                                                             => ~ ! [X3: $i] :
                                                                                                    ( ( X1 @ X3 )
                                                                                                   => ( X2 = X3 ) ) ) )
                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                          ( ( X1 = X2 )
                                                                                         => ! [X3: $i,X4: $i] :
                                                                                              ( ( X3 = X4 )
                                                                                             => ( ( in @ X3 @ X1 )
                                                                                               => ( in @ X4 @ X2 ) ) ) )
                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                            ( ( X1 = X2 )
                                                                                           => ! [X3: $i,X4: $i] :
                                                                                                ( ( X3 = X4 )
                                                                                               => ( ( in @ X3 @ X1 )
                                                                                                  = ( in @ X4 @ X2 ) ) ) )
                                                                                       => ( ! [X1: $i > $o] :
                                                                                              ( ~ ! [X2: $i] :
                                                                                                    ( ( X1 @ X2 )
                                                                                                   => ~ ! [X3: $i] :
                                                                                                          ( ( X1 @ X3 )
                                                                                                         => ( X2 = X3 ) ) )
                                                                                             => ! [X2: $i,X3: $i] :
                                                                                                  ( ( X1 @ X2 )
                                                                                                 => ( ( X1 @ X3 )
                                                                                                   => ( X2 = X3 ) ) ) )
                                                                                         => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                                ( ! [X3: $i,X4: $i] :
                                                                                                    ( ( X3 = X4 )
                                                                                                   => ( ( X1 @ X3 )
                                                                                                      = ( X2 @ X4 ) ) )
                                                                                               => ( ( ~ ! [X3: $i] :
                                                                                                          ( ( X1 @ X3 )
                                                                                                         => ~ ! [X4: $i] :
                                                                                                                ( ( X1 @ X4 )
                                                                                                               => ( X3 = X4 ) ) ) )
                                                                                                  = ( ~ ! [X3: $i] :
                                                                                                          ( ( X2 @ X3 )
                                                                                                         => ~ ! [X4: $i] :
                                                                                                                ( ( X2 @ X4 )
                                                                                                               => ( X3 = X4 ) ) ) ) ) )
                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                  ( ( X1 = X2 )
                                                                                                 => ! [X3: $i,X4: $i] :
                                                                                                      ( ( X3 = X4 )
                                                                                                     => ( ( setadjoin @ X1 @ X3 )
                                                                                                        = ( setadjoin @ X2 @ X4 ) ) ) )
                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                    ( ( X1 = X2 )
                                                                                                   => ( ( powerset @ X1 )
                                                                                                      = ( powerset @ X2 ) ) )
                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                      ( ( X1 = X2 )
                                                                                                     => ( ( setunion @ X1 )
                                                                                                        = ( setunion @ X2 ) ) )
                                                                                                 => ( ! [X1: $i > $o] :
                                                                                                        ( ~ ! [X2: $i] :
                                                                                                              ( ( X1 @ X2 )
                                                                                                             => ~ ! [X3: $i] :
                                                                                                                    ( ( X1 @ X3 )
                                                                                                                   => ( X2 = X3 ) ) )
                                                                                                       => ! [X2: $i,X3: $i] :
                                                                                                            ( ( X1 @ X2 )
                                                                                                           => ( ( X1 @ X3 )
                                                                                                             => ( X2 = X3 ) ) ) )
                                                                                                   => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                                          ( ! [X3: $i,X4: $i] :
                                                                                                              ( ( X3 = X4 )
                                                                                                             => ( ( X1 @ X3 )
                                                                                                                = ( X2 @ X4 ) ) )
                                                                                                         => ( ~ ! [X3: $i] :
                                                                                                                  ( ( X1 @ X3 )
                                                                                                                 => ~ ! [X4: $i] :
                                                                                                                        ( ( X1 @ X4 )
                                                                                                                       => ( X3 = X4 ) ) )
                                                                                                           => ( ~ ! [X3: $i] :
                                                                                                                    ( ( X2 @ X3 )
                                                                                                                   => ~ ! [X4: $i] :
                                                                                                                          ( ( X2 @ X4 )
                                                                                                                         => ( X3 = X4 ) ) )
                                                                                                             => ( ( descr @ X1 )
                                                                                                                = ( descr @ X2 ) ) ) ) )
                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                            ( ( X1 = X2 )
                                                                                                           => ! [X3: $i > $o,X4: $i > $o] :
                                                                                                                ( ! [X5: $i] :
                                                                                                                    ( ( in @ X5 @ X1 )
                                                                                                                   => ! [X6: $i] :
                                                                                                                        ( ( in @ X6 @ X2 )
                                                                                                                       => ( ( X5 = X6 )
                                                                                                                         => ( ( X3 @ X5 )
                                                                                                                            = ( X4 @ X6 ) ) ) ) )
                                                                                                               => ( ( dsetconstr @ X1 @ X3 )
                                                                                                                  = ( dsetconstr @ X2 @ X4 ) ) ) )
                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                              ( ! [X3: $i] :
                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                 => ( in @ X3 @ X2 ) )
                                                                                                             => ( subset @ X1 @ X2 ) )
                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                ( ( X1 = X2 )
                                                                                                               => ( subset @ X2 @ X1 ) )
                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                  ( ( X1 = X2 )
                                                                                                                 => ( subset @ X1 @ X2 ) )
                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                    ( ! [X3: $i] :
                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                       => ( in @ X3 @ X2 ) )
                                                                                                                   => ( subset @ X1 @ X2 ) )
                                                                                                               => ( ! [X1: $i] : ( subset @ emptyset @ X1 )
                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                        ( ( subset @ X1 @ X2 )
                                                                                                                       => ( ( in @ X3 @ X1 )
                                                                                                                         => ( in @ X3 @ X2 ) ) )
                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                          ( ( subset @ X1 @ X2 )
                                                                                                                         => ( ~ ( in @ X3 @ X2 )
                                                                                                                           => ~ ( in @ X3 @ X1 ) ) )
                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                           => ( ~ ( in @ X3 @ X2 )
                                                                                                                             => ~ ( subset @ X1 @ X2 ) ) )
                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                              ( ~ ( subset @ X1 @ X2 )
                                                                                                                             => ( X1 != X2 ) )
                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                               => ( ~ ( in @ X3 @ X2 )
                                                                                                                                 => ( X1 != X2 ) ) )
                                                                                                                           => ( ! [X1: $i] : ( subset @ X1 @ X1 )
                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                    ( ( subset @ X1 @ X2 )
                                                                                                                                   => ( ( subset @ X2 @ X3 )
                                                                                                                                     => ( subset @ X1 @ X3 ) ) )
                                                                                                                               => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                        ( ( subset @ X1 @ X3 )
                                                                                                                                       => ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                          ( ( subset @ X1 @ X2 )
                                                                                                                                         => ( in @ X1 @ ( powerset @ X2 ) ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                            ( ( subset @ X1 @ X2 )
                                                                                                                                           => ( ( subset @ X2 @ X1 )
                                                                                                                                             => ( X1 = X2 ) ) )
                                                                                                                                       => ( ! [X1: $i] :
                                                                                                                                              ( ( subset @ X1 @ emptyset )
                                                                                                                                             => ( X1 = emptyset ) )
                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                ( ( subset @ X2 @ X1 )
                                                                                                                                               => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                  ( ( in @ X2 @ ( powerset @ X1 ) )
                                                                                                                                                 => ( subset @ X2 @ X1 ) )
                                                                                                                                             => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                      ( ( subset @ X1 @ X2 )
                                                                                                                                                     => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
                                                                                                                                                 => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                                                                                                                                                   => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                           => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                                                                       => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                ( ( in @ X3 @ X2 )
                                                                                                                                                               => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                                                                                                                                                  ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                                 => ( ( ( in @ X3 @ X1 )
                                                                                                                                                                     => X4 )
                                                                                                                                                                   => ( ( ( in @ X3 @ X2 )
                                                                                                                                                                       => X4 )
                                                                                                                                                                     => X4 ) ) )
                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                    ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                                   => ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                     => ( in @ X3 @ X2 ) ) )
                                                                                                                                                               => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                                 => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                         => ( ( in @ X3 @ X2 )
                                                                                                                                                                           => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                            ( ( subset @ X3 @ X1 )
                                                                                                                                                                           => ( ( subset @ X3 @ X2 )
                                                                                                                                                                             => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                              ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                                                             => ( in @ X3 @ X1 ) )
                                                                                                                                                                         => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                  ( ( subset @ X1 @ X2 )
                                                                                                                                                                                 => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                    = X1 ) )
                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                    ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                      = X2 )
                                                                                                                                                                                   => ( subset @ X2 @ X1 ) )
                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                      ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                                                                     => ( in @ X3 @ X2 ) )
                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                        ( ! [X3: $i] :
                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                           => ~ ( in @ X3 @ X2 ) )
                                                                                                                                                                                       => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                          = emptyset ) )
                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                            ( ( subset @ X2 @ X1 )
                                                                                                                                                                                           => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                              = X2 ) )
                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                              ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                                = X1 )
                                                                                                                                                                                             => ( subset @ X1 @ X2 ) )
                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                                                                                                                                                                = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                 => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                   => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                    ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                   => ( in @ X3 @ X1 ) )
                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                      ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                     => ~ ( in @ X3 @ X2 ) )
                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                        ( ( subset @ X1 @ X2 )
                                                                                                                                                                                                       => ( ( setminus @ X1 @ X2 )
                                                                                                                                                                                                          = emptyset ) )
                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                          ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                         => ( ( in @ X3 @ X1 )
                                                                                                                                                                                                           => ( in @ X3 @ X2 ) ) )
                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                            ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                           => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                             => ~ ( in @ X3 @ X1 ) ) )
                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                              ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                             => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                ( ( in @ X3 @ X2 )
                                                                                                                                                                                                               => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                    ( ( ( setminus @ X1 @ X2 )
                                                                                                                                                                                                                      = emptyset )
                                                                                                                                                                                                                   => ( subset @ X1 @ X2 ) )
                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                      ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                                                                                                                                                     => ! [X4: $o] :
                                                                                                                                                                                                                          ( ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                           => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                             => X4 ) )
                                                                                                                                                                                                                         => ( ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                             => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                               => X4 ) )
                                                                                                                                                                                                                           => X4 ) ) )
                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                       => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                         => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                          ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                         => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                           => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                           => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                             => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                              ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                             => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                               => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                          ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                         => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                            ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                           => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                             => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                               => ( ( X3 != X1 )
                                                                                                                                                                                                                                                 => ( X3 = X2 ) ) )
                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                     => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                       => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                         => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                           => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                             => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                               => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                              ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                             => ~ ! [X4: $i] :
                                                                                                                                                                                                                                                                    ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                   => ! [X5: $i] :
                                                                                                                                                                                                                                                                        ( ( in @ X5 @ X2 )
                                                                                                                                                                                                                                                                       => ( X3
                                                                                                                                                                                                                                                                         != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                                                                                                                                                         => ( sP5
                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                  ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                                                                                                                                                                 => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                       => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                                                                                                                                                             => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                                                                                                                                                               => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                                                                 => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                        ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                                                                                                                                                        = X1 )
                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                                          ( ! [X3: $i] :
                                                                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                                                                                                                  ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                                 => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                                                   => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                                     => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                                                                         => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                 => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                                                                           => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                  ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                 => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                                   != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                                            ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                  ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                 => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                                   != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                                                                                                                                                           => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                 => ~ ( X2 @ X3 ) ) )
                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                             => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                                               => ( ! [X4: $i] :
                                                                                                                                                                                                                                                                                      ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                                     => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                                       => ( X4 = X3 ) ) )
                                                                                                                                                                                                                                                                                 => ~ ! [X4: $i] :
                                                                                                                                                                                                                                                                                        ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                       => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                                         != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                                                ( ! [X3: $i] :
                                                                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                                                                                                                                        ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                                       => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                                                         => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                                           => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                                                                               => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                       => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                                                                                 => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                        ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                       => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                                         != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                  ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                                                                                                                                                    = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                                 => ( X1 = X2 ) )
                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                    ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                   => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                               => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                      ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                                                     => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                            ( ( in @ X2
                                                                                                                                                                                                                                                                                              @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                                                                                                                                                           => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                                                                                             != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                                                                 => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                        ( ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                              ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                                                                             => ( X1
                                                                                                                                                                                                                                                                                               != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                       => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                          ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                          = X1 )
                                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                            ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                           => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                              ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                             => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                  = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                               => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                  ( ( X1 = X2 )
                                                                                                                                                                                                                                                                                                 => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                                                    = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                    ( ( X1 = X2 )
                                                                                                                                                                                                                                                                                                   => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                      = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                      ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                        = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                     => ( ( X3 = X4 )
                                                                                                                                                                                                                                                                                                       => ( X2 = X4 ) ) )
                                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                        ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                                                          = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                                                                                                                                                       => ( X1 = X2 ) )
                                                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                          ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                            = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                         => ( X2 = X4 ) )
                                                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                            ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                              = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                           => ( X2 = X4 ) )
                                                                                                                                                                                                                                                                                                       => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                                              ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                                                                             => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                                                    ( ( in @ X2
                                                                                                                                                                                                                                                                                                                      @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                                        @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                                                                            ( X1
                                                                                                                                                                                                                                                                                                                            = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                                                                                                                                                   => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                                        @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                                                                            ( X1
                                                                                                                                                                                                                                                                                                                            = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                                                                                                                                                     != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                                ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                = X2 )
                                                                                                                                                                                                                                                                                                           => ( sP8
                                                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                    ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                   => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                      ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                     => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                        ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                       => ( in @ X4 @ X2 ) )
                                                                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                                                             => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                                                = X3 ) ) )
                                                                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                                                               => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                                                  = X4 ) ) )
                                                                                                                                                                                                                                                                                                                       => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                            ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                           => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                                                                                                                                                              = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h31,assumption,
    ! [X1: $o,X2: $i] :
      ( ( in @ X2 @ ( prop2set @ X1 ) )
     => X1 ),
    introduced(assumption,[]) ).

thf(h32,assumption,
    ~ ( ! [X1: $i] :
          ( ( in @ X1 @ emptyset )
         => ! [X2: $o] : X2 )
     => ( ! [X1: $i] :
            ~ ( in @ X1 @ emptyset )
       => ( ! [X1: $i] :
              ~ ( in @ X1 @ emptyset )
         => ( ! [X1: $i > $o] :
                ( ~ ! [X2: $i] :
                      ( ( X1 @ X2 )
                     => ~ ! [X3: $i] :
                            ( ( X1 @ X3 )
                           => ( X2 = X3 ) ) )
               => ~ ! [X2: $i] :
                      ~ ( X1 @ X2 ) )
           => ( ! [X1: $i,X2: $i] :
                  ( ! [X3: $i] :
                      ( ( in @ X3 @ X1 )
                     => ( in @ X3 @ X2 ) )
                 => ( ! [X3: $i] :
                        ( ( in @ X3 @ X2 )
                       => ( in @ X3 @ X1 ) )
                   => ( X1 = X2 ) ) )
             => ( ! [X1: $i] :
                    ( ! [X2: $i] :
                        ~ ( in @ X2 @ X1 )
                   => ( X1 = emptyset ) )
               => ( ! [X1: $i] :
                      ( ! [X2: $i] :
                          ~ ( in @ X2 @ X1 )
                     => ( X1 = emptyset ) )
                 => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                        ( ( in @ X3 @ X1 )
                       => ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                          = ( X2 @ X3 ) ) )
                   => ( ! [X1: $i] :
                          ( ( X1 != emptyset )
                         => ~ ! [X2: $i] :
                                ~ ( in @ X2 @ X1 ) )
                     => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                            ( ( in @ X3 @ X1 )
                           => ( ( X2 @ X3 )
                             => ( ( dsetconstr @ X1 @ X2 )
                               != emptyset ) ) )
                       => ( ! [X1: $i] :
                              ( ~ ! [X2: $i] :
                                    ~ ( in @ X2 @ X1 )
                             => ( X1 != emptyset ) )
                         => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) )
                           => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                    ( ( in @ X3 @ X2 )
                                   => ( in @ X3 @ ( setadjoin @ X1 @ X2 ) ) )
                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                      ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                     => ! [X4: $o] :
                                          ( ( ( X3 = X1 )
                                           => X4 )
                                         => ( ( ( in @ X3 @ X2 )
                                             => X4 )
                                           => X4 ) ) )
                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                        ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                       => ( ( X3 != X1 )
                                         => ( in @ X3 @ X2 ) ) )
                                   => ( ! [X1: $i] :
                                          ( ( dsetconstr @ X1
                                            @ ^ [X2: $i] : ~ $false )
                                          = X1 )
                                     => ( ! [X1: $i,X2: $i] :
                                            ( ! [X3: $i] :
                                                ( ( in @ X3 @ X2 )
                                               => ( in @ X3 @ X1 ) )
                                           => ( in @ X2 @ ( powerset @ X1 ) ) )
                                       => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                         => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                  ( ( in @ X2 @ ( powerset @ X1 ) )
                                                 => ( ( in @ X3 @ X2 )
                                                   => ( in @ X3 @ X1 ) ) )
                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                    ( ( in @ X2 @ X3 )
                                                   => ( ( in @ X3 @ X1 )
                                                     => ( in @ X2 @ ( setunion @ X1 ) ) ) )
                                               => ( ! [X1: $i,X2: $i] :
                                                      ( ( in @ X2 @ ( setunion @ X1 ) )
                                                     => ! [X3: $o] :
                                                          ( ! [X4: $i] :
                                                              ( ( in @ X2 @ X4 )
                                                             => ( ( in @ X4 @ X1 )
                                                               => X3 ) )
                                                         => X3 ) )
                                                 => ( ! [X1: $i,X2: $i] :
                                                        ( ( in @ X2 @ X1 )
                                                       => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
                                                   => ( ! [X1: $i > $o] :
                                                          ( ~ ! [X2: $i] :
                                                                ( ( X1 @ X2 )
                                                               => ~ ! [X3: $i] :
                                                                      ( ( X1 @ X3 )
                                                                     => ( X2 = X3 ) ) )
                                                         => ~ ! [X2: $i] :
                                                                ~ ! [X3: $i] :
                                                                    ( ( X1 @ X3 )
                                                                    = ( X3 = X2 ) ) )
                                                     => ( ! [X1: $i] :
                                                            ( ( X1 != emptyset )
                                                           => ~ ! [X2: $i] :
                                                                  ~ ( in @ X2 @ X1 ) )
                                                       => ( ! [X1: $i,X2: $i] :
                                                              ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                             => ( X1 = X2 ) )
                                                         => ( ! [X1: $i,X2: $i] :
                                                                ( ( X1 != X2 )
                                                               => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                           => ( ! [X1: $i,X2: $i] :
                                                                  ( ( X1 = X2 )
                                                                 => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                             => ( ! [X1: $i,X2: $i] :
                                                                    ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                   => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                      ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                     => ( ( X3 != X1 )
                                                                       => ( X3 = X2 ) ) )
                                                                 => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                   => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                                            ( ~ ! [X3: $i] :
                                                                                  ( ( in @ X3 @ X1 )
                                                                                 => ~ ( X2 @ X3 ) )
                                                                           => ( ( dsetconstr @ X1 @ X2 )
                                                                             != emptyset ) )
                                                                       => ( ! [X1: $i > $o,X2: $i] :
                                                                              ( ( in @ X2 @ emptyset )
                                                                             => ( X1 @ X2 ) )
                                                                         => ( ! [X1: $o] :
                                                                                ( X1
                                                                               => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                                                           => ( ! [X1: $o] :
                                                                                  ( X1
                                                                                 => ( set2prop @ ( prop2set @ X1 ) ) )
                                                                             => ( ! [X1: $i > $o] :
                                                                                    ( ~ ! [X2: $i] :
                                                                                          ~ ( X1 @ X2 )
                                                                                   => ( ! [X2: $i,X3: $i] :
                                                                                          ( ( X1 @ X2 )
                                                                                         => ( ( X1 @ X3 )
                                                                                           => ( X2 = X3 ) ) )
                                                                                     => ~ ! [X2: $i] :
                                                                                            ( ( X1 @ X2 )
                                                                                           => ~ ! [X3: $i] :
                                                                                                  ( ( X1 @ X3 )
                                                                                                 => ( X2 = X3 ) ) ) ) )
                                                                               => ( ! [X1: $i > $o] :
                                                                                      ( ~ ! [X2: $i] :
                                                                                            ~ ! [X3: $i] :
                                                                                                ( ( X1 @ X3 )
                                                                                                = ( X3 = X2 ) )
                                                                                     => ~ ! [X2: $i] :
                                                                                            ( ( X1 @ X2 )
                                                                                           => ~ ! [X3: $i] :
                                                                                                  ( ( X1 @ X3 )
                                                                                                 => ( X2 = X3 ) ) ) )
                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                        ( ( X1 = X2 )
                                                                                       => ! [X3: $i,X4: $i] :
                                                                                            ( ( X3 = X4 )
                                                                                           => ( ( in @ X3 @ X1 )
                                                                                             => ( in @ X4 @ X2 ) ) ) )
                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                          ( ( X1 = X2 )
                                                                                         => ! [X3: $i,X4: $i] :
                                                                                              ( ( X3 = X4 )
                                                                                             => ( ( in @ X3 @ X1 )
                                                                                                = ( in @ X4 @ X2 ) ) ) )
                                                                                     => ( ! [X1: $i > $o] :
                                                                                            ( ~ ! [X2: $i] :
                                                                                                  ( ( X1 @ X2 )
                                                                                                 => ~ ! [X3: $i] :
                                                                                                        ( ( X1 @ X3 )
                                                                                                       => ( X2 = X3 ) ) )
                                                                                           => ! [X2: $i,X3: $i] :
                                                                                                ( ( X1 @ X2 )
                                                                                               => ( ( X1 @ X3 )
                                                                                                 => ( X2 = X3 ) ) ) )
                                                                                       => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                              ( ! [X3: $i,X4: $i] :
                                                                                                  ( ( X3 = X4 )
                                                                                                 => ( ( X1 @ X3 )
                                                                                                    = ( X2 @ X4 ) ) )
                                                                                             => ( ( ~ ! [X3: $i] :
                                                                                                        ( ( X1 @ X3 )
                                                                                                       => ~ ! [X4: $i] :
                                                                                                              ( ( X1 @ X4 )
                                                                                                             => ( X3 = X4 ) ) ) )
                                                                                                = ( ~ ! [X3: $i] :
                                                                                                        ( ( X2 @ X3 )
                                                                                                       => ~ ! [X4: $i] :
                                                                                                              ( ( X2 @ X4 )
                                                                                                             => ( X3 = X4 ) ) ) ) ) )
                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                ( ( X1 = X2 )
                                                                                               => ! [X3: $i,X4: $i] :
                                                                                                    ( ( X3 = X4 )
                                                                                                   => ( ( setadjoin @ X1 @ X3 )
                                                                                                      = ( setadjoin @ X2 @ X4 ) ) ) )
                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                  ( ( X1 = X2 )
                                                                                                 => ( ( powerset @ X1 )
                                                                                                    = ( powerset @ X2 ) ) )
                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                    ( ( X1 = X2 )
                                                                                                   => ( ( setunion @ X1 )
                                                                                                      = ( setunion @ X2 ) ) )
                                                                                               => ( ! [X1: $i > $o] :
                                                                                                      ( ~ ! [X2: $i] :
                                                                                                            ( ( X1 @ X2 )
                                                                                                           => ~ ! [X3: $i] :
                                                                                                                  ( ( X1 @ X3 )
                                                                                                                 => ( X2 = X3 ) ) )
                                                                                                     => ! [X2: $i,X3: $i] :
                                                                                                          ( ( X1 @ X2 )
                                                                                                         => ( ( X1 @ X3 )
                                                                                                           => ( X2 = X3 ) ) ) )
                                                                                                 => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                                        ( ! [X3: $i,X4: $i] :
                                                                                                            ( ( X3 = X4 )
                                                                                                           => ( ( X1 @ X3 )
                                                                                                              = ( X2 @ X4 ) ) )
                                                                                                       => ( ~ ! [X3: $i] :
                                                                                                                ( ( X1 @ X3 )
                                                                                                               => ~ ! [X4: $i] :
                                                                                                                      ( ( X1 @ X4 )
                                                                                                                     => ( X3 = X4 ) ) )
                                                                                                         => ( ~ ! [X3: $i] :
                                                                                                                  ( ( X2 @ X3 )
                                                                                                                 => ~ ! [X4: $i] :
                                                                                                                        ( ( X2 @ X4 )
                                                                                                                       => ( X3 = X4 ) ) )
                                                                                                           => ( ( descr @ X1 )
                                                                                                              = ( descr @ X2 ) ) ) ) )
                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                          ( ( X1 = X2 )
                                                                                                         => ! [X3: $i > $o,X4: $i > $o] :
                                                                                                              ( ! [X5: $i] :
                                                                                                                  ( ( in @ X5 @ X1 )
                                                                                                                 => ! [X6: $i] :
                                                                                                                      ( ( in @ X6 @ X2 )
                                                                                                                     => ( ( X5 = X6 )
                                                                                                                       => ( ( X3 @ X5 )
                                                                                                                          = ( X4 @ X6 ) ) ) ) )
                                                                                                             => ( ( dsetconstr @ X1 @ X3 )
                                                                                                                = ( dsetconstr @ X2 @ X4 ) ) ) )
                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                            ( ! [X3: $i] :
                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                               => ( in @ X3 @ X2 ) )
                                                                                                           => ( subset @ X1 @ X2 ) )
                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                              ( ( X1 = X2 )
                                                                                                             => ( subset @ X2 @ X1 ) )
                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                ( ( X1 = X2 )
                                                                                                               => ( subset @ X1 @ X2 ) )
                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                  ( ! [X3: $i] :
                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                     => ( in @ X3 @ X2 ) )
                                                                                                                 => ( subset @ X1 @ X2 ) )
                                                                                                             => ( ! [X1: $i] : ( subset @ emptyset @ X1 )
                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                      ( ( subset @ X1 @ X2 )
                                                                                                                     => ( ( in @ X3 @ X1 )
                                                                                                                       => ( in @ X3 @ X2 ) ) )
                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                        ( ( subset @ X1 @ X2 )
                                                                                                                       => ( ~ ( in @ X3 @ X2 )
                                                                                                                         => ~ ( in @ X3 @ X1 ) ) )
                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                         => ( ~ ( in @ X3 @ X2 )
                                                                                                                           => ~ ( subset @ X1 @ X2 ) ) )
                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                            ( ~ ( subset @ X1 @ X2 )
                                                                                                                           => ( X1 != X2 ) )
                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                             => ( ~ ( in @ X3 @ X2 )
                                                                                                                               => ( X1 != X2 ) ) )
                                                                                                                         => ( ! [X1: $i] : ( subset @ X1 @ X1 )
                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                  ( ( subset @ X1 @ X2 )
                                                                                                                                 => ( ( subset @ X2 @ X3 )
                                                                                                                                   => ( subset @ X1 @ X3 ) ) )
                                                                                                                             => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) )
                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                      ( ( subset @ X1 @ X3 )
                                                                                                                                     => ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                        ( ( subset @ X1 @ X2 )
                                                                                                                                       => ( in @ X1 @ ( powerset @ X2 ) ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                          ( ( subset @ X1 @ X2 )
                                                                                                                                         => ( ( subset @ X2 @ X1 )
                                                                                                                                           => ( X1 = X2 ) ) )
                                                                                                                                     => ( ! [X1: $i] :
                                                                                                                                            ( ( subset @ X1 @ emptyset )
                                                                                                                                           => ( X1 = emptyset ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                              ( ( subset @ X2 @ X1 )
                                                                                                                                             => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                ( ( in @ X2 @ ( powerset @ X1 ) )
                                                                                                                                               => ( subset @ X2 @ X1 ) )
                                                                                                                                           => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                    ( ( subset @ X1 @ X2 )
                                                                                                                                                   => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
                                                                                                                                               => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                                                                                                                                                 => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                         => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                                                                     => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                              ( ( in @ X3 @ X2 )
                                                                                                                                                             => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                                                                                                                                                ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                               => ( ( ( in @ X3 @ X1 )
                                                                                                                                                                   => X4 )
                                                                                                                                                                 => ( ( ( in @ X3 @ X2 )
                                                                                                                                                                     => X4 )
                                                                                                                                                                   => X4 ) ) )
                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                  ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                                 => ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                   => ( in @ X3 @ X2 ) ) )
                                                                                                                                                             => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                               => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                       => ( ( in @ X3 @ X2 )
                                                                                                                                                                         => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                          ( ( subset @ X3 @ X1 )
                                                                                                                                                                         => ( ( subset @ X3 @ X2 )
                                                                                                                                                                           => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                            ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                                                           => ( in @ X3 @ X1 ) )
                                                                                                                                                                       => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                ( ( subset @ X1 @ X2 )
                                                                                                                                                                               => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                  = X1 ) )
                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                  ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                    = X2 )
                                                                                                                                                                                 => ( subset @ X2 @ X1 ) )
                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                    ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                                                                   => ( in @ X3 @ X2 ) )
                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                      ( ! [X3: $i] :
                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                         => ~ ( in @ X3 @ X2 ) )
                                                                                                                                                                                     => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                        = emptyset ) )
                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                          ( ( subset @ X2 @ X1 )
                                                                                                                                                                                         => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                            = X2 ) )
                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                            ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                              = X1 )
                                                                                                                                                                                           => ( subset @ X1 @ X2 ) )
                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                              ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                                                                                                                                                              = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                               => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                 => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                  ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                 => ( in @ X3 @ X1 ) )
                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                    ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                   => ~ ( in @ X3 @ X2 ) )
                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                      ( ( subset @ X1 @ X2 )
                                                                                                                                                                                                     => ( ( setminus @ X1 @ X2 )
                                                                                                                                                                                                        = emptyset ) )
                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                        ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                       => ( ( in @ X3 @ X1 )
                                                                                                                                                                                                         => ( in @ X3 @ X2 ) ) )
                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                          ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                         => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                           => ~ ( in @ X3 @ X1 ) ) )
                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                            ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                           => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                              ( ( in @ X3 @ X2 )
                                                                                                                                                                                                             => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                  ( ( ( setminus @ X1 @ X2 )
                                                                                                                                                                                                                    = emptyset )
                                                                                                                                                                                                                 => ( subset @ X1 @ X2 ) )
                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                    ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                                                                                                                                                   => ! [X4: $o] :
                                                                                                                                                                                                                        ( ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                         => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                           => X4 ) )
                                                                                                                                                                                                                       => ( ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                           => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                             => X4 ) )
                                                                                                                                                                                                                         => X4 ) ) )
                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                     => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                       => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                        ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                       => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                         => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                         => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                           => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                            ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                           => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                             => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                        ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                       => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                          ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                         => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                           => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                              ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                             => ( ( X3 != X1 )
                                                                                                                                                                                                                                               => ( X3 = X2 ) ) )
                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                   => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                     => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                       => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                         => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                           => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                             => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                            ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                           => ~ ! [X4: $i] :
                                                                                                                                                                                                                                                                  ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                 => ! [X5: $i] :
                                                                                                                                                                                                                                                                      ( ( in @ X5 @ X2 )
                                                                                                                                                                                                                                                                     => ( X3
                                                                                                                                                                                                                                                                       != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                                                                                                                                                       => ( sP5
                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                                                                                                                                                               => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                     => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                                                                                                                                                           => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                                                                                                                                                             => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                                                               => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                      ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                                                                                                                                                      = X1 )
                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                                        ( ! [X3: $i] :
                                                                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                                                                                                                                ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                               => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                                                 => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                                   => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                                                                       => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                               => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                                                                         => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                               => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                                 != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                                          ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                               => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                                 != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                                                                                                                                                         => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                               => ~ ( X2 @ X3 ) ) )
                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                           => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                                             => ( ! [X4: $i] :
                                                                                                                                                                                                                                                                                    ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                                   => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                                     => ( X4 = X3 ) ) )
                                                                                                                                                                                                                                                                               => ~ ! [X4: $i] :
                                                                                                                                                                                                                                                                                      ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                     => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                                       != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                                              ( ! [X3: $i] :
                                                                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                                                                                                                                      ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                                     => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                                                       => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                                         => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                                                                             => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                     => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                                                                               => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                      ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                     => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                                       != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                                                                                                                                                  = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                               => ( X1 = X2 ) )
                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                  ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                 => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                             => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                    ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                                                   => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                          ( ( in @ X2
                                                                                                                                                                                                                                                                                            @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                              @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                                                                                                                                                         => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                              @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                                                                                           != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                                                               => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                      ( ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                            ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                                                                           => ( X1
                                                                                                                                                                                                                                                                                             != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                     => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                        ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                        = X1 )
                                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                         => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                            ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                              = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                           => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                              ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                             => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                ( ( X1 = X2 )
                                                                                                                                                                                                                                                                                               => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                                                  = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                  ( ( X1 = X2 )
                                                                                                                                                                                                                                                                                                 => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                    = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                    ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                      = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                   => ( ( X3 = X4 )
                                                                                                                                                                                                                                                                                                     => ( X2 = X4 ) ) )
                                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                      ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                                                        = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                                                                                                                                                     => ( X1 = X2 ) )
                                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                        ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                          = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                       => ( X2 = X4 ) )
                                                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                          ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                            = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                         => ( X2 = X4 ) )
                                                                                                                                                                                                                                                                                                     => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                                            ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                                                                           => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                                                  ( ( in @ X2
                                                                                                                                                                                                                                                                                                                    @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                                      @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                                                                          ( X1
                                                                                                                                                                                                                                                                                                                          = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                                                                                                                                                 => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                                      @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                                                                          ( X1
                                                                                                                                                                                                                                                                                                                          = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                                                                                                                                                   != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                              ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                              = X2 )
                                                                                                                                                                                                                                                                                                         => ( sP8
                                                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                  ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                 => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                    ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                   => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                      ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                     => ( in @ X4 @ X2 ) )
                                                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                                                           => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                                              = X3 ) ) )
                                                                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                                                             => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                                                = X4 ) ) )
                                                                                                                                                                                                                                                                                                                     => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                         => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                                                                                                                                                            = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h33,assumption,
    ! [X1: $i] :
      ( ( in @ X1 @ emptyset )
     => ! [X2: $o] : X2 ),
    introduced(assumption,[]) ).

thf(h34,assumption,
    ~ ( ! [X1: $i] :
          ~ ( in @ X1 @ emptyset )
     => ( ! [X1: $i] :
            ~ ( in @ X1 @ emptyset )
       => ( ! [X1: $i > $o] :
              ( ~ ! [X2: $i] :
                    ( ( X1 @ X2 )
                   => ~ ! [X3: $i] :
                          ( ( X1 @ X3 )
                         => ( X2 = X3 ) ) )
             => ~ ! [X2: $i] :
                    ~ ( X1 @ X2 ) )
         => ( ! [X1: $i,X2: $i] :
                ( ! [X3: $i] :
                    ( ( in @ X3 @ X1 )
                   => ( in @ X3 @ X2 ) )
               => ( ! [X3: $i] :
                      ( ( in @ X3 @ X2 )
                     => ( in @ X3 @ X1 ) )
                 => ( X1 = X2 ) ) )
           => ( ! [X1: $i] :
                  ( ! [X2: $i] :
                      ~ ( in @ X2 @ X1 )
                 => ( X1 = emptyset ) )
             => ( ! [X1: $i] :
                    ( ! [X2: $i] :
                        ~ ( in @ X2 @ X1 )
                   => ( X1 = emptyset ) )
               => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                      ( ( in @ X3 @ X1 )
                     => ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                        = ( X2 @ X3 ) ) )
                 => ( ! [X1: $i] :
                        ( ( X1 != emptyset )
                       => ~ ! [X2: $i] :
                              ~ ( in @ X2 @ X1 ) )
                   => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                          ( ( in @ X3 @ X1 )
                         => ( ( X2 @ X3 )
                           => ( ( dsetconstr @ X1 @ X2 )
                             != emptyset ) ) )
                     => ( ! [X1: $i] :
                            ( ~ ! [X2: $i] :
                                  ~ ( in @ X2 @ X1 )
                           => ( X1 != emptyset ) )
                       => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) )
                         => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                  ( ( in @ X3 @ X2 )
                                 => ( in @ X3 @ ( setadjoin @ X1 @ X2 ) ) )
                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                    ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                   => ! [X4: $o] :
                                        ( ( ( X3 = X1 )
                                         => X4 )
                                       => ( ( ( in @ X3 @ X2 )
                                           => X4 )
                                         => X4 ) ) )
                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                      ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                     => ( ( X3 != X1 )
                                       => ( in @ X3 @ X2 ) ) )
                                 => ( ! [X1: $i] :
                                        ( ( dsetconstr @ X1
                                          @ ^ [X2: $i] : ~ $false )
                                        = X1 )
                                   => ( ! [X1: $i,X2: $i] :
                                          ( ! [X3: $i] :
                                              ( ( in @ X3 @ X2 )
                                             => ( in @ X3 @ X1 ) )
                                         => ( in @ X2 @ ( powerset @ X1 ) ) )
                                     => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                       => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                ( ( in @ X2 @ ( powerset @ X1 ) )
                                               => ( ( in @ X3 @ X2 )
                                                 => ( in @ X3 @ X1 ) ) )
                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                  ( ( in @ X2 @ X3 )
                                                 => ( ( in @ X3 @ X1 )
                                                   => ( in @ X2 @ ( setunion @ X1 ) ) ) )
                                             => ( ! [X1: $i,X2: $i] :
                                                    ( ( in @ X2 @ ( setunion @ X1 ) )
                                                   => ! [X3: $o] :
                                                        ( ! [X4: $i] :
                                                            ( ( in @ X2 @ X4 )
                                                           => ( ( in @ X4 @ X1 )
                                                             => X3 ) )
                                                       => X3 ) )
                                               => ( ! [X1: $i,X2: $i] :
                                                      ( ( in @ X2 @ X1 )
                                                     => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
                                                 => ( ! [X1: $i > $o] :
                                                        ( ~ ! [X2: $i] :
                                                              ( ( X1 @ X2 )
                                                             => ~ ! [X3: $i] :
                                                                    ( ( X1 @ X3 )
                                                                   => ( X2 = X3 ) ) )
                                                       => ~ ! [X2: $i] :
                                                              ~ ! [X3: $i] :
                                                                  ( ( X1 @ X3 )
                                                                  = ( X3 = X2 ) ) )
                                                   => ( ! [X1: $i] :
                                                          ( ( X1 != emptyset )
                                                         => ~ ! [X2: $i] :
                                                                ~ ( in @ X2 @ X1 ) )
                                                     => ( ! [X1: $i,X2: $i] :
                                                            ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                           => ( X1 = X2 ) )
                                                       => ( ! [X1: $i,X2: $i] :
                                                              ( ( X1 != X2 )
                                                             => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                         => ( ! [X1: $i,X2: $i] :
                                                                ( ( X1 = X2 )
                                                               => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                           => ( ! [X1: $i,X2: $i] :
                                                                  ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                 => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                    ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                   => ( ( X3 != X1 )
                                                                     => ( X3 = X2 ) ) )
                                                               => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                 => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                                          ( ~ ! [X3: $i] :
                                                                                ( ( in @ X3 @ X1 )
                                                                               => ~ ( X2 @ X3 ) )
                                                                         => ( ( dsetconstr @ X1 @ X2 )
                                                                           != emptyset ) )
                                                                     => ( ! [X1: $i > $o,X2: $i] :
                                                                            ( ( in @ X2 @ emptyset )
                                                                           => ( X1 @ X2 ) )
                                                                       => ( ! [X1: $o] :
                                                                              ( X1
                                                                             => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                                                         => ( ! [X1: $o] :
                                                                                ( X1
                                                                               => ( set2prop @ ( prop2set @ X1 ) ) )
                                                                           => ( ! [X1: $i > $o] :
                                                                                  ( ~ ! [X2: $i] :
                                                                                        ~ ( X1 @ X2 )
                                                                                 => ( ! [X2: $i,X3: $i] :
                                                                                        ( ( X1 @ X2 )
                                                                                       => ( ( X1 @ X3 )
                                                                                         => ( X2 = X3 ) ) )
                                                                                   => ~ ! [X2: $i] :
                                                                                          ( ( X1 @ X2 )
                                                                                         => ~ ! [X3: $i] :
                                                                                                ( ( X1 @ X3 )
                                                                                               => ( X2 = X3 ) ) ) ) )
                                                                             => ( ! [X1: $i > $o] :
                                                                                    ( ~ ! [X2: $i] :
                                                                                          ~ ! [X3: $i] :
                                                                                              ( ( X1 @ X3 )
                                                                                              = ( X3 = X2 ) )
                                                                                   => ~ ! [X2: $i] :
                                                                                          ( ( X1 @ X2 )
                                                                                         => ~ ! [X3: $i] :
                                                                                                ( ( X1 @ X3 )
                                                                                               => ( X2 = X3 ) ) ) )
                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                      ( ( X1 = X2 )
                                                                                     => ! [X3: $i,X4: $i] :
                                                                                          ( ( X3 = X4 )
                                                                                         => ( ( in @ X3 @ X1 )
                                                                                           => ( in @ X4 @ X2 ) ) ) )
                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                        ( ( X1 = X2 )
                                                                                       => ! [X3: $i,X4: $i] :
                                                                                            ( ( X3 = X4 )
                                                                                           => ( ( in @ X3 @ X1 )
                                                                                              = ( in @ X4 @ X2 ) ) ) )
                                                                                   => ( ! [X1: $i > $o] :
                                                                                          ( ~ ! [X2: $i] :
                                                                                                ( ( X1 @ X2 )
                                                                                               => ~ ! [X3: $i] :
                                                                                                      ( ( X1 @ X3 )
                                                                                                     => ( X2 = X3 ) ) )
                                                                                         => ! [X2: $i,X3: $i] :
                                                                                              ( ( X1 @ X2 )
                                                                                             => ( ( X1 @ X3 )
                                                                                               => ( X2 = X3 ) ) ) )
                                                                                     => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                            ( ! [X3: $i,X4: $i] :
                                                                                                ( ( X3 = X4 )
                                                                                               => ( ( X1 @ X3 )
                                                                                                  = ( X2 @ X4 ) ) )
                                                                                           => ( ( ~ ! [X3: $i] :
                                                                                                      ( ( X1 @ X3 )
                                                                                                     => ~ ! [X4: $i] :
                                                                                                            ( ( X1 @ X4 )
                                                                                                           => ( X3 = X4 ) ) ) )
                                                                                              = ( ~ ! [X3: $i] :
                                                                                                      ( ( X2 @ X3 )
                                                                                                     => ~ ! [X4: $i] :
                                                                                                            ( ( X2 @ X4 )
                                                                                                           => ( X3 = X4 ) ) ) ) ) )
                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                              ( ( X1 = X2 )
                                                                                             => ! [X3: $i,X4: $i] :
                                                                                                  ( ( X3 = X4 )
                                                                                                 => ( ( setadjoin @ X1 @ X3 )
                                                                                                    = ( setadjoin @ X2 @ X4 ) ) ) )
                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                ( ( X1 = X2 )
                                                                                               => ( ( powerset @ X1 )
                                                                                                  = ( powerset @ X2 ) ) )
                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                  ( ( X1 = X2 )
                                                                                                 => ( ( setunion @ X1 )
                                                                                                    = ( setunion @ X2 ) ) )
                                                                                             => ( ! [X1: $i > $o] :
                                                                                                    ( ~ ! [X2: $i] :
                                                                                                          ( ( X1 @ X2 )
                                                                                                         => ~ ! [X3: $i] :
                                                                                                                ( ( X1 @ X3 )
                                                                                                               => ( X2 = X3 ) ) )
                                                                                                   => ! [X2: $i,X3: $i] :
                                                                                                        ( ( X1 @ X2 )
                                                                                                       => ( ( X1 @ X3 )
                                                                                                         => ( X2 = X3 ) ) ) )
                                                                                               => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                                      ( ! [X3: $i,X4: $i] :
                                                                                                          ( ( X3 = X4 )
                                                                                                         => ( ( X1 @ X3 )
                                                                                                            = ( X2 @ X4 ) ) )
                                                                                                     => ( ~ ! [X3: $i] :
                                                                                                              ( ( X1 @ X3 )
                                                                                                             => ~ ! [X4: $i] :
                                                                                                                    ( ( X1 @ X4 )
                                                                                                                   => ( X3 = X4 ) ) )
                                                                                                       => ( ~ ! [X3: $i] :
                                                                                                                ( ( X2 @ X3 )
                                                                                                               => ~ ! [X4: $i] :
                                                                                                                      ( ( X2 @ X4 )
                                                                                                                     => ( X3 = X4 ) ) )
                                                                                                         => ( ( descr @ X1 )
                                                                                                            = ( descr @ X2 ) ) ) ) )
                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                        ( ( X1 = X2 )
                                                                                                       => ! [X3: $i > $o,X4: $i > $o] :
                                                                                                            ( ! [X5: $i] :
                                                                                                                ( ( in @ X5 @ X1 )
                                                                                                               => ! [X6: $i] :
                                                                                                                    ( ( in @ X6 @ X2 )
                                                                                                                   => ( ( X5 = X6 )
                                                                                                                     => ( ( X3 @ X5 )
                                                                                                                        = ( X4 @ X6 ) ) ) ) )
                                                                                                           => ( ( dsetconstr @ X1 @ X3 )
                                                                                                              = ( dsetconstr @ X2 @ X4 ) ) ) )
                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                          ( ! [X3: $i] :
                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                             => ( in @ X3 @ X2 ) )
                                                                                                         => ( subset @ X1 @ X2 ) )
                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                            ( ( X1 = X2 )
                                                                                                           => ( subset @ X2 @ X1 ) )
                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                              ( ( X1 = X2 )
                                                                                                             => ( subset @ X1 @ X2 ) )
                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                ( ! [X3: $i] :
                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                   => ( in @ X3 @ X2 ) )
                                                                                                               => ( subset @ X1 @ X2 ) )
                                                                                                           => ( ! [X1: $i] : ( subset @ emptyset @ X1 )
                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                    ( ( subset @ X1 @ X2 )
                                                                                                                   => ( ( in @ X3 @ X1 )
                                                                                                                     => ( in @ X3 @ X2 ) ) )
                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                      ( ( subset @ X1 @ X2 )
                                                                                                                     => ( ~ ( in @ X3 @ X2 )
                                                                                                                       => ~ ( in @ X3 @ X1 ) ) )
                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                       => ( ~ ( in @ X3 @ X2 )
                                                                                                                         => ~ ( subset @ X1 @ X2 ) ) )
                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                          ( ~ ( subset @ X1 @ X2 )
                                                                                                                         => ( X1 != X2 ) )
                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                           => ( ~ ( in @ X3 @ X2 )
                                                                                                                             => ( X1 != X2 ) ) )
                                                                                                                       => ( ! [X1: $i] : ( subset @ X1 @ X1 )
                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                ( ( subset @ X1 @ X2 )
                                                                                                                               => ( ( subset @ X2 @ X3 )
                                                                                                                                 => ( subset @ X1 @ X3 ) ) )
                                                                                                                           => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) )
                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                    ( ( subset @ X1 @ X3 )
                                                                                                                                   => ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                      ( ( subset @ X1 @ X2 )
                                                                                                                                     => ( in @ X1 @ ( powerset @ X2 ) ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                        ( ( subset @ X1 @ X2 )
                                                                                                                                       => ( ( subset @ X2 @ X1 )
                                                                                                                                         => ( X1 = X2 ) ) )
                                                                                                                                   => ( ! [X1: $i] :
                                                                                                                                          ( ( subset @ X1 @ emptyset )
                                                                                                                                         => ( X1 = emptyset ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                            ( ( subset @ X2 @ X1 )
                                                                                                                                           => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                              ( ( in @ X2 @ ( powerset @ X1 ) )
                                                                                                                                             => ( subset @ X2 @ X1 ) )
                                                                                                                                         => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                  ( ( subset @ X1 @ X2 )
                                                                                                                                                 => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
                                                                                                                                             => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                                                                                                                                               => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                       => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                                                                   => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                            ( ( in @ X3 @ X2 )
                                                                                                                                                           => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                                                                                                                                              ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                             => ( ( ( in @ X3 @ X1 )
                                                                                                                                                                 => X4 )
                                                                                                                                                               => ( ( ( in @ X3 @ X2 )
                                                                                                                                                                   => X4 )
                                                                                                                                                                 => X4 ) ) )
                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                               => ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                 => ( in @ X3 @ X2 ) ) )
                                                                                                                                                           => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                             => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                     => ( ( in @ X3 @ X2 )
                                                                                                                                                                       => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                        ( ( subset @ X3 @ X1 )
                                                                                                                                                                       => ( ( subset @ X3 @ X2 )
                                                                                                                                                                         => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                          ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                                                         => ( in @ X3 @ X1 ) )
                                                                                                                                                                     => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                              ( ( subset @ X1 @ X2 )
                                                                                                                                                                             => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                = X1 ) )
                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                  = X2 )
                                                                                                                                                                               => ( subset @ X2 @ X1 ) )
                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                  ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                                                                 => ( in @ X3 @ X2 ) )
                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                    ( ! [X3: $i] :
                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                       => ~ ( in @ X3 @ X2 ) )
                                                                                                                                                                                   => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                      = emptyset ) )
                                                                                                                                                                               => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                        ( ( subset @ X2 @ X1 )
                                                                                                                                                                                       => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                          = X2 ) )
                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                          ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                            = X1 )
                                                                                                                                                                                         => ( subset @ X1 @ X2 ) )
                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                            ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                                                                                                                                                            = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                             => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                               => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                               => ( in @ X3 @ X1 ) )
                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                  ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                 => ~ ( in @ X3 @ X2 ) )
                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                    ( ( subset @ X1 @ X2 )
                                                                                                                                                                                                   => ( ( setminus @ X1 @ X2 )
                                                                                                                                                                                                      = emptyset ) )
                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                      ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                     => ( ( in @ X3 @ X1 )
                                                                                                                                                                                                       => ( in @ X3 @ X2 ) ) )
                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                        ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                       => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                         => ~ ( in @ X3 @ X1 ) ) )
                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                          ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                         => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                            ( ( in @ X3 @ X2 )
                                                                                                                                                                                                           => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                ( ( ( setminus @ X1 @ X2 )
                                                                                                                                                                                                                  = emptyset )
                                                                                                                                                                                                               => ( subset @ X1 @ X2 ) )
                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                  ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                                                                                                                                                 => ! [X4: $o] :
                                                                                                                                                                                                                      ( ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                       => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                         => X4 ) )
                                                                                                                                                                                                                     => ( ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                         => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                           => X4 ) )
                                                                                                                                                                                                                       => X4 ) ) )
                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                   => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                     => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                      ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                     => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                       => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                       => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                         => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                          ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                         => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                           => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                      ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                     => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                        ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                       => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                         => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                            ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                           => ( ( X3 != X1 )
                                                                                                                                                                                                                                             => ( X3 = X2 ) ) )
                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                 => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                   => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                     => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                       => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                         => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                           => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                         => ~ ! [X4: $i] :
                                                                                                                                                                                                                                                                ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                               => ! [X5: $i] :
                                                                                                                                                                                                                                                                    ( ( in @ X5 @ X2 )
                                                                                                                                                                                                                                                                   => ( X3
                                                                                                                                                                                                                                                                     != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                                                                                                                                                     => ( sP5
                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                              ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                                                                                                                                                             => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                   => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                                                                                                                                                         => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                                                                                                                                                           => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                                                             => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                    ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                                                                                                                                                    = X1 )
                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                                      ( ! [X3: $i] :
                                                                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                                                                                                                              ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                             => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                                               => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                                 => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                                                                     => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                             => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                                                                       => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                              ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                             => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                               != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                                        ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                              ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                             => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                               != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                                                                                                                                                       => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                             => ~ ( X2 @ X3 ) ) )
                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                         => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                                           => ( ! [X4: $i] :
                                                                                                                                                                                                                                                                                  ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                                 => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                                   => ( X4 = X3 ) ) )
                                                                                                                                                                                                                                                                             => ~ ! [X4: $i] :
                                                                                                                                                                                                                                                                                    ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                   => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                                     != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                                            ( ! [X3: $i] :
                                                                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                                                                                                                    ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                                   => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                                                     => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                                       => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                                                                           => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                   => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                                                                             => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                    ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                   => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                                     != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                              ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                                                                                                                                                = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                             => ( X1 = X2 ) )
                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                               => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                           => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                  ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                                                 => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                        ( ( in @ X2
                                                                                                                                                                                                                                                                                          @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                            @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                                                                                                                                                       => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                            @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                                                                                         != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                                                             => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                    ( ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                          ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                                                                         => ( X1
                                                                                                                                                                                                                                                                                           != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                   => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                      ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                      = X1 )
                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                       => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                          ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                            = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                         => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                            ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                                                              = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                           => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                              ( ( X1 = X2 )
                                                                                                                                                                                                                                                                                             => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                                                = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                ( ( X1 = X2 )
                                                                                                                                                                                                                                                                                               => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                  = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                  ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                    = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                 => ( ( X3 = X4 )
                                                                                                                                                                                                                                                                                                   => ( X2 = X4 ) ) )
                                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                    ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                                                      = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                                                                                                                                                   => ( X1 = X2 ) )
                                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                      ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                        = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                     => ( X2 = X4 ) )
                                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                        ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                          = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                       => ( X2 = X4 ) )
                                                                                                                                                                                                                                                                                                   => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                                          ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                                                                         => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                                                ( ( in @ X2
                                                                                                                                                                                                                                                                                                                  @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                                    @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                                                                        ( X1
                                                                                                                                                                                                                                                                                                                        = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                                                                                                                                               => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                                    @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                                                                        ( X1
                                                                                                                                                                                                                                                                                                                        = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                                                                                                                                                 != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                            ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                            = X2 )
                                                                                                                                                                                                                                                                                                       => ( sP8
                                                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                               => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                  ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                 => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                    ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                   => ( in @ X4 @ X2 ) )
                                                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                                                         => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                                            = X3 ) ) )
                                                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                                                           => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                                              = X4 ) ) )
                                                                                                                                                                                                                                                                                                                   => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                       => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                                                                                                                                                          = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h35,assumption,
    ~ ( ! [X1: $i] :
          ~ ( in @ X1 @ emptyset )
     => ( ! [X1: $i > $o] :
            ( ~ ! [X2: $i] :
                  ( ( X1 @ X2 )
                 => ~ ! [X3: $i] :
                        ( ( X1 @ X3 )
                       => ( X2 = X3 ) ) )
           => ~ ! [X2: $i] :
                  ~ ( X1 @ X2 ) )
       => ( ! [X1: $i,X2: $i] :
              ( ! [X3: $i] :
                  ( ( in @ X3 @ X1 )
                 => ( in @ X3 @ X2 ) )
             => ( ! [X3: $i] :
                    ( ( in @ X3 @ X2 )
                   => ( in @ X3 @ X1 ) )
               => ( X1 = X2 ) ) )
         => ( ! [X1: $i] :
                ( ! [X2: $i] :
                    ~ ( in @ X2 @ X1 )
               => ( X1 = emptyset ) )
           => ( ! [X1: $i] :
                  ( ! [X2: $i] :
                      ~ ( in @ X2 @ X1 )
                 => ( X1 = emptyset ) )
             => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                    ( ( in @ X3 @ X1 )
                   => ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                      = ( X2 @ X3 ) ) )
               => ( ! [X1: $i] :
                      ( ( X1 != emptyset )
                     => ~ ! [X2: $i] :
                            ~ ( in @ X2 @ X1 ) )
                 => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                        ( ( in @ X3 @ X1 )
                       => ( ( X2 @ X3 )
                         => ( ( dsetconstr @ X1 @ X2 )
                           != emptyset ) ) )
                   => ( ! [X1: $i] :
                          ( ~ ! [X2: $i] :
                                ~ ( in @ X2 @ X1 )
                         => ( X1 != emptyset ) )
                     => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) )
                       => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                ( ( in @ X3 @ X2 )
                               => ( in @ X3 @ ( setadjoin @ X1 @ X2 ) ) )
                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                  ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                 => ! [X4: $o] :
                                      ( ( ( X3 = X1 )
                                       => X4 )
                                     => ( ( ( in @ X3 @ X2 )
                                         => X4 )
                                       => X4 ) ) )
                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                    ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                   => ( ( X3 != X1 )
                                     => ( in @ X3 @ X2 ) ) )
                               => ( ! [X1: $i] :
                                      ( ( dsetconstr @ X1
                                        @ ^ [X2: $i] : ~ $false )
                                      = X1 )
                                 => ( ! [X1: $i,X2: $i] :
                                        ( ! [X3: $i] :
                                            ( ( in @ X3 @ X2 )
                                           => ( in @ X3 @ X1 ) )
                                       => ( in @ X2 @ ( powerset @ X1 ) ) )
                                   => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                     => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                              ( ( in @ X2 @ ( powerset @ X1 ) )
                                             => ( ( in @ X3 @ X2 )
                                               => ( in @ X3 @ X1 ) ) )
                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                ( ( in @ X2 @ X3 )
                                               => ( ( in @ X3 @ X1 )
                                                 => ( in @ X2 @ ( setunion @ X1 ) ) ) )
                                           => ( ! [X1: $i,X2: $i] :
                                                  ( ( in @ X2 @ ( setunion @ X1 ) )
                                                 => ! [X3: $o] :
                                                      ( ! [X4: $i] :
                                                          ( ( in @ X2 @ X4 )
                                                         => ( ( in @ X4 @ X1 )
                                                           => X3 ) )
                                                     => X3 ) )
                                             => ( ! [X1: $i,X2: $i] :
                                                    ( ( in @ X2 @ X1 )
                                                   => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
                                               => ( ! [X1: $i > $o] :
                                                      ( ~ ! [X2: $i] :
                                                            ( ( X1 @ X2 )
                                                           => ~ ! [X3: $i] :
                                                                  ( ( X1 @ X3 )
                                                                 => ( X2 = X3 ) ) )
                                                     => ~ ! [X2: $i] :
                                                            ~ ! [X3: $i] :
                                                                ( ( X1 @ X3 )
                                                                = ( X3 = X2 ) ) )
                                                 => ( ! [X1: $i] :
                                                        ( ( X1 != emptyset )
                                                       => ~ ! [X2: $i] :
                                                              ~ ( in @ X2 @ X1 ) )
                                                   => ( ! [X1: $i,X2: $i] :
                                                          ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                         => ( X1 = X2 ) )
                                                     => ( ! [X1: $i,X2: $i] :
                                                            ( ( X1 != X2 )
                                                           => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                       => ( ! [X1: $i,X2: $i] :
                                                              ( ( X1 = X2 )
                                                             => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                         => ( ! [X1: $i,X2: $i] :
                                                                ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                               => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                  ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                 => ( ( X3 != X1 )
                                                                   => ( X3 = X2 ) ) )
                                                             => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                               => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                                        ( ~ ! [X3: $i] :
                                                                              ( ( in @ X3 @ X1 )
                                                                             => ~ ( X2 @ X3 ) )
                                                                       => ( ( dsetconstr @ X1 @ X2 )
                                                                         != emptyset ) )
                                                                   => ( ! [X1: $i > $o,X2: $i] :
                                                                          ( ( in @ X2 @ emptyset )
                                                                         => ( X1 @ X2 ) )
                                                                     => ( ! [X1: $o] :
                                                                            ( X1
                                                                           => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                                                       => ( ! [X1: $o] :
                                                                              ( X1
                                                                             => ( set2prop @ ( prop2set @ X1 ) ) )
                                                                         => ( ! [X1: $i > $o] :
                                                                                ( ~ ! [X2: $i] :
                                                                                      ~ ( X1 @ X2 )
                                                                               => ( ! [X2: $i,X3: $i] :
                                                                                      ( ( X1 @ X2 )
                                                                                     => ( ( X1 @ X3 )
                                                                                       => ( X2 = X3 ) ) )
                                                                                 => ~ ! [X2: $i] :
                                                                                        ( ( X1 @ X2 )
                                                                                       => ~ ! [X3: $i] :
                                                                                              ( ( X1 @ X3 )
                                                                                             => ( X2 = X3 ) ) ) ) )
                                                                           => ( ! [X1: $i > $o] :
                                                                                  ( ~ ! [X2: $i] :
                                                                                        ~ ! [X3: $i] :
                                                                                            ( ( X1 @ X3 )
                                                                                            = ( X3 = X2 ) )
                                                                                 => ~ ! [X2: $i] :
                                                                                        ( ( X1 @ X2 )
                                                                                       => ~ ! [X3: $i] :
                                                                                              ( ( X1 @ X3 )
                                                                                             => ( X2 = X3 ) ) ) )
                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                    ( ( X1 = X2 )
                                                                                   => ! [X3: $i,X4: $i] :
                                                                                        ( ( X3 = X4 )
                                                                                       => ( ( in @ X3 @ X1 )
                                                                                         => ( in @ X4 @ X2 ) ) ) )
                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                      ( ( X1 = X2 )
                                                                                     => ! [X3: $i,X4: $i] :
                                                                                          ( ( X3 = X4 )
                                                                                         => ( ( in @ X3 @ X1 )
                                                                                            = ( in @ X4 @ X2 ) ) ) )
                                                                                 => ( ! [X1: $i > $o] :
                                                                                        ( ~ ! [X2: $i] :
                                                                                              ( ( X1 @ X2 )
                                                                                             => ~ ! [X3: $i] :
                                                                                                    ( ( X1 @ X3 )
                                                                                                   => ( X2 = X3 ) ) )
                                                                                       => ! [X2: $i,X3: $i] :
                                                                                            ( ( X1 @ X2 )
                                                                                           => ( ( X1 @ X3 )
                                                                                             => ( X2 = X3 ) ) ) )
                                                                                   => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                          ( ! [X3: $i,X4: $i] :
                                                                                              ( ( X3 = X4 )
                                                                                             => ( ( X1 @ X3 )
                                                                                                = ( X2 @ X4 ) ) )
                                                                                         => ( ( ~ ! [X3: $i] :
                                                                                                    ( ( X1 @ X3 )
                                                                                                   => ~ ! [X4: $i] :
                                                                                                          ( ( X1 @ X4 )
                                                                                                         => ( X3 = X4 ) ) ) )
                                                                                            = ( ~ ! [X3: $i] :
                                                                                                    ( ( X2 @ X3 )
                                                                                                   => ~ ! [X4: $i] :
                                                                                                          ( ( X2 @ X4 )
                                                                                                         => ( X3 = X4 ) ) ) ) ) )
                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                            ( ( X1 = X2 )
                                                                                           => ! [X3: $i,X4: $i] :
                                                                                                ( ( X3 = X4 )
                                                                                               => ( ( setadjoin @ X1 @ X3 )
                                                                                                  = ( setadjoin @ X2 @ X4 ) ) ) )
                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                              ( ( X1 = X2 )
                                                                                             => ( ( powerset @ X1 )
                                                                                                = ( powerset @ X2 ) ) )
                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                ( ( X1 = X2 )
                                                                                               => ( ( setunion @ X1 )
                                                                                                  = ( setunion @ X2 ) ) )
                                                                                           => ( ! [X1: $i > $o] :
                                                                                                  ( ~ ! [X2: $i] :
                                                                                                        ( ( X1 @ X2 )
                                                                                                       => ~ ! [X3: $i] :
                                                                                                              ( ( X1 @ X3 )
                                                                                                             => ( X2 = X3 ) ) )
                                                                                                 => ! [X2: $i,X3: $i] :
                                                                                                      ( ( X1 @ X2 )
                                                                                                     => ( ( X1 @ X3 )
                                                                                                       => ( X2 = X3 ) ) ) )
                                                                                             => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                                    ( ! [X3: $i,X4: $i] :
                                                                                                        ( ( X3 = X4 )
                                                                                                       => ( ( X1 @ X3 )
                                                                                                          = ( X2 @ X4 ) ) )
                                                                                                   => ( ~ ! [X3: $i] :
                                                                                                            ( ( X1 @ X3 )
                                                                                                           => ~ ! [X4: $i] :
                                                                                                                  ( ( X1 @ X4 )
                                                                                                                 => ( X3 = X4 ) ) )
                                                                                                     => ( ~ ! [X3: $i] :
                                                                                                              ( ( X2 @ X3 )
                                                                                                             => ~ ! [X4: $i] :
                                                                                                                    ( ( X2 @ X4 )
                                                                                                                   => ( X3 = X4 ) ) )
                                                                                                       => ( ( descr @ X1 )
                                                                                                          = ( descr @ X2 ) ) ) ) )
                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                      ( ( X1 = X2 )
                                                                                                     => ! [X3: $i > $o,X4: $i > $o] :
                                                                                                          ( ! [X5: $i] :
                                                                                                              ( ( in @ X5 @ X1 )
                                                                                                             => ! [X6: $i] :
                                                                                                                  ( ( in @ X6 @ X2 )
                                                                                                                 => ( ( X5 = X6 )
                                                                                                                   => ( ( X3 @ X5 )
                                                                                                                      = ( X4 @ X6 ) ) ) ) )
                                                                                                         => ( ( dsetconstr @ X1 @ X3 )
                                                                                                            = ( dsetconstr @ X2 @ X4 ) ) ) )
                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                        ( ! [X3: $i] :
                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                           => ( in @ X3 @ X2 ) )
                                                                                                       => ( subset @ X1 @ X2 ) )
                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                          ( ( X1 = X2 )
                                                                                                         => ( subset @ X2 @ X1 ) )
                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                            ( ( X1 = X2 )
                                                                                                           => ( subset @ X1 @ X2 ) )
                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                              ( ! [X3: $i] :
                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                 => ( in @ X3 @ X2 ) )
                                                                                                             => ( subset @ X1 @ X2 ) )
                                                                                                         => ( ! [X1: $i] : ( subset @ emptyset @ X1 )
                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                  ( ( subset @ X1 @ X2 )
                                                                                                                 => ( ( in @ X3 @ X1 )
                                                                                                                   => ( in @ X3 @ X2 ) ) )
                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                    ( ( subset @ X1 @ X2 )
                                                                                                                   => ( ~ ( in @ X3 @ X2 )
                                                                                                                     => ~ ( in @ X3 @ X1 ) ) )
                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                     => ( ~ ( in @ X3 @ X2 )
                                                                                                                       => ~ ( subset @ X1 @ X2 ) ) )
                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                        ( ~ ( subset @ X1 @ X2 )
                                                                                                                       => ( X1 != X2 ) )
                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                         => ( ~ ( in @ X3 @ X2 )
                                                                                                                           => ( X1 != X2 ) ) )
                                                                                                                     => ( ! [X1: $i] : ( subset @ X1 @ X1 )
                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                              ( ( subset @ X1 @ X2 )
                                                                                                                             => ( ( subset @ X2 @ X3 )
                                                                                                                               => ( subset @ X1 @ X3 ) ) )
                                                                                                                         => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) )
                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                  ( ( subset @ X1 @ X3 )
                                                                                                                                 => ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                    ( ( subset @ X1 @ X2 )
                                                                                                                                   => ( in @ X1 @ ( powerset @ X2 ) ) )
                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                      ( ( subset @ X1 @ X2 )
                                                                                                                                     => ( ( subset @ X2 @ X1 )
                                                                                                                                       => ( X1 = X2 ) ) )
                                                                                                                                 => ( ! [X1: $i] :
                                                                                                                                        ( ( subset @ X1 @ emptyset )
                                                                                                                                       => ( X1 = emptyset ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                          ( ( subset @ X2 @ X1 )
                                                                                                                                         => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                            ( ( in @ X2 @ ( powerset @ X1 ) )
                                                                                                                                           => ( subset @ X2 @ X1 ) )
                                                                                                                                       => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                ( ( subset @ X1 @ X2 )
                                                                                                                                               => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
                                                                                                                                           => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                                                                                                                                             => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                     => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                                                                 => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                          ( ( in @ X3 @ X2 )
                                                                                                                                                         => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                                                                                                                                            ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                           => ( ( ( in @ X3 @ X1 )
                                                                                                                                                               => X4 )
                                                                                                                                                             => ( ( ( in @ X3 @ X2 )
                                                                                                                                                                 => X4 )
                                                                                                                                                               => X4 ) ) )
                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                              ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                             => ( ~ ( in @ X3 @ X1 )
                                                                                                                                                               => ( in @ X3 @ X2 ) ) )
                                                                                                                                                         => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                           => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                   => ( ( in @ X3 @ X2 )
                                                                                                                                                                     => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                      ( ( subset @ X3 @ X1 )
                                                                                                                                                                     => ( ( subset @ X3 @ X2 )
                                                                                                                                                                       => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                        ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                                                       => ( in @ X3 @ X1 ) )
                                                                                                                                                                   => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                            ( ( subset @ X1 @ X2 )
                                                                                                                                                                           => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                              = X1 ) )
                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                              ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                = X2 )
                                                                                                                                                                             => ( subset @ X2 @ X1 ) )
                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                                                               => ( in @ X3 @ X2 ) )
                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                  ( ! [X3: $i] :
                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                     => ~ ( in @ X3 @ X2 ) )
                                                                                                                                                                                 => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                    = emptyset ) )
                                                                                                                                                                             => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                      ( ( subset @ X2 @ X1 )
                                                                                                                                                                                     => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                        = X2 ) )
                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                        ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                          = X1 )
                                                                                                                                                                                       => ( subset @ X1 @ X2 ) )
                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                          ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                                                                                                                                                          = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                           => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                             => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                              ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                             => ( in @ X3 @ X1 ) )
                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                               => ~ ( in @ X3 @ X2 ) )
                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                  ( ( subset @ X1 @ X2 )
                                                                                                                                                                                                 => ( ( setminus @ X1 @ X2 )
                                                                                                                                                                                                    = emptyset ) )
                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                    ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                   => ( ( in @ X3 @ X1 )
                                                                                                                                                                                                     => ( in @ X3 @ X2 ) ) )
                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                      ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                     => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                       => ~ ( in @ X3 @ X1 ) ) )
                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                        ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                       => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                          ( ( in @ X3 @ X2 )
                                                                                                                                                                                                         => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                              ( ( ( setminus @ X1 @ X2 )
                                                                                                                                                                                                                = emptyset )
                                                                                                                                                                                                             => ( subset @ X1 @ X2 ) )
                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                                                                                                                                               => ! [X4: $o] :
                                                                                                                                                                                                                    ( ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                     => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                       => X4 ) )
                                                                                                                                                                                                                   => ( ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                       => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                         => X4 ) )
                                                                                                                                                                                                                     => X4 ) ) )
                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                 => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                   => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                    ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                   => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                     => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                     => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                       => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                        ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                       => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                         => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                    ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                   => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                      ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                     => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                       => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                          ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                         => ( ( X3 != X1 )
                                                                                                                                                                                                                                           => ( X3 = X2 ) ) )
                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                               => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                 => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                   => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                     => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                       => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                         => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                       => ~ ! [X4: $i] :
                                                                                                                                                                                                                                                              ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                             => ! [X5: $i] :
                                                                                                                                                                                                                                                                  ( ( in @ X5 @ X2 )
                                                                                                                                                                                                                                                                 => ( X3
                                                                                                                                                                                                                                                                   != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                                                                                                                                                   => ( sP5
                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                            ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                                                                                                                                                           => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                 => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                                                                                                                                                       => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                                                                                                                                                         => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                                                           => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                  ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                                                                                                                                                  = X1 )
                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                                    ( ! [X3: $i] :
                                                                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                                                                                                                            ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                           => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                                             => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                               => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                                                                   => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                           => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                                                                     => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                            ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                           => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                             != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                                      ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                            ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                           => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                             != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                                                                                                                                                     => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                           => ~ ( X2 @ X3 ) ) )
                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                       => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                                         => ( ! [X4: $i] :
                                                                                                                                                                                                                                                                                ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                               => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                                 => ( X4 = X3 ) ) )
                                                                                                                                                                                                                                                                           => ~ ! [X4: $i] :
                                                                                                                                                                                                                                                                                  ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                 => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                                   != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                                          ( ! [X3: $i] :
                                                                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                                                                                                                  ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                                 => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                                                   => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                                     => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                                                                         => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                 => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                                                                           => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                  ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                 => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                                   != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                            ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                                                                                                                                              = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                           => ( X1 = X2 ) )
                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                              ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                             => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                         => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                                               => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                      ( ( in @ X2
                                                                                                                                                                                                                                                                                        @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                          @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                                                                                                                                                     => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                          @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                                                                                       != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                                                           => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                  ( ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                        ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                                                                       => ( X1
                                                                                                                                                                                                                                                                                         != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                 => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                    ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                    = X1 )
                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                      ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                     => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                        ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                          = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                       => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                          ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                                                            = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                         => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                            ( ( X1 = X2 )
                                                                                                                                                                                                                                                                                           => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                                              = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                              ( ( X1 = X2 )
                                                                                                                                                                                                                                                                                             => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                  = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                               => ( ( X3 = X4 )
                                                                                                                                                                                                                                                                                                 => ( X2 = X4 ) ) )
                                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                  ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                                                    = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                                                                                                                                                 => ( X1 = X2 ) )
                                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                    ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                      = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                   => ( X2 = X4 ) )
                                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                      ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                        = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                     => ( X2 = X4 ) )
                                                                                                                                                                                                                                                                                                 => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                                        ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                                                                       => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                                              ( ( in @ X2
                                                                                                                                                                                                                                                                                                                @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                                  @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                                                                      ( X1
                                                                                                                                                                                                                                                                                                                      = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                                                                                                                                             => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                                  @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                                                                      ( X1
                                                                                                                                                                                                                                                                                                                      = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                                                                                                                                               != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                          ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                          = X2 )
                                                                                                                                                                                                                                                                                                     => ( sP8
                                                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                              ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                             => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                               => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                  ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                 => ( in @ X4 @ X2 ) )
                                                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                                                       => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                                          = X3 ) ) )
                                                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                                                         => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                                            = X4 ) ) )
                                                                                                                                                                                                                                                                                                                 => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                      ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                     => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                                                                                                                                                        = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h36,assumption,
    ~ ( ! [X1: $i > $o] :
          ( ~ ! [X2: $i] :
                ( ( X1 @ X2 )
               => ~ ! [X3: $i] :
                      ( ( X1 @ X3 )
                     => ( X2 = X3 ) ) )
         => ~ ! [X2: $i] :
                ~ ( X1 @ X2 ) )
     => ( ! [X1: $i,X2: $i] :
            ( ! [X3: $i] :
                ( ( in @ X3 @ X1 )
               => ( in @ X3 @ X2 ) )
           => ( ! [X3: $i] :
                  ( ( in @ X3 @ X2 )
                 => ( in @ X3 @ X1 ) )
             => ( X1 = X2 ) ) )
       => ( ! [X1: $i] :
              ( ! [X2: $i] :
                  ~ ( in @ X2 @ X1 )
             => ( X1 = emptyset ) )
         => ( ! [X1: $i] :
                ( ! [X2: $i] :
                    ~ ( in @ X2 @ X1 )
               => ( X1 = emptyset ) )
           => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                  ( ( in @ X3 @ X1 )
                 => ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                    = ( X2 @ X3 ) ) )
             => ( ! [X1: $i] :
                    ( ( X1 != emptyset )
                   => ~ ! [X2: $i] :
                          ~ ( in @ X2 @ X1 ) )
               => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                      ( ( in @ X3 @ X1 )
                     => ( ( X2 @ X3 )
                       => ( ( dsetconstr @ X1 @ X2 )
                         != emptyset ) ) )
                 => ( ! [X1: $i] :
                        ( ~ ! [X2: $i] :
                              ~ ( in @ X2 @ X1 )
                       => ( X1 != emptyset ) )
                   => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) )
                     => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
                       => ( ! [X1: $i,X2: $i,X3: $i] :
                              ( ( in @ X3 @ X2 )
                             => ( in @ X3 @ ( setadjoin @ X1 @ X2 ) ) )
                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                               => ! [X4: $o] :
                                    ( ( ( X3 = X1 )
                                     => X4 )
                                   => ( ( ( in @ X3 @ X2 )
                                       => X4 )
                                     => X4 ) ) )
                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                  ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                 => ( ( X3 != X1 )
                                   => ( in @ X3 @ X2 ) ) )
                             => ( ! [X1: $i] :
                                    ( ( dsetconstr @ X1
                                      @ ^ [X2: $i] : ~ $false )
                                    = X1 )
                               => ( ! [X1: $i,X2: $i] :
                                      ( ! [X3: $i] :
                                          ( ( in @ X3 @ X2 )
                                         => ( in @ X3 @ X1 ) )
                                     => ( in @ X2 @ ( powerset @ X1 ) ) )
                                 => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                   => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                            ( ( in @ X2 @ ( powerset @ X1 ) )
                                           => ( ( in @ X3 @ X2 )
                                             => ( in @ X3 @ X1 ) ) )
                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                              ( ( in @ X2 @ X3 )
                                             => ( ( in @ X3 @ X1 )
                                               => ( in @ X2 @ ( setunion @ X1 ) ) ) )
                                         => ( ! [X1: $i,X2: $i] :
                                                ( ( in @ X2 @ ( setunion @ X1 ) )
                                               => ! [X3: $o] :
                                                    ( ! [X4: $i] :
                                                        ( ( in @ X2 @ X4 )
                                                       => ( ( in @ X4 @ X1 )
                                                         => X3 ) )
                                                   => X3 ) )
                                           => ( ! [X1: $i,X2: $i] :
                                                  ( ( in @ X2 @ X1 )
                                                 => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
                                             => ( ! [X1: $i > $o] :
                                                    ( ~ ! [X2: $i] :
                                                          ( ( X1 @ X2 )
                                                         => ~ ! [X3: $i] :
                                                                ( ( X1 @ X3 )
                                                               => ( X2 = X3 ) ) )
                                                   => ~ ! [X2: $i] :
                                                          ~ ! [X3: $i] :
                                                              ( ( X1 @ X3 )
                                                              = ( X3 = X2 ) ) )
                                               => ( ! [X1: $i] :
                                                      ( ( X1 != emptyset )
                                                     => ~ ! [X2: $i] :
                                                            ~ ( in @ X2 @ X1 ) )
                                                 => ( ! [X1: $i,X2: $i] :
                                                        ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                       => ( X1 = X2 ) )
                                                   => ( ! [X1: $i,X2: $i] :
                                                          ( ( X1 != X2 )
                                                         => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                     => ( ! [X1: $i,X2: $i] :
                                                            ( ( X1 = X2 )
                                                           => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                       => ( ! [X1: $i,X2: $i] :
                                                              ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                             => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                               => ( ( X3 != X1 )
                                                                 => ( X3 = X2 ) ) )
                                                           => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                             => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                               => ( ! [X1: $i,X2: $i > $o] :
                                                                      ( ~ ! [X3: $i] :
                                                                            ( ( in @ X3 @ X1 )
                                                                           => ~ ( X2 @ X3 ) )
                                                                     => ( ( dsetconstr @ X1 @ X2 )
                                                                       != emptyset ) )
                                                                 => ( ! [X1: $i > $o,X2: $i] :
                                                                        ( ( in @ X2 @ emptyset )
                                                                       => ( X1 @ X2 ) )
                                                                   => ( ! [X1: $o] :
                                                                          ( X1
                                                                         => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                                                     => ( ! [X1: $o] :
                                                                            ( X1
                                                                           => ( set2prop @ ( prop2set @ X1 ) ) )
                                                                       => ( ! [X1: $i > $o] :
                                                                              ( ~ ! [X2: $i] :
                                                                                    ~ ( X1 @ X2 )
                                                                             => ( ! [X2: $i,X3: $i] :
                                                                                    ( ( X1 @ X2 )
                                                                                   => ( ( X1 @ X3 )
                                                                                     => ( X2 = X3 ) ) )
                                                                               => ~ ! [X2: $i] :
                                                                                      ( ( X1 @ X2 )
                                                                                     => ~ ! [X3: $i] :
                                                                                            ( ( X1 @ X3 )
                                                                                           => ( X2 = X3 ) ) ) ) )
                                                                         => ( ! [X1: $i > $o] :
                                                                                ( ~ ! [X2: $i] :
                                                                                      ~ ! [X3: $i] :
                                                                                          ( ( X1 @ X3 )
                                                                                          = ( X3 = X2 ) )
                                                                               => ~ ! [X2: $i] :
                                                                                      ( ( X1 @ X2 )
                                                                                     => ~ ! [X3: $i] :
                                                                                            ( ( X1 @ X3 )
                                                                                           => ( X2 = X3 ) ) ) )
                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                  ( ( X1 = X2 )
                                                                                 => ! [X3: $i,X4: $i] :
                                                                                      ( ( X3 = X4 )
                                                                                     => ( ( in @ X3 @ X1 )
                                                                                       => ( in @ X4 @ X2 ) ) ) )
                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                    ( ( X1 = X2 )
                                                                                   => ! [X3: $i,X4: $i] :
                                                                                        ( ( X3 = X4 )
                                                                                       => ( ( in @ X3 @ X1 )
                                                                                          = ( in @ X4 @ X2 ) ) ) )
                                                                               => ( ! [X1: $i > $o] :
                                                                                      ( ~ ! [X2: $i] :
                                                                                            ( ( X1 @ X2 )
                                                                                           => ~ ! [X3: $i] :
                                                                                                  ( ( X1 @ X3 )
                                                                                                 => ( X2 = X3 ) ) )
                                                                                     => ! [X2: $i,X3: $i] :
                                                                                          ( ( X1 @ X2 )
                                                                                         => ( ( X1 @ X3 )
                                                                                           => ( X2 = X3 ) ) ) )
                                                                                 => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                        ( ! [X3: $i,X4: $i] :
                                                                                            ( ( X3 = X4 )
                                                                                           => ( ( X1 @ X3 )
                                                                                              = ( X2 @ X4 ) ) )
                                                                                       => ( ( ~ ! [X3: $i] :
                                                                                                  ( ( X1 @ X3 )
                                                                                                 => ~ ! [X4: $i] :
                                                                                                        ( ( X1 @ X4 )
                                                                                                       => ( X3 = X4 ) ) ) )
                                                                                          = ( ~ ! [X3: $i] :
                                                                                                  ( ( X2 @ X3 )
                                                                                                 => ~ ! [X4: $i] :
                                                                                                        ( ( X2 @ X4 )
                                                                                                       => ( X3 = X4 ) ) ) ) ) )
                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                          ( ( X1 = X2 )
                                                                                         => ! [X3: $i,X4: $i] :
                                                                                              ( ( X3 = X4 )
                                                                                             => ( ( setadjoin @ X1 @ X3 )
                                                                                                = ( setadjoin @ X2 @ X4 ) ) ) )
                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                            ( ( X1 = X2 )
                                                                                           => ( ( powerset @ X1 )
                                                                                              = ( powerset @ X2 ) ) )
                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                              ( ( X1 = X2 )
                                                                                             => ( ( setunion @ X1 )
                                                                                                = ( setunion @ X2 ) ) )
                                                                                         => ( ! [X1: $i > $o] :
                                                                                                ( ~ ! [X2: $i] :
                                                                                                      ( ( X1 @ X2 )
                                                                                                     => ~ ! [X3: $i] :
                                                                                                            ( ( X1 @ X3 )
                                                                                                           => ( X2 = X3 ) ) )
                                                                                               => ! [X2: $i,X3: $i] :
                                                                                                    ( ( X1 @ X2 )
                                                                                                   => ( ( X1 @ X3 )
                                                                                                     => ( X2 = X3 ) ) ) )
                                                                                           => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                                  ( ! [X3: $i,X4: $i] :
                                                                                                      ( ( X3 = X4 )
                                                                                                     => ( ( X1 @ X3 )
                                                                                                        = ( X2 @ X4 ) ) )
                                                                                                 => ( ~ ! [X3: $i] :
                                                                                                          ( ( X1 @ X3 )
                                                                                                         => ~ ! [X4: $i] :
                                                                                                                ( ( X1 @ X4 )
                                                                                                               => ( X3 = X4 ) ) )
                                                                                                   => ( ~ ! [X3: $i] :
                                                                                                            ( ( X2 @ X3 )
                                                                                                           => ~ ! [X4: $i] :
                                                                                                                  ( ( X2 @ X4 )
                                                                                                                 => ( X3 = X4 ) ) )
                                                                                                     => ( ( descr @ X1 )
                                                                                                        = ( descr @ X2 ) ) ) ) )
                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                    ( ( X1 = X2 )
                                                                                                   => ! [X3: $i > $o,X4: $i > $o] :
                                                                                                        ( ! [X5: $i] :
                                                                                                            ( ( in @ X5 @ X1 )
                                                                                                           => ! [X6: $i] :
                                                                                                                ( ( in @ X6 @ X2 )
                                                                                                               => ( ( X5 = X6 )
                                                                                                                 => ( ( X3 @ X5 )
                                                                                                                    = ( X4 @ X6 ) ) ) ) )
                                                                                                       => ( ( dsetconstr @ X1 @ X3 )
                                                                                                          = ( dsetconstr @ X2 @ X4 ) ) ) )
                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                      ( ! [X3: $i] :
                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                         => ( in @ X3 @ X2 ) )
                                                                                                     => ( subset @ X1 @ X2 ) )
                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                        ( ( X1 = X2 )
                                                                                                       => ( subset @ X2 @ X1 ) )
                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                          ( ( X1 = X2 )
                                                                                                         => ( subset @ X1 @ X2 ) )
                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                            ( ! [X3: $i] :
                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                               => ( in @ X3 @ X2 ) )
                                                                                                           => ( subset @ X1 @ X2 ) )
                                                                                                       => ( ! [X1: $i] : ( subset @ emptyset @ X1 )
                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                ( ( subset @ X1 @ X2 )
                                                                                                               => ( ( in @ X3 @ X1 )
                                                                                                                 => ( in @ X3 @ X2 ) ) )
                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                  ( ( subset @ X1 @ X2 )
                                                                                                                 => ( ~ ( in @ X3 @ X2 )
                                                                                                                   => ~ ( in @ X3 @ X1 ) ) )
                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                   => ( ~ ( in @ X3 @ X2 )
                                                                                                                     => ~ ( subset @ X1 @ X2 ) ) )
                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                      ( ~ ( subset @ X1 @ X2 )
                                                                                                                     => ( X1 != X2 ) )
                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                       => ( ~ ( in @ X3 @ X2 )
                                                                                                                         => ( X1 != X2 ) ) )
                                                                                                                   => ( ! [X1: $i] : ( subset @ X1 @ X1 )
                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                            ( ( subset @ X1 @ X2 )
                                                                                                                           => ( ( subset @ X2 @ X3 )
                                                                                                                             => ( subset @ X1 @ X3 ) ) )
                                                                                                                       => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) )
                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                ( ( subset @ X1 @ X3 )
                                                                                                                               => ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                  ( ( subset @ X1 @ X2 )
                                                                                                                                 => ( in @ X1 @ ( powerset @ X2 ) ) )
                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                    ( ( subset @ X1 @ X2 )
                                                                                                                                   => ( ( subset @ X2 @ X1 )
                                                                                                                                     => ( X1 = X2 ) ) )
                                                                                                                               => ( ! [X1: $i] :
                                                                                                                                      ( ( subset @ X1 @ emptyset )
                                                                                                                                     => ( X1 = emptyset ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                        ( ( subset @ X2 @ X1 )
                                                                                                                                       => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                          ( ( in @ X2 @ ( powerset @ X1 ) )
                                                                                                                                         => ( subset @ X2 @ X1 ) )
                                                                                                                                     => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                              ( ( subset @ X1 @ X2 )
                                                                                                                                             => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
                                                                                                                                         => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                                                                                                                                           => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                   => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                                                               => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                        ( ( in @ X3 @ X2 )
                                                                                                                                                       => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                                                                                                                                          ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                         => ( ( ( in @ X3 @ X1 )
                                                                                                                                                             => X4 )
                                                                                                                                                           => ( ( ( in @ X3 @ X2 )
                                                                                                                                                               => X4 )
                                                                                                                                                             => X4 ) ) )
                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                            ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                           => ( ~ ( in @ X3 @ X1 )
                                                                                                                                                             => ( in @ X3 @ X2 ) ) )
                                                                                                                                                       => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                         => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                 => ( ( in @ X3 @ X2 )
                                                                                                                                                                   => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                    ( ( subset @ X3 @ X1 )
                                                                                                                                                                   => ( ( subset @ X3 @ X2 )
                                                                                                                                                                     => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                      ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                                                     => ( in @ X3 @ X1 ) )
                                                                                                                                                                 => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                          ( ( subset @ X1 @ X2 )
                                                                                                                                                                         => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                            = X1 ) )
                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                            ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                              = X2 )
                                                                                                                                                                           => ( subset @ X2 @ X1 ) )
                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                              ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                                                             => ( in @ X3 @ X2 ) )
                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                ( ! [X3: $i] :
                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                   => ~ ( in @ X3 @ X2 ) )
                                                                                                                                                                               => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                  = emptyset ) )
                                                                                                                                                                           => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                    ( ( subset @ X2 @ X1 )
                                                                                                                                                                                   => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                      = X2 ) )
                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                      ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                        = X1 )
                                                                                                                                                                                     => ( subset @ X1 @ X2 ) )
                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                        ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                                                                                                                                                        = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                         => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                           => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                            ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                           => ( in @ X3 @ X1 ) )
                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                              ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                             => ~ ( in @ X3 @ X2 ) )
                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                ( ( subset @ X1 @ X2 )
                                                                                                                                                                                               => ( ( setminus @ X1 @ X2 )
                                                                                                                                                                                                  = emptyset ) )
                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                  ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                 => ( ( in @ X3 @ X1 )
                                                                                                                                                                                                   => ( in @ X3 @ X2 ) ) )
                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                    ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                   => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                     => ~ ( in @ X3 @ X1 ) ) )
                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                      ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                     => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                        ( ( in @ X3 @ X2 )
                                                                                                                                                                                                       => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                            ( ( ( setminus @ X1 @ X2 )
                                                                                                                                                                                                              = emptyset )
                                                                                                                                                                                                           => ( subset @ X1 @ X2 ) )
                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                              ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                                                                                                                                             => ! [X4: $o] :
                                                                                                                                                                                                                  ( ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                   => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                     => X4 ) )
                                                                                                                                                                                                                 => ( ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                     => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                       => X4 ) )
                                                                                                                                                                                                                   => X4 ) ) )
                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                               => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                 => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                  ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                 => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                   => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                   => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                     => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                      ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                     => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                       => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                  ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                 => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                    ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                   => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                     => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                        ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                       => ( ( X3 != X1 )
                                                                                                                                                                                                                                         => ( X3 = X2 ) ) )
                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                             => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                               => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                 => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                   => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                     => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                       => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                      ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                     => ~ ! [X4: $i] :
                                                                                                                                                                                                                                                            ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                           => ! [X5: $i] :
                                                                                                                                                                                                                                                                ( ( in @ X5 @ X2 )
                                                                                                                                                                                                                                                               => ( X3
                                                                                                                                                                                                                                                                 != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                                                                                                                                                 => ( sP5
                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                          ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                                                                                                                                                         => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                               => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                                                                                                                                                     => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                                                                                                                                                       => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                                                         => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                                                                                                                                                = X1 )
                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                                  ( ! [X3: $i] :
                                                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                                                                                                                          ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                         => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                                           => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                             => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                                                                 => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                         => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                                                                   => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                          ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                         => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                           != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                                    ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                          ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                         => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                           != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                                                                                                                                                   => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                         => ~ ( X2 @ X3 ) ) )
                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                     => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                                       => ( ! [X4: $i] :
                                                                                                                                                                                                                                                                              ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                             => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                               => ( X4 = X3 ) ) )
                                                                                                                                                                                                                                                                         => ~ ! [X4: $i] :
                                                                                                                                                                                                                                                                                ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                               => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                                 != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                                        ( ! [X3: $i] :
                                                                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                                                                                                                                ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                               => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                                                 => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                                   => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                                                                       => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                               => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                                                                         => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                               => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                                 != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                          ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                                                                                                                                            = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                         => ( X1 = X2 ) )
                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                            ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                           => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                       => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                              ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                                             => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                    ( ( in @ X2
                                                                                                                                                                                                                                                                                      @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                        @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                                                                                                                                                   => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                        @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                                                                                     != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                                                         => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                ( ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                      ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                                                                     => ( X1
                                                                                                                                                                                                                                                                                       != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                                                               => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                  ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                  = X1 )
                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                    ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                   => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                      ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                        = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                     => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                        ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                                                          = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                       => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                          ( ( X1 = X2 )
                                                                                                                                                                                                                                                                                         => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                                            = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                            ( ( X1 = X2 )
                                                                                                                                                                                                                                                                                           => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                              = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                              ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                             => ( ( X3 = X4 )
                                                                                                                                                                                                                                                                                               => ( X2 = X4 ) ) )
                                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                                                  = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                                                                                                                                               => ( X1 = X2 ) )
                                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                  ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                    = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                 => ( X2 = X4 ) )
                                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                    ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                      = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                   => ( X2 = X4 ) )
                                                                                                                                                                                                                                                                                               => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                                      ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                                                                     => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                                            ( ( in @ X2
                                                                                                                                                                                                                                                                                                              @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                                @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                                                                    ( X1
                                                                                                                                                                                                                                                                                                                    = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                                                                                                                                           => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                                @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                                                                    ( X1
                                                                                                                                                                                                                                                                                                                    = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                                                                                                                                             != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                        ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                        = X2 )
                                                                                                                                                                                                                                                                                                   => ( sP8
                                                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                            ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                           => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                              ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                             => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                               => ( in @ X4 @ X2 ) )
                                                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                                                     => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                                        = X3 ) ) )
                                                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                                                       => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                                          = X4 ) ) )
                                                                                                                                                                                                                                                                                                               => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                    ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                   => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                                                                                                                                                      = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h37,assumption,
    ! [X1: $i > $o] :
      ( ~ ! [X2: $i] :
            ( ( X1 @ X2 )
           => ~ ! [X3: $i] :
                  ( ( X1 @ X3 )
                 => ( X2 = X3 ) ) )
     => ~ ! [X2: $i] :
            ~ ( X1 @ X2 ) ),
    introduced(assumption,[]) ).

thf(h38,assumption,
    ~ ( ! [X1: $i,X2: $i] :
          ( ! [X3: $i] :
              ( ( in @ X3 @ X1 )
             => ( in @ X3 @ X2 ) )
         => ( ! [X3: $i] :
                ( ( in @ X3 @ X2 )
               => ( in @ X3 @ X1 ) )
           => ( X1 = X2 ) ) )
     => ( ! [X1: $i] :
            ( ! [X2: $i] :
                ~ ( in @ X2 @ X1 )
           => ( X1 = emptyset ) )
       => ( ! [X1: $i] :
              ( ! [X2: $i] :
                  ~ ( in @ X2 @ X1 )
             => ( X1 = emptyset ) )
         => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                ( ( in @ X3 @ X1 )
               => ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                  = ( X2 @ X3 ) ) )
           => ( ! [X1: $i] :
                  ( ( X1 != emptyset )
                 => ~ ! [X2: $i] :
                        ~ ( in @ X2 @ X1 ) )
             => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                    ( ( in @ X3 @ X1 )
                   => ( ( X2 @ X3 )
                     => ( ( dsetconstr @ X1 @ X2 )
                       != emptyset ) ) )
               => ( ! [X1: $i] :
                      ( ~ ! [X2: $i] :
                            ~ ( in @ X2 @ X1 )
                     => ( X1 != emptyset ) )
                 => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) )
                   => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
                     => ( ! [X1: $i,X2: $i,X3: $i] :
                            ( ( in @ X3 @ X2 )
                           => ( in @ X3 @ ( setadjoin @ X1 @ X2 ) ) )
                       => ( ! [X1: $i,X2: $i,X3: $i] :
                              ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                             => ! [X4: $o] :
                                  ( ( ( X3 = X1 )
                                   => X4 )
                                 => ( ( ( in @ X3 @ X2 )
                                     => X4 )
                                   => X4 ) ) )
                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                               => ( ( X3 != X1 )
                                 => ( in @ X3 @ X2 ) ) )
                           => ( ! [X1: $i] :
                                  ( ( dsetconstr @ X1
                                    @ ^ [X2: $i] : ~ $false )
                                  = X1 )
                             => ( ! [X1: $i,X2: $i] :
                                    ( ! [X3: $i] :
                                        ( ( in @ X3 @ X2 )
                                       => ( in @ X3 @ X1 ) )
                                   => ( in @ X2 @ ( powerset @ X1 ) ) )
                               => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                 => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                          ( ( in @ X2 @ ( powerset @ X1 ) )
                                         => ( ( in @ X3 @ X2 )
                                           => ( in @ X3 @ X1 ) ) )
                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                            ( ( in @ X2 @ X3 )
                                           => ( ( in @ X3 @ X1 )
                                             => ( in @ X2 @ ( setunion @ X1 ) ) ) )
                                       => ( ! [X1: $i,X2: $i] :
                                              ( ( in @ X2 @ ( setunion @ X1 ) )
                                             => ! [X3: $o] :
                                                  ( ! [X4: $i] :
                                                      ( ( in @ X2 @ X4 )
                                                     => ( ( in @ X4 @ X1 )
                                                       => X3 ) )
                                                 => X3 ) )
                                         => ( ! [X1: $i,X2: $i] :
                                                ( ( in @ X2 @ X1 )
                                               => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
                                           => ( ! [X1: $i > $o] :
                                                  ( ~ ! [X2: $i] :
                                                        ( ( X1 @ X2 )
                                                       => ~ ! [X3: $i] :
                                                              ( ( X1 @ X3 )
                                                             => ( X2 = X3 ) ) )
                                                 => ~ ! [X2: $i] :
                                                        ~ ! [X3: $i] :
                                                            ( ( X1 @ X3 )
                                                            = ( X3 = X2 ) ) )
                                             => ( ! [X1: $i] :
                                                    ( ( X1 != emptyset )
                                                   => ~ ! [X2: $i] :
                                                          ~ ( in @ X2 @ X1 ) )
                                               => ( ! [X1: $i,X2: $i] :
                                                      ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                     => ( X1 = X2 ) )
                                                 => ( ! [X1: $i,X2: $i] :
                                                        ( ( X1 != X2 )
                                                       => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                   => ( ! [X1: $i,X2: $i] :
                                                          ( ( X1 = X2 )
                                                         => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                     => ( ! [X1: $i,X2: $i] :
                                                            ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                           => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                              ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                             => ( ( X3 != X1 )
                                                               => ( X3 = X2 ) ) )
                                                         => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                           => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                             => ( ! [X1: $i,X2: $i > $o] :
                                                                    ( ~ ! [X3: $i] :
                                                                          ( ( in @ X3 @ X1 )
                                                                         => ~ ( X2 @ X3 ) )
                                                                   => ( ( dsetconstr @ X1 @ X2 )
                                                                     != emptyset ) )
                                                               => ( ! [X1: $i > $o,X2: $i] :
                                                                      ( ( in @ X2 @ emptyset )
                                                                     => ( X1 @ X2 ) )
                                                                 => ( ! [X1: $o] :
                                                                        ( X1
                                                                       => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                                                   => ( ! [X1: $o] :
                                                                          ( X1
                                                                         => ( set2prop @ ( prop2set @ X1 ) ) )
                                                                     => ( ! [X1: $i > $o] :
                                                                            ( ~ ! [X2: $i] :
                                                                                  ~ ( X1 @ X2 )
                                                                           => ( ! [X2: $i,X3: $i] :
                                                                                  ( ( X1 @ X2 )
                                                                                 => ( ( X1 @ X3 )
                                                                                   => ( X2 = X3 ) ) )
                                                                             => ~ ! [X2: $i] :
                                                                                    ( ( X1 @ X2 )
                                                                                   => ~ ! [X3: $i] :
                                                                                          ( ( X1 @ X3 )
                                                                                         => ( X2 = X3 ) ) ) ) )
                                                                       => ( ! [X1: $i > $o] :
                                                                              ( ~ ! [X2: $i] :
                                                                                    ~ ! [X3: $i] :
                                                                                        ( ( X1 @ X3 )
                                                                                        = ( X3 = X2 ) )
                                                                             => ~ ! [X2: $i] :
                                                                                    ( ( X1 @ X2 )
                                                                                   => ~ ! [X3: $i] :
                                                                                          ( ( X1 @ X3 )
                                                                                         => ( X2 = X3 ) ) ) )
                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                ( ( X1 = X2 )
                                                                               => ! [X3: $i,X4: $i] :
                                                                                    ( ( X3 = X4 )
                                                                                   => ( ( in @ X3 @ X1 )
                                                                                     => ( in @ X4 @ X2 ) ) ) )
                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                  ( ( X1 = X2 )
                                                                                 => ! [X3: $i,X4: $i] :
                                                                                      ( ( X3 = X4 )
                                                                                     => ( ( in @ X3 @ X1 )
                                                                                        = ( in @ X4 @ X2 ) ) ) )
                                                                             => ( ! [X1: $i > $o] :
                                                                                    ( ~ ! [X2: $i] :
                                                                                          ( ( X1 @ X2 )
                                                                                         => ~ ! [X3: $i] :
                                                                                                ( ( X1 @ X3 )
                                                                                               => ( X2 = X3 ) ) )
                                                                                   => ! [X2: $i,X3: $i] :
                                                                                        ( ( X1 @ X2 )
                                                                                       => ( ( X1 @ X3 )
                                                                                         => ( X2 = X3 ) ) ) )
                                                                               => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                      ( ! [X3: $i,X4: $i] :
                                                                                          ( ( X3 = X4 )
                                                                                         => ( ( X1 @ X3 )
                                                                                            = ( X2 @ X4 ) ) )
                                                                                     => ( ( ~ ! [X3: $i] :
                                                                                                ( ( X1 @ X3 )
                                                                                               => ~ ! [X4: $i] :
                                                                                                      ( ( X1 @ X4 )
                                                                                                     => ( X3 = X4 ) ) ) )
                                                                                        = ( ~ ! [X3: $i] :
                                                                                                ( ( X2 @ X3 )
                                                                                               => ~ ! [X4: $i] :
                                                                                                      ( ( X2 @ X4 )
                                                                                                     => ( X3 = X4 ) ) ) ) ) )
                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                        ( ( X1 = X2 )
                                                                                       => ! [X3: $i,X4: $i] :
                                                                                            ( ( X3 = X4 )
                                                                                           => ( ( setadjoin @ X1 @ X3 )
                                                                                              = ( setadjoin @ X2 @ X4 ) ) ) )
                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                          ( ( X1 = X2 )
                                                                                         => ( ( powerset @ X1 )
                                                                                            = ( powerset @ X2 ) ) )
                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                            ( ( X1 = X2 )
                                                                                           => ( ( setunion @ X1 )
                                                                                              = ( setunion @ X2 ) ) )
                                                                                       => ( ! [X1: $i > $o] :
                                                                                              ( ~ ! [X2: $i] :
                                                                                                    ( ( X1 @ X2 )
                                                                                                   => ~ ! [X3: $i] :
                                                                                                          ( ( X1 @ X3 )
                                                                                                         => ( X2 = X3 ) ) )
                                                                                             => ! [X2: $i,X3: $i] :
                                                                                                  ( ( X1 @ X2 )
                                                                                                 => ( ( X1 @ X3 )
                                                                                                   => ( X2 = X3 ) ) ) )
                                                                                         => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                                ( ! [X3: $i,X4: $i] :
                                                                                                    ( ( X3 = X4 )
                                                                                                   => ( ( X1 @ X3 )
                                                                                                      = ( X2 @ X4 ) ) )
                                                                                               => ( ~ ! [X3: $i] :
                                                                                                        ( ( X1 @ X3 )
                                                                                                       => ~ ! [X4: $i] :
                                                                                                              ( ( X1 @ X4 )
                                                                                                             => ( X3 = X4 ) ) )
                                                                                                 => ( ~ ! [X3: $i] :
                                                                                                          ( ( X2 @ X3 )
                                                                                                         => ~ ! [X4: $i] :
                                                                                                                ( ( X2 @ X4 )
                                                                                                               => ( X3 = X4 ) ) )
                                                                                                   => ( ( descr @ X1 )
                                                                                                      = ( descr @ X2 ) ) ) ) )
                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                  ( ( X1 = X2 )
                                                                                                 => ! [X3: $i > $o,X4: $i > $o] :
                                                                                                      ( ! [X5: $i] :
                                                                                                          ( ( in @ X5 @ X1 )
                                                                                                         => ! [X6: $i] :
                                                                                                              ( ( in @ X6 @ X2 )
                                                                                                             => ( ( X5 = X6 )
                                                                                                               => ( ( X3 @ X5 )
                                                                                                                  = ( X4 @ X6 ) ) ) ) )
                                                                                                     => ( ( dsetconstr @ X1 @ X3 )
                                                                                                        = ( dsetconstr @ X2 @ X4 ) ) ) )
                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                    ( ! [X3: $i] :
                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                       => ( in @ X3 @ X2 ) )
                                                                                                   => ( subset @ X1 @ X2 ) )
                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                      ( ( X1 = X2 )
                                                                                                     => ( subset @ X2 @ X1 ) )
                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                        ( ( X1 = X2 )
                                                                                                       => ( subset @ X1 @ X2 ) )
                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                          ( ! [X3: $i] :
                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                             => ( in @ X3 @ X2 ) )
                                                                                                         => ( subset @ X1 @ X2 ) )
                                                                                                     => ( ! [X1: $i] : ( subset @ emptyset @ X1 )
                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                              ( ( subset @ X1 @ X2 )
                                                                                                             => ( ( in @ X3 @ X1 )
                                                                                                               => ( in @ X3 @ X2 ) ) )
                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                ( ( subset @ X1 @ X2 )
                                                                                                               => ( ~ ( in @ X3 @ X2 )
                                                                                                                 => ~ ( in @ X3 @ X1 ) ) )
                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                 => ( ~ ( in @ X3 @ X2 )
                                                                                                                   => ~ ( subset @ X1 @ X2 ) ) )
                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                    ( ~ ( subset @ X1 @ X2 )
                                                                                                                   => ( X1 != X2 ) )
                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                     => ( ~ ( in @ X3 @ X2 )
                                                                                                                       => ( X1 != X2 ) ) )
                                                                                                                 => ( ! [X1: $i] : ( subset @ X1 @ X1 )
                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                          ( ( subset @ X1 @ X2 )
                                                                                                                         => ( ( subset @ X2 @ X3 )
                                                                                                                           => ( subset @ X1 @ X3 ) ) )
                                                                                                                     => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) )
                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                              ( ( subset @ X1 @ X3 )
                                                                                                                             => ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                ( ( subset @ X1 @ X2 )
                                                                                                                               => ( in @ X1 @ ( powerset @ X2 ) ) )
                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                  ( ( subset @ X1 @ X2 )
                                                                                                                                 => ( ( subset @ X2 @ X1 )
                                                                                                                                   => ( X1 = X2 ) ) )
                                                                                                                             => ( ! [X1: $i] :
                                                                                                                                    ( ( subset @ X1 @ emptyset )
                                                                                                                                   => ( X1 = emptyset ) )
                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                      ( ( subset @ X2 @ X1 )
                                                                                                                                     => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                        ( ( in @ X2 @ ( powerset @ X1 ) )
                                                                                                                                       => ( subset @ X2 @ X1 ) )
                                                                                                                                   => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                            ( ( subset @ X1 @ X2 )
                                                                                                                                           => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                                                                                                                                         => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                 => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                                                             => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                      ( ( in @ X3 @ X2 )
                                                                                                                                                     => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                                                                                                                                        ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                       => ( ( ( in @ X3 @ X1 )
                                                                                                                                                           => X4 )
                                                                                                                                                         => ( ( ( in @ X3 @ X2 )
                                                                                                                                                             => X4 )
                                                                                                                                                           => X4 ) ) )
                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                          ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                         => ( ~ ( in @ X3 @ X1 )
                                                                                                                                                           => ( in @ X3 @ X2 ) ) )
                                                                                                                                                     => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                       => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                               => ( ( in @ X3 @ X2 )
                                                                                                                                                                 => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                  ( ( subset @ X3 @ X1 )
                                                                                                                                                                 => ( ( subset @ X3 @ X2 )
                                                                                                                                                                   => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                    ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                                                   => ( in @ X3 @ X1 ) )
                                                                                                                                                               => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                        ( ( subset @ X1 @ X2 )
                                                                                                                                                                       => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                          = X1 ) )
                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                          ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                            = X2 )
                                                                                                                                                                         => ( subset @ X2 @ X1 ) )
                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                            ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                                                           => ( in @ X3 @ X2 ) )
                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                              ( ! [X3: $i] :
                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                 => ~ ( in @ X3 @ X2 ) )
                                                                                                                                                                             => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                = emptyset ) )
                                                                                                                                                                         => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                  ( ( subset @ X2 @ X1 )
                                                                                                                                                                                 => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                    = X2 ) )
                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                    ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                      = X1 )
                                                                                                                                                                                   => ( subset @ X1 @ X2 ) )
                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                      ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                                                                                                                                                      = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                       => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                         => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                          ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                         => ( in @ X3 @ X1 ) )
                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                            ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                           => ~ ( in @ X3 @ X2 ) )
                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                              ( ( subset @ X1 @ X2 )
                                                                                                                                                                                             => ( ( setminus @ X1 @ X2 )
                                                                                                                                                                                                = emptyset ) )
                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                               => ( ( in @ X3 @ X1 )
                                                                                                                                                                                                 => ( in @ X3 @ X2 ) ) )
                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                  ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                 => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                   => ~ ( in @ X3 @ X1 ) ) )
                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                    ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                   => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                      ( ( in @ X3 @ X2 )
                                                                                                                                                                                                     => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                          ( ( ( setminus @ X1 @ X2 )
                                                                                                                                                                                                            = emptyset )
                                                                                                                                                                                                         => ( subset @ X1 @ X2 ) )
                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                            ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                                                                                                                                           => ! [X4: $o] :
                                                                                                                                                                                                                ( ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                 => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                   => X4 ) )
                                                                                                                                                                                                               => ( ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                   => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                     => X4 ) )
                                                                                                                                                                                                                 => X4 ) ) )
                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                             => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                               => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                               => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                 => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                 => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                   => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                    ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                   => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                     => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                               => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                  ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                 => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                   => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                      ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                     => ( ( X3 != X1 )
                                                                                                                                                                                                                                       => ( X3 = X2 ) ) )
                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                           => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                             => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                               => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                 => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                   => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                     => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                    ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                   => ~ ! [X4: $i] :
                                                                                                                                                                                                                                                          ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                         => ! [X5: $i] :
                                                                                                                                                                                                                                                              ( ( in @ X5 @ X2 )
                                                                                                                                                                                                                                                             => ( X3
                                                                                                                                                                                                                                                               != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                                                                                                                                               => ( sP5
                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                        ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                                                                                                                                                       => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                             => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                                                                                                                                                   => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                                                                                                                                                     => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                                                       => ( ! [X1: $i] :
                                                                                                                                                                                                                                                              ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                                                                                                                                              = X1 )
                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                                ( ! [X3: $i] :
                                                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                                                                                                                        ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                       => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                                         => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                           => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                                                               => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                       => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                                                                 => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                        ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                       => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                         != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                                  ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                        ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                       => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                         != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                                                                                                                                                 => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                       => ~ ( X2 @ X3 ) ) )
                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                   => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                                     => ( ! [X4: $i] :
                                                                                                                                                                                                                                                                            ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                           => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                             => ( X4 = X3 ) ) )
                                                                                                                                                                                                                                                                       => ~ ! [X4: $i] :
                                                                                                                                                                                                                                                                              ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                             => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                               != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                                      ( ! [X3: $i] :
                                                                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                                                                                                                              ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                             => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                                               => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                                 => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                                                                     => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                             => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                                                                       => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                              ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                             => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                               != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                        ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                                                                                                                                          = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                       => ( X1 = X2 ) )
                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                          ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                         => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                     => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                            ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                                           => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                  ( ( in @ X2
                                                                                                                                                                                                                                                                                    @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                      @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                                                                                                                                                 => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                      @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                                                                                   != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                                                       => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                              ( ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                    ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                                                                   => ( X1
                                                                                                                                                                                                                                                                                     != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                                                             => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                = X1 )
                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                  ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                 => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                    ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                      = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                   => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                      ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                                                        = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                     => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                        ( ( X1 = X2 )
                                                                                                                                                                                                                                                                                       => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                                          = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                          ( ( X1 = X2 )
                                                                                                                                                                                                                                                                                         => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                            = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                            ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                              = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                           => ( ( X3 = X4 )
                                                                                                                                                                                                                                                                                             => ( X2 = X4 ) ) )
                                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                              ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                                                = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                                                                                                                                             => ( X1 = X2 ) )
                                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                  = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                               => ( X2 = X4 ) )
                                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                  ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                    = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                 => ( X2 = X4 ) )
                                                                                                                                                                                                                                                                                             => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                                    ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                                                                   => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                                          ( ( in @ X2
                                                                                                                                                                                                                                                                                                            @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                              @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                                                                  ( X1
                                                                                                                                                                                                                                                                                                                  = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                                                                                                                                         => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                              @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                                                                  ( X1
                                                                                                                                                                                                                                                                                                                  = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                                                                                                                                           != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                      ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                      = X2 )
                                                                                                                                                                                                                                                                                                 => ( sP8
                                                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                         => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                            ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                           => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                              ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                             => ( in @ X4 @ X2 ) )
                                                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                                                   => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                                      = X3 ) ) )
                                                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                                                     => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                                        = X4 ) ) )
                                                                                                                                                                                                                                                                                                             => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                  ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                 => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                                                                                                                                                    = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h39,assumption,
    ! [X1: $i,X2: $i] :
      ( ! [X3: $i] :
          ( ( in @ X3 @ X1 )
         => ( in @ X3 @ X2 ) )
     => ( ! [X3: $i] :
            ( ( in @ X3 @ X2 )
           => ( in @ X3 @ X1 ) )
       => ( X1 = X2 ) ) ),
    introduced(assumption,[]) ).

thf(h40,assumption,
    ~ ( ! [X1: $i] :
          ( ! [X2: $i] :
              ~ ( in @ X2 @ X1 )
         => ( X1 = emptyset ) )
     => ( ! [X1: $i] :
            ( ! [X2: $i] :
                ~ ( in @ X2 @ X1 )
           => ( X1 = emptyset ) )
       => ( ! [X1: $i,X2: $i > $o,X3: $i] :
              ( ( in @ X3 @ X1 )
             => ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                = ( X2 @ X3 ) ) )
         => ( ! [X1: $i] :
                ( ( X1 != emptyset )
               => ~ ! [X2: $i] :
                      ~ ( in @ X2 @ X1 ) )
           => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                  ( ( in @ X3 @ X1 )
                 => ( ( X2 @ X3 )
                   => ( ( dsetconstr @ X1 @ X2 )
                     != emptyset ) ) )
             => ( ! [X1: $i] :
                    ( ~ ! [X2: $i] :
                          ~ ( in @ X2 @ X1 )
                   => ( X1 != emptyset ) )
               => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) )
                 => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
                   => ( ! [X1: $i,X2: $i,X3: $i] :
                          ( ( in @ X3 @ X2 )
                         => ( in @ X3 @ ( setadjoin @ X1 @ X2 ) ) )
                     => ( ! [X1: $i,X2: $i,X3: $i] :
                            ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                           => ! [X4: $o] :
                                ( ( ( X3 = X1 )
                                 => X4 )
                               => ( ( ( in @ X3 @ X2 )
                                   => X4 )
                                 => X4 ) ) )
                       => ( ! [X1: $i,X2: $i,X3: $i] :
                              ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                             => ( ( X3 != X1 )
                               => ( in @ X3 @ X2 ) ) )
                         => ( ! [X1: $i] :
                                ( ( dsetconstr @ X1
                                  @ ^ [X2: $i] : ~ $false )
                                = X1 )
                           => ( ! [X1: $i,X2: $i] :
                                  ( ! [X3: $i] :
                                      ( ( in @ X3 @ X2 )
                                     => ( in @ X3 @ X1 ) )
                                 => ( in @ X2 @ ( powerset @ X1 ) ) )
                             => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                               => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                        ( ( in @ X2 @ ( powerset @ X1 ) )
                                       => ( ( in @ X3 @ X2 )
                                         => ( in @ X3 @ X1 ) ) )
                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                          ( ( in @ X2 @ X3 )
                                         => ( ( in @ X3 @ X1 )
                                           => ( in @ X2 @ ( setunion @ X1 ) ) ) )
                                     => ( ! [X1: $i,X2: $i] :
                                            ( ( in @ X2 @ ( setunion @ X1 ) )
                                           => ! [X3: $o] :
                                                ( ! [X4: $i] :
                                                    ( ( in @ X2 @ X4 )
                                                   => ( ( in @ X4 @ X1 )
                                                     => X3 ) )
                                               => X3 ) )
                                       => ( ! [X1: $i,X2: $i] :
                                              ( ( in @ X2 @ X1 )
                                             => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
                                         => ( ! [X1: $i > $o] :
                                                ( ~ ! [X2: $i] :
                                                      ( ( X1 @ X2 )
                                                     => ~ ! [X3: $i] :
                                                            ( ( X1 @ X3 )
                                                           => ( X2 = X3 ) ) )
                                               => ~ ! [X2: $i] :
                                                      ~ ! [X3: $i] :
                                                          ( ( X1 @ X3 )
                                                          = ( X3 = X2 ) ) )
                                           => ( ! [X1: $i] :
                                                  ( ( X1 != emptyset )
                                                 => ~ ! [X2: $i] :
                                                        ~ ( in @ X2 @ X1 ) )
                                             => ( ! [X1: $i,X2: $i] :
                                                    ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                   => ( X1 = X2 ) )
                                               => ( ! [X1: $i,X2: $i] :
                                                      ( ( X1 != X2 )
                                                     => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                 => ( ! [X1: $i,X2: $i] :
                                                        ( ( X1 = X2 )
                                                       => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                   => ( ! [X1: $i,X2: $i] :
                                                          ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                         => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                            ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                           => ( ( X3 != X1 )
                                                             => ( X3 = X2 ) ) )
                                                       => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                         => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                           => ( ! [X1: $i,X2: $i > $o] :
                                                                  ( ~ ! [X3: $i] :
                                                                        ( ( in @ X3 @ X1 )
                                                                       => ~ ( X2 @ X3 ) )
                                                                 => ( ( dsetconstr @ X1 @ X2 )
                                                                   != emptyset ) )
                                                             => ( ! [X1: $i > $o,X2: $i] :
                                                                    ( ( in @ X2 @ emptyset )
                                                                   => ( X1 @ X2 ) )
                                                               => ( ! [X1: $o] :
                                                                      ( X1
                                                                     => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                                                 => ( ! [X1: $o] :
                                                                        ( X1
                                                                       => ( set2prop @ ( prop2set @ X1 ) ) )
                                                                   => ( ! [X1: $i > $o] :
                                                                          ( ~ ! [X2: $i] :
                                                                                ~ ( X1 @ X2 )
                                                                         => ( ! [X2: $i,X3: $i] :
                                                                                ( ( X1 @ X2 )
                                                                               => ( ( X1 @ X3 )
                                                                                 => ( X2 = X3 ) ) )
                                                                           => ~ ! [X2: $i] :
                                                                                  ( ( X1 @ X2 )
                                                                                 => ~ ! [X3: $i] :
                                                                                        ( ( X1 @ X3 )
                                                                                       => ( X2 = X3 ) ) ) ) )
                                                                     => ( ! [X1: $i > $o] :
                                                                            ( ~ ! [X2: $i] :
                                                                                  ~ ! [X3: $i] :
                                                                                      ( ( X1 @ X3 )
                                                                                      = ( X3 = X2 ) )
                                                                           => ~ ! [X2: $i] :
                                                                                  ( ( X1 @ X2 )
                                                                                 => ~ ! [X3: $i] :
                                                                                        ( ( X1 @ X3 )
                                                                                       => ( X2 = X3 ) ) ) )
                                                                       => ( ! [X1: $i,X2: $i] :
                                                                              ( ( X1 = X2 )
                                                                             => ! [X3: $i,X4: $i] :
                                                                                  ( ( X3 = X4 )
                                                                                 => ( ( in @ X3 @ X1 )
                                                                                   => ( in @ X4 @ X2 ) ) ) )
                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                ( ( X1 = X2 )
                                                                               => ! [X3: $i,X4: $i] :
                                                                                    ( ( X3 = X4 )
                                                                                   => ( ( in @ X3 @ X1 )
                                                                                      = ( in @ X4 @ X2 ) ) ) )
                                                                           => ( ! [X1: $i > $o] :
                                                                                  ( ~ ! [X2: $i] :
                                                                                        ( ( X1 @ X2 )
                                                                                       => ~ ! [X3: $i] :
                                                                                              ( ( X1 @ X3 )
                                                                                             => ( X2 = X3 ) ) )
                                                                                 => ! [X2: $i,X3: $i] :
                                                                                      ( ( X1 @ X2 )
                                                                                     => ( ( X1 @ X3 )
                                                                                       => ( X2 = X3 ) ) ) )
                                                                             => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                    ( ! [X3: $i,X4: $i] :
                                                                                        ( ( X3 = X4 )
                                                                                       => ( ( X1 @ X3 )
                                                                                          = ( X2 @ X4 ) ) )
                                                                                   => ( ( ~ ! [X3: $i] :
                                                                                              ( ( X1 @ X3 )
                                                                                             => ~ ! [X4: $i] :
                                                                                                    ( ( X1 @ X4 )
                                                                                                   => ( X3 = X4 ) ) ) )
                                                                                      = ( ~ ! [X3: $i] :
                                                                                              ( ( X2 @ X3 )
                                                                                             => ~ ! [X4: $i] :
                                                                                                    ( ( X2 @ X4 )
                                                                                                   => ( X3 = X4 ) ) ) ) ) )
                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                      ( ( X1 = X2 )
                                                                                     => ! [X3: $i,X4: $i] :
                                                                                          ( ( X3 = X4 )
                                                                                         => ( ( setadjoin @ X1 @ X3 )
                                                                                            = ( setadjoin @ X2 @ X4 ) ) ) )
                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                        ( ( X1 = X2 )
                                                                                       => ( ( powerset @ X1 )
                                                                                          = ( powerset @ X2 ) ) )
                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                          ( ( X1 = X2 )
                                                                                         => ( ( setunion @ X1 )
                                                                                            = ( setunion @ X2 ) ) )
                                                                                     => ( ! [X1: $i > $o] :
                                                                                            ( ~ ! [X2: $i] :
                                                                                                  ( ( X1 @ X2 )
                                                                                                 => ~ ! [X3: $i] :
                                                                                                        ( ( X1 @ X3 )
                                                                                                       => ( X2 = X3 ) ) )
                                                                                           => ! [X2: $i,X3: $i] :
                                                                                                ( ( X1 @ X2 )
                                                                                               => ( ( X1 @ X3 )
                                                                                                 => ( X2 = X3 ) ) ) )
                                                                                       => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                              ( ! [X3: $i,X4: $i] :
                                                                                                  ( ( X3 = X4 )
                                                                                                 => ( ( X1 @ X3 )
                                                                                                    = ( X2 @ X4 ) ) )
                                                                                             => ( ~ ! [X3: $i] :
                                                                                                      ( ( X1 @ X3 )
                                                                                                     => ~ ! [X4: $i] :
                                                                                                            ( ( X1 @ X4 )
                                                                                                           => ( X3 = X4 ) ) )
                                                                                               => ( ~ ! [X3: $i] :
                                                                                                        ( ( X2 @ X3 )
                                                                                                       => ~ ! [X4: $i] :
                                                                                                              ( ( X2 @ X4 )
                                                                                                             => ( X3 = X4 ) ) )
                                                                                                 => ( ( descr @ X1 )
                                                                                                    = ( descr @ X2 ) ) ) ) )
                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                ( ( X1 = X2 )
                                                                                               => ! [X3: $i > $o,X4: $i > $o] :
                                                                                                    ( ! [X5: $i] :
                                                                                                        ( ( in @ X5 @ X1 )
                                                                                                       => ! [X6: $i] :
                                                                                                            ( ( in @ X6 @ X2 )
                                                                                                           => ( ( X5 = X6 )
                                                                                                             => ( ( X3 @ X5 )
                                                                                                                = ( X4 @ X6 ) ) ) ) )
                                                                                                   => ( ( dsetconstr @ X1 @ X3 )
                                                                                                      = ( dsetconstr @ X2 @ X4 ) ) ) )
                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                  ( ! [X3: $i] :
                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                     => ( in @ X3 @ X2 ) )
                                                                                                 => ( subset @ X1 @ X2 ) )
                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                    ( ( X1 = X2 )
                                                                                                   => ( subset @ X2 @ X1 ) )
                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                      ( ( X1 = X2 )
                                                                                                     => ( subset @ X1 @ X2 ) )
                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                        ( ! [X3: $i] :
                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                           => ( in @ X3 @ X2 ) )
                                                                                                       => ( subset @ X1 @ X2 ) )
                                                                                                   => ( ! [X1: $i] : ( subset @ emptyset @ X1 )
                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                            ( ( subset @ X1 @ X2 )
                                                                                                           => ( ( in @ X3 @ X1 )
                                                                                                             => ( in @ X3 @ X2 ) ) )
                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                              ( ( subset @ X1 @ X2 )
                                                                                                             => ( ~ ( in @ X3 @ X2 )
                                                                                                               => ~ ( in @ X3 @ X1 ) ) )
                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                               => ( ~ ( in @ X3 @ X2 )
                                                                                                                 => ~ ( subset @ X1 @ X2 ) ) )
                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                  ( ~ ( subset @ X1 @ X2 )
                                                                                                                 => ( X1 != X2 ) )
                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                   => ( ~ ( in @ X3 @ X2 )
                                                                                                                     => ( X1 != X2 ) ) )
                                                                                                               => ( ! [X1: $i] : ( subset @ X1 @ X1 )
                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                        ( ( subset @ X1 @ X2 )
                                                                                                                       => ( ( subset @ X2 @ X3 )
                                                                                                                         => ( subset @ X1 @ X3 ) ) )
                                                                                                                   => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) )
                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                            ( ( subset @ X1 @ X3 )
                                                                                                                           => ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                              ( ( subset @ X1 @ X2 )
                                                                                                                             => ( in @ X1 @ ( powerset @ X2 ) ) )
                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                ( ( subset @ X1 @ X2 )
                                                                                                                               => ( ( subset @ X2 @ X1 )
                                                                                                                                 => ( X1 = X2 ) ) )
                                                                                                                           => ( ! [X1: $i] :
                                                                                                                                  ( ( subset @ X1 @ emptyset )
                                                                                                                                 => ( X1 = emptyset ) )
                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                    ( ( subset @ X2 @ X1 )
                                                                                                                                   => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                      ( ( in @ X2 @ ( powerset @ X1 ) )
                                                                                                                                     => ( subset @ X2 @ X1 ) )
                                                                                                                                 => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                          ( ( subset @ X1 @ X2 )
                                                                                                                                         => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                               => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                                                           => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                    ( ( in @ X3 @ X2 )
                                                                                                                                                   => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                                                                                                                                      ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                     => ( ( ( in @ X3 @ X1 )
                                                                                                                                                         => X4 )
                                                                                                                                                       => ( ( ( in @ X3 @ X2 )
                                                                                                                                                           => X4 )
                                                                                                                                                         => X4 ) ) )
                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                        ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                       => ( ~ ( in @ X3 @ X1 )
                                                                                                                                                         => ( in @ X3 @ X2 ) ) )
                                                                                                                                                   => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                     => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                             => ( ( in @ X3 @ X2 )
                                                                                                                                                               => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                ( ( subset @ X3 @ X1 )
                                                                                                                                                               => ( ( subset @ X3 @ X2 )
                                                                                                                                                                 => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                  ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                                                 => ( in @ X3 @ X1 ) )
                                                                                                                                                             => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                      ( ( subset @ X1 @ X2 )
                                                                                                                                                                     => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                        = X1 ) )
                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                        ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                          = X2 )
                                                                                                                                                                       => ( subset @ X2 @ X1 ) )
                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                          ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                                                         => ( in @ X3 @ X2 ) )
                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                            ( ! [X3: $i] :
                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                               => ~ ( in @ X3 @ X2 ) )
                                                                                                                                                                           => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                              = emptyset ) )
                                                                                                                                                                       => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                ( ( subset @ X2 @ X1 )
                                                                                                                                                                               => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                  = X2 ) )
                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                  ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                    = X1 )
                                                                                                                                                                                 => ( subset @ X1 @ X2 ) )
                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                    ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                                                                                                                                                    = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                     => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                       => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                        ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                       => ( in @ X3 @ X1 ) )
                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                          ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                         => ~ ( in @ X3 @ X2 ) )
                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                            ( ( subset @ X1 @ X2 )
                                                                                                                                                                                           => ( ( setminus @ X1 @ X2 )
                                                                                                                                                                                              = emptyset ) )
                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                              ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                             => ( ( in @ X3 @ X1 )
                                                                                                                                                                                               => ( in @ X3 @ X2 ) ) )
                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                               => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                 => ~ ( in @ X3 @ X1 ) ) )
                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                  ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                 => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                    ( ( in @ X3 @ X2 )
                                                                                                                                                                                                   => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                        ( ( ( setminus @ X1 @ X2 )
                                                                                                                                                                                                          = emptyset )
                                                                                                                                                                                                       => ( subset @ X1 @ X2 ) )
                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                          ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                                                                                                                                         => ! [X4: $o] :
                                                                                                                                                                                                              ( ( ( in @ X3 @ X1 )
                                                                                                                                                                                                               => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                 => X4 ) )
                                                                                                                                                                                                             => ( ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                 => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                   => X4 ) )
                                                                                                                                                                                                               => X4 ) ) )
                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                           => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                             => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                              ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                             => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                               => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                               => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                 => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                  ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                 => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                   => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                              ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                             => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                               => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                 => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                    ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                   => ( ( X3 != X1 )
                                                                                                                                                                                                                                     => ( X3 = X2 ) ) )
                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                         => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                           => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                             => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                               => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                 => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                   => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                  ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                 => ~ ! [X4: $i] :
                                                                                                                                                                                                                                                        ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                       => ! [X5: $i] :
                                                                                                                                                                                                                                                            ( ( in @ X5 @ X2 )
                                                                                                                                                                                                                                                           => ( X3
                                                                                                                                                                                                                                                             != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                                                                                                                                             => ( sP5
                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                      ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                                                                                                                                                     => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                           => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                                                                                                                                                 => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                                                                                                                                                   => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                                                     => ( ! [X1: $i] :
                                                                                                                                                                                                                                                            ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                                                                                                                                            = X1 )
                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                              ( ! [X3: $i] :
                                                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                                                                                                                      ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                     => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                                       => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                         => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                                                             => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                     => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                                                               => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                      ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                     => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                       != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                                ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                      ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                     => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                       != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                                                                                                                                               => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                     => ~ ( X2 @ X3 ) ) )
                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                 => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                                   => ( ! [X4: $i] :
                                                                                                                                                                                                                                                                          ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                         => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                           => ( X4 = X3 ) ) )
                                                                                                                                                                                                                                                                     => ~ ! [X4: $i] :
                                                                                                                                                                                                                                                                            ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                           => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                             != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                                    ( ! [X3: $i] :
                                                                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                                                                                                                            ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                           => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                                             => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                               => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                                                                   => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                           => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                                                                     => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                            ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                           => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                             != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                      ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                                                                                                                                        = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                     => ( X1 = X2 ) )
                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                        ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                       => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                   => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                          ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                                         => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                ( ( in @ X2
                                                                                                                                                                                                                                                                                  @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                    @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                                                                                                                                               => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                    @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                                                                                 != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                                                     => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                            ( ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                  ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                                                                 => ( X1
                                                                                                                                                                                                                                                                                   != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                                                           => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                              ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                              = X1 )
                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                               => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                  ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                    = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                 => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                    ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                                                      = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                   => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                      ( ( X1 = X2 )
                                                                                                                                                                                                                                                                                     => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                                        = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                        ( ( X1 = X2 )
                                                                                                                                                                                                                                                                                       => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                          = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                          ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                            = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                         => ( ( X3 = X4 )
                                                                                                                                                                                                                                                                                           => ( X2 = X4 ) ) )
                                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                            ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                                              = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                                                                                                                                           => ( X1 = X2 ) )
                                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                              ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                             => ( X2 = X4 ) )
                                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                  = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                               => ( X2 = X4 ) )
                                                                                                                                                                                                                                                                                           => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                                  ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                                                                 => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                                        ( ( in @ X2
                                                                                                                                                                                                                                                                                                          @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                            @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                                                                ( X1
                                                                                                                                                                                                                                                                                                                = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                                                                                                                                       => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                            @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                                                                ( X1
                                                                                                                                                                                                                                                                                                                = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                                                                                                                                         != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                    ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                    = X2 )
                                                                                                                                                                                                                                                                                               => ( sP8
                                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                       => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                          ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                         => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                            ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                           => ( in @ X4 @ X2 ) )
                                                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                                                 => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                                    = X3 ) ) )
                                                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                                                   => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                                      = X4 ) ) )
                                                                                                                                                                                                                                                                                                           => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                               => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                                                                                                                                                  = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h41,assumption,
    ! [X1: $i] :
      ( ! [X2: $i] :
          ~ ( in @ X2 @ X1 )
     => ( X1 = emptyset ) ),
    introduced(assumption,[]) ).

thf(h42,assumption,
    ~ ( ! [X1: $i] :
          ( ! [X2: $i] :
              ~ ( in @ X2 @ X1 )
         => ( X1 = emptyset ) )
     => ( ! [X1: $i,X2: $i > $o,X3: $i] :
            ( ( in @ X3 @ X1 )
           => ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
              = ( X2 @ X3 ) ) )
       => ( ! [X1: $i] :
              ( ( X1 != emptyset )
             => ~ ! [X2: $i] :
                    ~ ( in @ X2 @ X1 ) )
         => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                ( ( in @ X3 @ X1 )
               => ( ( X2 @ X3 )
                 => ( ( dsetconstr @ X1 @ X2 )
                   != emptyset ) ) )
           => ( ! [X1: $i] :
                  ( ~ ! [X2: $i] :
                        ~ ( in @ X2 @ X1 )
                 => ( X1 != emptyset ) )
             => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) )
               => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
                 => ( ! [X1: $i,X2: $i,X3: $i] :
                        ( ( in @ X3 @ X2 )
                       => ( in @ X3 @ ( setadjoin @ X1 @ X2 ) ) )
                   => ( ! [X1: $i,X2: $i,X3: $i] :
                          ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                         => ! [X4: $o] :
                              ( ( ( X3 = X1 )
                               => X4 )
                             => ( ( ( in @ X3 @ X2 )
                                 => X4 )
                               => X4 ) ) )
                     => ( ! [X1: $i,X2: $i,X3: $i] :
                            ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                           => ( ( X3 != X1 )
                             => ( in @ X3 @ X2 ) ) )
                       => ( ! [X1: $i] :
                              ( ( dsetconstr @ X1
                                @ ^ [X2: $i] : ~ $false )
                              = X1 )
                         => ( ! [X1: $i,X2: $i] :
                                ( ! [X3: $i] :
                                    ( ( in @ X3 @ X2 )
                                   => ( in @ X3 @ X1 ) )
                               => ( in @ X2 @ ( powerset @ X1 ) ) )
                           => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                             => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                      ( ( in @ X2 @ ( powerset @ X1 ) )
                                     => ( ( in @ X3 @ X2 )
                                       => ( in @ X3 @ X1 ) ) )
                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                        ( ( in @ X2 @ X3 )
                                       => ( ( in @ X3 @ X1 )
                                         => ( in @ X2 @ ( setunion @ X1 ) ) ) )
                                   => ( ! [X1: $i,X2: $i] :
                                          ( ( in @ X2 @ ( setunion @ X1 ) )
                                         => ! [X3: $o] :
                                              ( ! [X4: $i] :
                                                  ( ( in @ X2 @ X4 )
                                                 => ( ( in @ X4 @ X1 )
                                                   => X3 ) )
                                             => X3 ) )
                                     => ( ! [X1: $i,X2: $i] :
                                            ( ( in @ X2 @ X1 )
                                           => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
                                       => ( ! [X1: $i > $o] :
                                              ( ~ ! [X2: $i] :
                                                    ( ( X1 @ X2 )
                                                   => ~ ! [X3: $i] :
                                                          ( ( X1 @ X3 )
                                                         => ( X2 = X3 ) ) )
                                             => ~ ! [X2: $i] :
                                                    ~ ! [X3: $i] :
                                                        ( ( X1 @ X3 )
                                                        = ( X3 = X2 ) ) )
                                         => ( ! [X1: $i] :
                                                ( ( X1 != emptyset )
                                               => ~ ! [X2: $i] :
                                                      ~ ( in @ X2 @ X1 ) )
                                           => ( ! [X1: $i,X2: $i] :
                                                  ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                 => ( X1 = X2 ) )
                                             => ( ! [X1: $i,X2: $i] :
                                                    ( ( X1 != X2 )
                                                   => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                               => ( ! [X1: $i,X2: $i] :
                                                      ( ( X1 = X2 )
                                                     => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                 => ( ! [X1: $i,X2: $i] :
                                                        ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                       => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                          ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                         => ( ( X3 != X1 )
                                                           => ( X3 = X2 ) ) )
                                                     => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                       => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                         => ( ! [X1: $i,X2: $i > $o] :
                                                                ( ~ ! [X3: $i] :
                                                                      ( ( in @ X3 @ X1 )
                                                                     => ~ ( X2 @ X3 ) )
                                                               => ( ( dsetconstr @ X1 @ X2 )
                                                                 != emptyset ) )
                                                           => ( ! [X1: $i > $o,X2: $i] :
                                                                  ( ( in @ X2 @ emptyset )
                                                                 => ( X1 @ X2 ) )
                                                             => ( ! [X1: $o] :
                                                                    ( X1
                                                                   => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                                               => ( ! [X1: $o] :
                                                                      ( X1
                                                                     => ( set2prop @ ( prop2set @ X1 ) ) )
                                                                 => ( ! [X1: $i > $o] :
                                                                        ( ~ ! [X2: $i] :
                                                                              ~ ( X1 @ X2 )
                                                                       => ( ! [X2: $i,X3: $i] :
                                                                              ( ( X1 @ X2 )
                                                                             => ( ( X1 @ X3 )
                                                                               => ( X2 = X3 ) ) )
                                                                         => ~ ! [X2: $i] :
                                                                                ( ( X1 @ X2 )
                                                                               => ~ ! [X3: $i] :
                                                                                      ( ( X1 @ X3 )
                                                                                     => ( X2 = X3 ) ) ) ) )
                                                                   => ( ! [X1: $i > $o] :
                                                                          ( ~ ! [X2: $i] :
                                                                                ~ ! [X3: $i] :
                                                                                    ( ( X1 @ X3 )
                                                                                    = ( X3 = X2 ) )
                                                                         => ~ ! [X2: $i] :
                                                                                ( ( X1 @ X2 )
                                                                               => ~ ! [X3: $i] :
                                                                                      ( ( X1 @ X3 )
                                                                                     => ( X2 = X3 ) ) ) )
                                                                     => ( ! [X1: $i,X2: $i] :
                                                                            ( ( X1 = X2 )
                                                                           => ! [X3: $i,X4: $i] :
                                                                                ( ( X3 = X4 )
                                                                               => ( ( in @ X3 @ X1 )
                                                                                 => ( in @ X4 @ X2 ) ) ) )
                                                                       => ( ! [X1: $i,X2: $i] :
                                                                              ( ( X1 = X2 )
                                                                             => ! [X3: $i,X4: $i] :
                                                                                  ( ( X3 = X4 )
                                                                                 => ( ( in @ X3 @ X1 )
                                                                                    = ( in @ X4 @ X2 ) ) ) )
                                                                         => ( ! [X1: $i > $o] :
                                                                                ( ~ ! [X2: $i] :
                                                                                      ( ( X1 @ X2 )
                                                                                     => ~ ! [X3: $i] :
                                                                                            ( ( X1 @ X3 )
                                                                                           => ( X2 = X3 ) ) )
                                                                               => ! [X2: $i,X3: $i] :
                                                                                    ( ( X1 @ X2 )
                                                                                   => ( ( X1 @ X3 )
                                                                                     => ( X2 = X3 ) ) ) )
                                                                           => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                  ( ! [X3: $i,X4: $i] :
                                                                                      ( ( X3 = X4 )
                                                                                     => ( ( X1 @ X3 )
                                                                                        = ( X2 @ X4 ) ) )
                                                                                 => ( ( ~ ! [X3: $i] :
                                                                                            ( ( X1 @ X3 )
                                                                                           => ~ ! [X4: $i] :
                                                                                                  ( ( X1 @ X4 )
                                                                                                 => ( X3 = X4 ) ) ) )
                                                                                    = ( ~ ! [X3: $i] :
                                                                                            ( ( X2 @ X3 )
                                                                                           => ~ ! [X4: $i] :
                                                                                                  ( ( X2 @ X4 )
                                                                                                 => ( X3 = X4 ) ) ) ) ) )
                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                    ( ( X1 = X2 )
                                                                                   => ! [X3: $i,X4: $i] :
                                                                                        ( ( X3 = X4 )
                                                                                       => ( ( setadjoin @ X1 @ X3 )
                                                                                          = ( setadjoin @ X2 @ X4 ) ) ) )
                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                      ( ( X1 = X2 )
                                                                                     => ( ( powerset @ X1 )
                                                                                        = ( powerset @ X2 ) ) )
                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                        ( ( X1 = X2 )
                                                                                       => ( ( setunion @ X1 )
                                                                                          = ( setunion @ X2 ) ) )
                                                                                   => ( ! [X1: $i > $o] :
                                                                                          ( ~ ! [X2: $i] :
                                                                                                ( ( X1 @ X2 )
                                                                                               => ~ ! [X3: $i] :
                                                                                                      ( ( X1 @ X3 )
                                                                                                     => ( X2 = X3 ) ) )
                                                                                         => ! [X2: $i,X3: $i] :
                                                                                              ( ( X1 @ X2 )
                                                                                             => ( ( X1 @ X3 )
                                                                                               => ( X2 = X3 ) ) ) )
                                                                                     => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                            ( ! [X3: $i,X4: $i] :
                                                                                                ( ( X3 = X4 )
                                                                                               => ( ( X1 @ X3 )
                                                                                                  = ( X2 @ X4 ) ) )
                                                                                           => ( ~ ! [X3: $i] :
                                                                                                    ( ( X1 @ X3 )
                                                                                                   => ~ ! [X4: $i] :
                                                                                                          ( ( X1 @ X4 )
                                                                                                         => ( X3 = X4 ) ) )
                                                                                             => ( ~ ! [X3: $i] :
                                                                                                      ( ( X2 @ X3 )
                                                                                                     => ~ ! [X4: $i] :
                                                                                                            ( ( X2 @ X4 )
                                                                                                           => ( X3 = X4 ) ) )
                                                                                               => ( ( descr @ X1 )
                                                                                                  = ( descr @ X2 ) ) ) ) )
                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                              ( ( X1 = X2 )
                                                                                             => ! [X3: $i > $o,X4: $i > $o] :
                                                                                                  ( ! [X5: $i] :
                                                                                                      ( ( in @ X5 @ X1 )
                                                                                                     => ! [X6: $i] :
                                                                                                          ( ( in @ X6 @ X2 )
                                                                                                         => ( ( X5 = X6 )
                                                                                                           => ( ( X3 @ X5 )
                                                                                                              = ( X4 @ X6 ) ) ) ) )
                                                                                                 => ( ( dsetconstr @ X1 @ X3 )
                                                                                                    = ( dsetconstr @ X2 @ X4 ) ) ) )
                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                ( ! [X3: $i] :
                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                   => ( in @ X3 @ X2 ) )
                                                                                               => ( subset @ X1 @ X2 ) )
                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                  ( ( X1 = X2 )
                                                                                                 => ( subset @ X2 @ X1 ) )
                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                    ( ( X1 = X2 )
                                                                                                   => ( subset @ X1 @ X2 ) )
                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                      ( ! [X3: $i] :
                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                         => ( in @ X3 @ X2 ) )
                                                                                                     => ( subset @ X1 @ X2 ) )
                                                                                                 => ( ! [X1: $i] : ( subset @ emptyset @ X1 )
                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                          ( ( subset @ X1 @ X2 )
                                                                                                         => ( ( in @ X3 @ X1 )
                                                                                                           => ( in @ X3 @ X2 ) ) )
                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                            ( ( subset @ X1 @ X2 )
                                                                                                           => ( ~ ( in @ X3 @ X2 )
                                                                                                             => ~ ( in @ X3 @ X1 ) ) )
                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                             => ( ~ ( in @ X3 @ X2 )
                                                                                                               => ~ ( subset @ X1 @ X2 ) ) )
                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                ( ~ ( subset @ X1 @ X2 )
                                                                                                               => ( X1 != X2 ) )
                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                 => ( ~ ( in @ X3 @ X2 )
                                                                                                                   => ( X1 != X2 ) ) )
                                                                                                             => ( ! [X1: $i] : ( subset @ X1 @ X1 )
                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                      ( ( subset @ X1 @ X2 )
                                                                                                                     => ( ( subset @ X2 @ X3 )
                                                                                                                       => ( subset @ X1 @ X3 ) ) )
                                                                                                                 => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) )
                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                          ( ( subset @ X1 @ X3 )
                                                                                                                         => ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                            ( ( subset @ X1 @ X2 )
                                                                                                                           => ( in @ X1 @ ( powerset @ X2 ) ) )
                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                              ( ( subset @ X1 @ X2 )
                                                                                                                             => ( ( subset @ X2 @ X1 )
                                                                                                                               => ( X1 = X2 ) ) )
                                                                                                                         => ( ! [X1: $i] :
                                                                                                                                ( ( subset @ X1 @ emptyset )
                                                                                                                               => ( X1 = emptyset ) )
                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                  ( ( subset @ X2 @ X1 )
                                                                                                                                 => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                    ( ( in @ X2 @ ( powerset @ X1 ) )
                                                                                                                                   => ( subset @ X2 @ X1 ) )
                                                                                                                               => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                        ( ( subset @ X1 @ X2 )
                                                                                                                                       => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                             => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                                                         => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                  ( ( in @ X3 @ X2 )
                                                                                                                                                 => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                                                                                                                                    ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                   => ( ( ( in @ X3 @ X1 )
                                                                                                                                                       => X4 )
                                                                                                                                                     => ( ( ( in @ X3 @ X2 )
                                                                                                                                                         => X4 )
                                                                                                                                                       => X4 ) ) )
                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                      ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                     => ( ~ ( in @ X3 @ X1 )
                                                                                                                                                       => ( in @ X3 @ X2 ) ) )
                                                                                                                                                 => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                   => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                           => ( ( in @ X3 @ X2 )
                                                                                                                                                             => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                              ( ( subset @ X3 @ X1 )
                                                                                                                                                             => ( ( subset @ X3 @ X2 )
                                                                                                                                                               => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                                               => ( in @ X3 @ X1 ) )
                                                                                                                                                           => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                    ( ( subset @ X1 @ X2 )
                                                                                                                                                                   => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                      = X1 ) )
                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                      ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                        = X2 )
                                                                                                                                                                     => ( subset @ X2 @ X1 ) )
                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                        ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                                                       => ( in @ X3 @ X2 ) )
                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                          ( ! [X3: $i] :
                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                             => ~ ( in @ X3 @ X2 ) )
                                                                                                                                                                         => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                            = emptyset ) )
                                                                                                                                                                     => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                              ( ( subset @ X2 @ X1 )
                                                                                                                                                                             => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                = X2 ) )
                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                  = X1 )
                                                                                                                                                                               => ( subset @ X1 @ X2 ) )
                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                  ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                                                                                                                                                  = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                   => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                     => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                      ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                     => ( in @ X3 @ X1 ) )
                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                        ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                       => ~ ( in @ X3 @ X2 ) )
                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                          ( ( subset @ X1 @ X2 )
                                                                                                                                                                                         => ( ( setminus @ X1 @ X2 )
                                                                                                                                                                                            = emptyset ) )
                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                            ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                           => ( ( in @ X3 @ X1 )
                                                                                                                                                                                             => ( in @ X3 @ X2 ) ) )
                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                              ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                             => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                               => ~ ( in @ X3 @ X1 ) ) )
                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                               => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                  ( ( in @ X3 @ X2 )
                                                                                                                                                                                                 => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                      ( ( ( setminus @ X1 @ X2 )
                                                                                                                                                                                                        = emptyset )
                                                                                                                                                                                                     => ( subset @ X1 @ X2 ) )
                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                        ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                                                                                                                                       => ! [X4: $o] :
                                                                                                                                                                                                            ( ( ( in @ X3 @ X1 )
                                                                                                                                                                                                             => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                               => X4 ) )
                                                                                                                                                                                                           => ( ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                               => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                 => X4 ) )
                                                                                                                                                                                                             => X4 ) ) )
                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                         => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                           => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                            ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                           => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                             => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                             => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                               => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                               => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                 => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                            ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                           => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                              ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                             => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                               => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                  ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                 => ( ( X3 != X1 )
                                                                                                                                                                                                                                   => ( X3 = X2 ) ) )
                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                       => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                         => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                           => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                             => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                               => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                 => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                               => ~ ! [X4: $i] :
                                                                                                                                                                                                                                                      ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                     => ! [X5: $i] :
                                                                                                                                                                                                                                                          ( ( in @ X5 @ X2 )
                                                                                                                                                                                                                                                         => ( X3
                                                                                                                                                                                                                                                           != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                                                                                                                                           => ( sP5
                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                    ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                                                                                                                                                   => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                         => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                                                                                                                                               => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                                                                                                                                                 => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                                                   => ( ! [X1: $i] :
                                                                                                                                                                                                                                                          ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                                                                                                                                          = X1 )
                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                            ( ! [X3: $i] :
                                                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                                                                                                    ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                   => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                                     => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                       => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                                                           => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                   => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                                                             => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                    ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                   => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                     != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                              ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                    ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                   => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                     != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                                                                                                                                             => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                   => ~ ( X2 @ X3 ) ) )
                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                               => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                                 => ( ! [X4: $i] :
                                                                                                                                                                                                                                                                        ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                       => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                         => ( X4 = X3 ) ) )
                                                                                                                                                                                                                                                                   => ~ ! [X4: $i] :
                                                                                                                                                                                                                                                                          ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                         => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                           != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                                  ( ! [X3: $i] :
                                                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                                                                                                                          ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                         => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                                           => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                             => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                                                                 => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                         => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                                                                   => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                          ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                         => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                           != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                    ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                                                                                                                                      = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                   => ( X1 = X2 ) )
                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                      ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                     => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                 => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                        ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                                       => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                              ( ( in @ X2
                                                                                                                                                                                                                                                                                @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                  @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                                                                                                                                             => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                  @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                                                                               != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                                                   => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                          ( ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                                                               => ( X1
                                                                                                                                                                                                                                                                                 != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                                                         => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                            ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                            = X1 )
                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                              ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                             => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                  = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                               => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                  ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                                                    = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                 => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                    ( ( X1 = X2 )
                                                                                                                                                                                                                                                                                   => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                                      = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                      ( ( X1 = X2 )
                                                                                                                                                                                                                                                                                     => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                        = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                        ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                          = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                       => ( ( X3 = X4 )
                                                                                                                                                                                                                                                                                         => ( X2 = X4 ) ) )
                                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                          ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                                            = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                                                                                                                                         => ( X1 = X2 ) )
                                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                            ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                              = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                           => ( X2 = X4 ) )
                                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                              ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                             => ( X2 = X4 ) )
                                                                                                                                                                                                                                                                                         => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                                ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                                                               => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                                      ( ( in @ X2
                                                                                                                                                                                                                                                                                                        @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                          @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                                                              ( X1
                                                                                                                                                                                                                                                                                                              = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                                                                                                                                     => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                          @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                                                              ( X1
                                                                                                                                                                                                                                                                                                              = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                                                                                                                                       != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                  ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                  = X2 )
                                                                                                                                                                                                                                                                                             => ( sP8
                                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                      ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                     => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                        ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                       => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                          ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                         => ( in @ X4 @ X2 ) )
                                                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                                               => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                                  = X3 ) ) )
                                                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                                                 => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                                    = X4 ) ) )
                                                                                                                                                                                                                                                                                                         => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                              ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                             => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                                                                                                                                                = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h43,assumption,
    ~ ( ! [X1: $i,X2: $i > $o,X3: $i] :
          ( ( in @ X3 @ X1 )
         => ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
            = ( X2 @ X3 ) ) )
     => ( ! [X1: $i] :
            ( ( X1 != emptyset )
           => ~ ! [X2: $i] :
                  ~ ( in @ X2 @ X1 ) )
       => ( ! [X1: $i,X2: $i > $o,X3: $i] :
              ( ( in @ X3 @ X1 )
             => ( ( X2 @ X3 )
               => ( ( dsetconstr @ X1 @ X2 )
                 != emptyset ) ) )
         => ( ! [X1: $i] :
                ( ~ ! [X2: $i] :
                      ~ ( in @ X2 @ X1 )
               => ( X1 != emptyset ) )
           => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) )
             => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
               => ( ! [X1: $i,X2: $i,X3: $i] :
                      ( ( in @ X3 @ X2 )
                     => ( in @ X3 @ ( setadjoin @ X1 @ X2 ) ) )
                 => ( ! [X1: $i,X2: $i,X3: $i] :
                        ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                       => ! [X4: $o] :
                            ( ( ( X3 = X1 )
                             => X4 )
                           => ( ( ( in @ X3 @ X2 )
                               => X4 )
                             => X4 ) ) )
                   => ( ! [X1: $i,X2: $i,X3: $i] :
                          ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                         => ( ( X3 != X1 )
                           => ( in @ X3 @ X2 ) ) )
                     => ( ! [X1: $i] :
                            ( ( dsetconstr @ X1
                              @ ^ [X2: $i] : ~ $false )
                            = X1 )
                       => ( ! [X1: $i,X2: $i] :
                              ( ! [X3: $i] :
                                  ( ( in @ X3 @ X2 )
                                 => ( in @ X3 @ X1 ) )
                             => ( in @ X2 @ ( powerset @ X1 ) ) )
                         => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                           => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                    ( ( in @ X2 @ ( powerset @ X1 ) )
                                   => ( ( in @ X3 @ X2 )
                                     => ( in @ X3 @ X1 ) ) )
                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                      ( ( in @ X2 @ X3 )
                                     => ( ( in @ X3 @ X1 )
                                       => ( in @ X2 @ ( setunion @ X1 ) ) ) )
                                 => ( ! [X1: $i,X2: $i] :
                                        ( ( in @ X2 @ ( setunion @ X1 ) )
                                       => ! [X3: $o] :
                                            ( ! [X4: $i] :
                                                ( ( in @ X2 @ X4 )
                                               => ( ( in @ X4 @ X1 )
                                                 => X3 ) )
                                           => X3 ) )
                                   => ( ! [X1: $i,X2: $i] :
                                          ( ( in @ X2 @ X1 )
                                         => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
                                     => ( ! [X1: $i > $o] :
                                            ( ~ ! [X2: $i] :
                                                  ( ( X1 @ X2 )
                                                 => ~ ! [X3: $i] :
                                                        ( ( X1 @ X3 )
                                                       => ( X2 = X3 ) ) )
                                           => ~ ! [X2: $i] :
                                                  ~ ! [X3: $i] :
                                                      ( ( X1 @ X3 )
                                                      = ( X3 = X2 ) ) )
                                       => ( ! [X1: $i] :
                                              ( ( X1 != emptyset )
                                             => ~ ! [X2: $i] :
                                                    ~ ( in @ X2 @ X1 ) )
                                         => ( ! [X1: $i,X2: $i] :
                                                ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                               => ( X1 = X2 ) )
                                           => ( ! [X1: $i,X2: $i] :
                                                  ( ( X1 != X2 )
                                                 => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                             => ( ! [X1: $i,X2: $i] :
                                                    ( ( X1 = X2 )
                                                   => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                               => ( ! [X1: $i,X2: $i] :
                                                      ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                     => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                        ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                       => ( ( X3 != X1 )
                                                         => ( X3 = X2 ) ) )
                                                   => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                     => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                       => ( ! [X1: $i,X2: $i > $o] :
                                                              ( ~ ! [X3: $i] :
                                                                    ( ( in @ X3 @ X1 )
                                                                   => ~ ( X2 @ X3 ) )
                                                             => ( ( dsetconstr @ X1 @ X2 )
                                                               != emptyset ) )
                                                         => ( ! [X1: $i > $o,X2: $i] :
                                                                ( ( in @ X2 @ emptyset )
                                                               => ( X1 @ X2 ) )
                                                           => ( ! [X1: $o] :
                                                                  ( X1
                                                                 => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                                             => ( ! [X1: $o] :
                                                                    ( X1
                                                                   => ( set2prop @ ( prop2set @ X1 ) ) )
                                                               => ( ! [X1: $i > $o] :
                                                                      ( ~ ! [X2: $i] :
                                                                            ~ ( X1 @ X2 )
                                                                     => ( ! [X2: $i,X3: $i] :
                                                                            ( ( X1 @ X2 )
                                                                           => ( ( X1 @ X3 )
                                                                             => ( X2 = X3 ) ) )
                                                                       => ~ ! [X2: $i] :
                                                                              ( ( X1 @ X2 )
                                                                             => ~ ! [X3: $i] :
                                                                                    ( ( X1 @ X3 )
                                                                                   => ( X2 = X3 ) ) ) ) )
                                                                 => ( ! [X1: $i > $o] :
                                                                        ( ~ ! [X2: $i] :
                                                                              ~ ! [X3: $i] :
                                                                                  ( ( X1 @ X3 )
                                                                                  = ( X3 = X2 ) )
                                                                       => ~ ! [X2: $i] :
                                                                              ( ( X1 @ X2 )
                                                                             => ~ ! [X3: $i] :
                                                                                    ( ( X1 @ X3 )
                                                                                   => ( X2 = X3 ) ) ) )
                                                                   => ( ! [X1: $i,X2: $i] :
                                                                          ( ( X1 = X2 )
                                                                         => ! [X3: $i,X4: $i] :
                                                                              ( ( X3 = X4 )
                                                                             => ( ( in @ X3 @ X1 )
                                                                               => ( in @ X4 @ X2 ) ) ) )
                                                                     => ( ! [X1: $i,X2: $i] :
                                                                            ( ( X1 = X2 )
                                                                           => ! [X3: $i,X4: $i] :
                                                                                ( ( X3 = X4 )
                                                                               => ( ( in @ X3 @ X1 )
                                                                                  = ( in @ X4 @ X2 ) ) ) )
                                                                       => ( ! [X1: $i > $o] :
                                                                              ( ~ ! [X2: $i] :
                                                                                    ( ( X1 @ X2 )
                                                                                   => ~ ! [X3: $i] :
                                                                                          ( ( X1 @ X3 )
                                                                                         => ( X2 = X3 ) ) )
                                                                             => ! [X2: $i,X3: $i] :
                                                                                  ( ( X1 @ X2 )
                                                                                 => ( ( X1 @ X3 )
                                                                                   => ( X2 = X3 ) ) ) )
                                                                         => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                ( ! [X3: $i,X4: $i] :
                                                                                    ( ( X3 = X4 )
                                                                                   => ( ( X1 @ X3 )
                                                                                      = ( X2 @ X4 ) ) )
                                                                               => ( ( ~ ! [X3: $i] :
                                                                                          ( ( X1 @ X3 )
                                                                                         => ~ ! [X4: $i] :
                                                                                                ( ( X1 @ X4 )
                                                                                               => ( X3 = X4 ) ) ) )
                                                                                  = ( ~ ! [X3: $i] :
                                                                                          ( ( X2 @ X3 )
                                                                                         => ~ ! [X4: $i] :
                                                                                                ( ( X2 @ X4 )
                                                                                               => ( X3 = X4 ) ) ) ) ) )
                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                  ( ( X1 = X2 )
                                                                                 => ! [X3: $i,X4: $i] :
                                                                                      ( ( X3 = X4 )
                                                                                     => ( ( setadjoin @ X1 @ X3 )
                                                                                        = ( setadjoin @ X2 @ X4 ) ) ) )
                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                    ( ( X1 = X2 )
                                                                                   => ( ( powerset @ X1 )
                                                                                      = ( powerset @ X2 ) ) )
                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                      ( ( X1 = X2 )
                                                                                     => ( ( setunion @ X1 )
                                                                                        = ( setunion @ X2 ) ) )
                                                                                 => ( ! [X1: $i > $o] :
                                                                                        ( ~ ! [X2: $i] :
                                                                                              ( ( X1 @ X2 )
                                                                                             => ~ ! [X3: $i] :
                                                                                                    ( ( X1 @ X3 )
                                                                                                   => ( X2 = X3 ) ) )
                                                                                       => ! [X2: $i,X3: $i] :
                                                                                            ( ( X1 @ X2 )
                                                                                           => ( ( X1 @ X3 )
                                                                                             => ( X2 = X3 ) ) ) )
                                                                                   => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                          ( ! [X3: $i,X4: $i] :
                                                                                              ( ( X3 = X4 )
                                                                                             => ( ( X1 @ X3 )
                                                                                                = ( X2 @ X4 ) ) )
                                                                                         => ( ~ ! [X3: $i] :
                                                                                                  ( ( X1 @ X3 )
                                                                                                 => ~ ! [X4: $i] :
                                                                                                        ( ( X1 @ X4 )
                                                                                                       => ( X3 = X4 ) ) )
                                                                                           => ( ~ ! [X3: $i] :
                                                                                                    ( ( X2 @ X3 )
                                                                                                   => ~ ! [X4: $i] :
                                                                                                          ( ( X2 @ X4 )
                                                                                                         => ( X3 = X4 ) ) )
                                                                                             => ( ( descr @ X1 )
                                                                                                = ( descr @ X2 ) ) ) ) )
                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                            ( ( X1 = X2 )
                                                                                           => ! [X3: $i > $o,X4: $i > $o] :
                                                                                                ( ! [X5: $i] :
                                                                                                    ( ( in @ X5 @ X1 )
                                                                                                   => ! [X6: $i] :
                                                                                                        ( ( in @ X6 @ X2 )
                                                                                                       => ( ( X5 = X6 )
                                                                                                         => ( ( X3 @ X5 )
                                                                                                            = ( X4 @ X6 ) ) ) ) )
                                                                                               => ( ( dsetconstr @ X1 @ X3 )
                                                                                                  = ( dsetconstr @ X2 @ X4 ) ) ) )
                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                              ( ! [X3: $i] :
                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                 => ( in @ X3 @ X2 ) )
                                                                                             => ( subset @ X1 @ X2 ) )
                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                ( ( X1 = X2 )
                                                                                               => ( subset @ X2 @ X1 ) )
                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                  ( ( X1 = X2 )
                                                                                                 => ( subset @ X1 @ X2 ) )
                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                    ( ! [X3: $i] :
                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                       => ( in @ X3 @ X2 ) )
                                                                                                   => ( subset @ X1 @ X2 ) )
                                                                                               => ( ! [X1: $i] : ( subset @ emptyset @ X1 )
                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                        ( ( subset @ X1 @ X2 )
                                                                                                       => ( ( in @ X3 @ X1 )
                                                                                                         => ( in @ X3 @ X2 ) ) )
                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                          ( ( subset @ X1 @ X2 )
                                                                                                         => ( ~ ( in @ X3 @ X2 )
                                                                                                           => ~ ( in @ X3 @ X1 ) ) )
                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                           => ( ~ ( in @ X3 @ X2 )
                                                                                                             => ~ ( subset @ X1 @ X2 ) ) )
                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                              ( ~ ( subset @ X1 @ X2 )
                                                                                                             => ( X1 != X2 ) )
                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                               => ( ~ ( in @ X3 @ X2 )
                                                                                                                 => ( X1 != X2 ) ) )
                                                                                                           => ( ! [X1: $i] : ( subset @ X1 @ X1 )
                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                    ( ( subset @ X1 @ X2 )
                                                                                                                   => ( ( subset @ X2 @ X3 )
                                                                                                                     => ( subset @ X1 @ X3 ) ) )
                                                                                                               => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) )
                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                        ( ( subset @ X1 @ X3 )
                                                                                                                       => ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                          ( ( subset @ X1 @ X2 )
                                                                                                                         => ( in @ X1 @ ( powerset @ X2 ) ) )
                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                            ( ( subset @ X1 @ X2 )
                                                                                                                           => ( ( subset @ X2 @ X1 )
                                                                                                                             => ( X1 = X2 ) ) )
                                                                                                                       => ( ! [X1: $i] :
                                                                                                                              ( ( subset @ X1 @ emptyset )
                                                                                                                             => ( X1 = emptyset ) )
                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                ( ( subset @ X2 @ X1 )
                                                                                                                               => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                  ( ( in @ X2 @ ( powerset @ X1 ) )
                                                                                                                                 => ( subset @ X2 @ X1 ) )
                                                                                                                             => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                      ( ( subset @ X1 @ X2 )
                                                                                                                                     => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                           => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                ( ( in @ X3 @ X2 )
                                                                                                                                               => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                                                                                                                                  ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                 => ( ( ( in @ X3 @ X1 )
                                                                                                                                                     => X4 )
                                                                                                                                                   => ( ( ( in @ X3 @ X2 )
                                                                                                                                                       => X4 )
                                                                                                                                                     => X4 ) ) )
                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                    ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                   => ( ~ ( in @ X3 @ X1 )
                                                                                                                                                     => ( in @ X3 @ X2 ) ) )
                                                                                                                                               => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                 => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                         => ( ( in @ X3 @ X2 )
                                                                                                                                                           => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                            ( ( subset @ X3 @ X1 )
                                                                                                                                                           => ( ( subset @ X3 @ X2 )
                                                                                                                                                             => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                              ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                                             => ( in @ X3 @ X1 ) )
                                                                                                                                                         => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                  ( ( subset @ X1 @ X2 )
                                                                                                                                                                 => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                    = X1 ) )
                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                    ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                      = X2 )
                                                                                                                                                                   => ( subset @ X2 @ X1 ) )
                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                      ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                                                     => ( in @ X3 @ X2 ) )
                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                        ( ! [X3: $i] :
                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                           => ~ ( in @ X3 @ X2 ) )
                                                                                                                                                                       => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                          = emptyset ) )
                                                                                                                                                                   => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                            ( ( subset @ X2 @ X1 )
                                                                                                                                                                           => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                              = X2 ) )
                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                              ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                = X1 )
                                                                                                                                                                             => ( subset @ X1 @ X2 ) )
                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                                                                                                                                                = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                 => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                   => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                    ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                   => ( in @ X3 @ X1 ) )
                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                      ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                     => ~ ( in @ X3 @ X2 ) )
                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                        ( ( subset @ X1 @ X2 )
                                                                                                                                                                                       => ( ( setminus @ X1 @ X2 )
                                                                                                                                                                                          = emptyset ) )
                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                          ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                         => ( ( in @ X3 @ X1 )
                                                                                                                                                                                           => ( in @ X3 @ X2 ) ) )
                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                            ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                           => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                             => ~ ( in @ X3 @ X1 ) ) )
                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                              ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                             => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                ( ( in @ X3 @ X2 )
                                                                                                                                                                                               => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                    ( ( ( setminus @ X1 @ X2 )
                                                                                                                                                                                                      = emptyset )
                                                                                                                                                                                                   => ( subset @ X1 @ X2 ) )
                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                      ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                                                                                                                                     => ! [X4: $o] :
                                                                                                                                                                                                          ( ( ( in @ X3 @ X1 )
                                                                                                                                                                                                           => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                             => X4 ) )
                                                                                                                                                                                                         => ( ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                             => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                               => X4 ) )
                                                                                                                                                                                                           => X4 ) ) )
                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                       => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                         => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                          ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                         => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                           => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                           => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                             => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                              ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                             => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                               => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                          ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                         => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                            ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                           => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                             => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                               => ( ( X3 != X1 )
                                                                                                                                                                                                                                 => ( X3 = X2 ) ) )
                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                     => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                       => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                         => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                           => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                             => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                               => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                              ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                             => ~ ! [X4: $i] :
                                                                                                                                                                                                                                                    ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                   => ! [X5: $i] :
                                                                                                                                                                                                                                                        ( ( in @ X5 @ X2 )
                                                                                                                                                                                                                                                       => ( X3
                                                                                                                                                                                                                                                         != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                                                                                                                                         => ( sP5
                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                  ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                                                                                                                                                 => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                       => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                                                                                                                                             => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                                                                                                                                               => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                                                 => ( ! [X1: $i] :
                                                                                                                                                                                                                                                        ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                                                                                                                                        = X1 )
                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                          ( ! [X3: $i] :
                                                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                                                                                                  ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                 => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                                   => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                     => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                                                         => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                 => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                                                           => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                  ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                 => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                   != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                            ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                  ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                 => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                   != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                                                                                                                                           => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                 => ~ ( X2 @ X3 ) ) )
                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                             => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                               => ( ! [X4: $i] :
                                                                                                                                                                                                                                                                      ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                     => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                       => ( X4 = X3 ) ) )
                                                                                                                                                                                                                                                                 => ~ ! [X4: $i] :
                                                                                                                                                                                                                                                                        ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                       => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                         != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                                ( ! [X3: $i] :
                                                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                                                                                                                        ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                       => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                                         => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                           => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                                                               => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                       => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                                                                 => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                        ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                       => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                         != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                  ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                                                                                                                                    = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                 => ( X1 = X2 ) )
                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                    ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                   => ( X1 = X3 ) )
                                                                                                                                                                                                                                                               => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                      ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                                     => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                            ( ( in @ X2
                                                                                                                                                                                                                                                                              @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                                                                                                                                           => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                                                                             != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                                                 => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                        ( ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                              ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                                                             => ( X1
                                                                                                                                                                                                                                                                               != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                                                       => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                          ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                          = X1 )
                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                            ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                           => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                              ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                             => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                                                  = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                               => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                  ( ( X1 = X2 )
                                                                                                                                                                                                                                                                                 => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                                    = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                    ( ( X1 = X2 )
                                                                                                                                                                                                                                                                                   => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                      = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                      ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                        = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                     => ( ( X3 = X4 )
                                                                                                                                                                                                                                                                                       => ( X2 = X4 ) ) )
                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                        ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                                          = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                                                                                                                                       => ( X1 = X2 ) )
                                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                          ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                            = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                         => ( X2 = X4 ) )
                                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                            ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                                                              = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                           => ( X2 = X4 ) )
                                                                                                                                                                                                                                                                                       => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                              ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                                                             => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                                    ( ( in @ X2
                                                                                                                                                                                                                                                                                                      @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                        @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                                                            ( X1
                                                                                                                                                                                                                                                                                                            = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                                                                                                                                   => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                        @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                                                            ( X1
                                                                                                                                                                                                                                                                                                            = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                                                                                                                                     != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                = X2 )
                                                                                                                                                                                                                                                                                           => ( sP8
                                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                    ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                   => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                      ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                     => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                        ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                       => ( in @ X4 @ X2 ) )
                                                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                                             => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                                = X3 ) ) )
                                                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                                               => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                                  = X4 ) ) )
                                                                                                                                                                                                                                                                                                       => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                            ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                           => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                                                                                                                                              = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h44,assumption,
    ! [X1: $i,X2: $i > $o,X3: $i] :
      ( ( in @ X3 @ X1 )
     => ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
        = ( X2 @ X3 ) ) ),
    introduced(assumption,[]) ).

thf(h45,assumption,
    ~ ( ! [X1: $i] :
          ( ( X1 != emptyset )
         => ~ ! [X2: $i] :
                ~ ( in @ X2 @ X1 ) )
     => ( ! [X1: $i,X2: $i > $o,X3: $i] :
            ( ( in @ X3 @ X1 )
           => ( ( X2 @ X3 )
             => ( ( dsetconstr @ X1 @ X2 )
               != emptyset ) ) )
       => ( ! [X1: $i] :
              ( ~ ! [X2: $i] :
                    ~ ( in @ X2 @ X1 )
             => ( X1 != emptyset ) )
         => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) )
           => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
             => ( ! [X1: $i,X2: $i,X3: $i] :
                    ( ( in @ X3 @ X2 )
                   => ( in @ X3 @ ( setadjoin @ X1 @ X2 ) ) )
               => ( ! [X1: $i,X2: $i,X3: $i] :
                      ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                     => ! [X4: $o] :
                          ( ( ( X3 = X1 )
                           => X4 )
                         => ( ( ( in @ X3 @ X2 )
                             => X4 )
                           => X4 ) ) )
                 => ( ! [X1: $i,X2: $i,X3: $i] :
                        ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                       => ( ( X3 != X1 )
                         => ( in @ X3 @ X2 ) ) )
                   => ( ! [X1: $i] :
                          ( ( dsetconstr @ X1
                            @ ^ [X2: $i] : ~ $false )
                          = X1 )
                     => ( ! [X1: $i,X2: $i] :
                            ( ! [X3: $i] :
                                ( ( in @ X3 @ X2 )
                               => ( in @ X3 @ X1 ) )
                           => ( in @ X2 @ ( powerset @ X1 ) ) )
                       => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                         => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                  ( ( in @ X2 @ ( powerset @ X1 ) )
                                 => ( ( in @ X3 @ X2 )
                                   => ( in @ X3 @ X1 ) ) )
                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                    ( ( in @ X2 @ X3 )
                                   => ( ( in @ X3 @ X1 )
                                     => ( in @ X2 @ ( setunion @ X1 ) ) ) )
                               => ( ! [X1: $i,X2: $i] :
                                      ( ( in @ X2 @ ( setunion @ X1 ) )
                                     => ! [X3: $o] :
                                          ( ! [X4: $i] :
                                              ( ( in @ X2 @ X4 )
                                             => ( ( in @ X4 @ X1 )
                                               => X3 ) )
                                         => X3 ) )
                                 => ( ! [X1: $i,X2: $i] :
                                        ( ( in @ X2 @ X1 )
                                       => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
                                   => ( ! [X1: $i > $o] :
                                          ( ~ ! [X2: $i] :
                                                ( ( X1 @ X2 )
                                               => ~ ! [X3: $i] :
                                                      ( ( X1 @ X3 )
                                                     => ( X2 = X3 ) ) )
                                         => ~ ! [X2: $i] :
                                                ~ ! [X3: $i] :
                                                    ( ( X1 @ X3 )
                                                    = ( X3 = X2 ) ) )
                                     => ( ! [X1: $i] :
                                            ( ( X1 != emptyset )
                                           => ~ ! [X2: $i] :
                                                  ~ ( in @ X2 @ X1 ) )
                                       => ( ! [X1: $i,X2: $i] :
                                              ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                             => ( X1 = X2 ) )
                                         => ( ! [X1: $i,X2: $i] :
                                                ( ( X1 != X2 )
                                               => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                           => ( ! [X1: $i,X2: $i] :
                                                  ( ( X1 = X2 )
                                                 => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                             => ( ! [X1: $i,X2: $i] :
                                                    ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                   => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                      ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                     => ( ( X3 != X1 )
                                                       => ( X3 = X2 ) ) )
                                                 => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                   => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                            ( ~ ! [X3: $i] :
                                                                  ( ( in @ X3 @ X1 )
                                                                 => ~ ( X2 @ X3 ) )
                                                           => ( ( dsetconstr @ X1 @ X2 )
                                                             != emptyset ) )
                                                       => ( ! [X1: $i > $o,X2: $i] :
                                                              ( ( in @ X2 @ emptyset )
                                                             => ( X1 @ X2 ) )
                                                         => ( ! [X1: $o] :
                                                                ( X1
                                                               => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                                           => ( ! [X1: $o] :
                                                                  ( X1
                                                                 => ( set2prop @ ( prop2set @ X1 ) ) )
                                                             => ( ! [X1: $i > $o] :
                                                                    ( ~ ! [X2: $i] :
                                                                          ~ ( X1 @ X2 )
                                                                   => ( ! [X2: $i,X3: $i] :
                                                                          ( ( X1 @ X2 )
                                                                         => ( ( X1 @ X3 )
                                                                           => ( X2 = X3 ) ) )
                                                                     => ~ ! [X2: $i] :
                                                                            ( ( X1 @ X2 )
                                                                           => ~ ! [X3: $i] :
                                                                                  ( ( X1 @ X3 )
                                                                                 => ( X2 = X3 ) ) ) ) )
                                                               => ( ! [X1: $i > $o] :
                                                                      ( ~ ! [X2: $i] :
                                                                            ~ ! [X3: $i] :
                                                                                ( ( X1 @ X3 )
                                                                                = ( X3 = X2 ) )
                                                                     => ~ ! [X2: $i] :
                                                                            ( ( X1 @ X2 )
                                                                           => ~ ! [X3: $i] :
                                                                                  ( ( X1 @ X3 )
                                                                                 => ( X2 = X3 ) ) ) )
                                                                 => ( ! [X1: $i,X2: $i] :
                                                                        ( ( X1 = X2 )
                                                                       => ! [X3: $i,X4: $i] :
                                                                            ( ( X3 = X4 )
                                                                           => ( ( in @ X3 @ X1 )
                                                                             => ( in @ X4 @ X2 ) ) ) )
                                                                   => ( ! [X1: $i,X2: $i] :
                                                                          ( ( X1 = X2 )
                                                                         => ! [X3: $i,X4: $i] :
                                                                              ( ( X3 = X4 )
                                                                             => ( ( in @ X3 @ X1 )
                                                                                = ( in @ X4 @ X2 ) ) ) )
                                                                     => ( ! [X1: $i > $o] :
                                                                            ( ~ ! [X2: $i] :
                                                                                  ( ( X1 @ X2 )
                                                                                 => ~ ! [X3: $i] :
                                                                                        ( ( X1 @ X3 )
                                                                                       => ( X2 = X3 ) ) )
                                                                           => ! [X2: $i,X3: $i] :
                                                                                ( ( X1 @ X2 )
                                                                               => ( ( X1 @ X3 )
                                                                                 => ( X2 = X3 ) ) ) )
                                                                       => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                              ( ! [X3: $i,X4: $i] :
                                                                                  ( ( X3 = X4 )
                                                                                 => ( ( X1 @ X3 )
                                                                                    = ( X2 @ X4 ) ) )
                                                                             => ( ( ~ ! [X3: $i] :
                                                                                        ( ( X1 @ X3 )
                                                                                       => ~ ! [X4: $i] :
                                                                                              ( ( X1 @ X4 )
                                                                                             => ( X3 = X4 ) ) ) )
                                                                                = ( ~ ! [X3: $i] :
                                                                                        ( ( X2 @ X3 )
                                                                                       => ~ ! [X4: $i] :
                                                                                              ( ( X2 @ X4 )
                                                                                             => ( X3 = X4 ) ) ) ) ) )
                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                ( ( X1 = X2 )
                                                                               => ! [X3: $i,X4: $i] :
                                                                                    ( ( X3 = X4 )
                                                                                   => ( ( setadjoin @ X1 @ X3 )
                                                                                      = ( setadjoin @ X2 @ X4 ) ) ) )
                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                  ( ( X1 = X2 )
                                                                                 => ( ( powerset @ X1 )
                                                                                    = ( powerset @ X2 ) ) )
                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                    ( ( X1 = X2 )
                                                                                   => ( ( setunion @ X1 )
                                                                                      = ( setunion @ X2 ) ) )
                                                                               => ( ! [X1: $i > $o] :
                                                                                      ( ~ ! [X2: $i] :
                                                                                            ( ( X1 @ X2 )
                                                                                           => ~ ! [X3: $i] :
                                                                                                  ( ( X1 @ X3 )
                                                                                                 => ( X2 = X3 ) ) )
                                                                                     => ! [X2: $i,X3: $i] :
                                                                                          ( ( X1 @ X2 )
                                                                                         => ( ( X1 @ X3 )
                                                                                           => ( X2 = X3 ) ) ) )
                                                                                 => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                        ( ! [X3: $i,X4: $i] :
                                                                                            ( ( X3 = X4 )
                                                                                           => ( ( X1 @ X3 )
                                                                                              = ( X2 @ X4 ) ) )
                                                                                       => ( ~ ! [X3: $i] :
                                                                                                ( ( X1 @ X3 )
                                                                                               => ~ ! [X4: $i] :
                                                                                                      ( ( X1 @ X4 )
                                                                                                     => ( X3 = X4 ) ) )
                                                                                         => ( ~ ! [X3: $i] :
                                                                                                  ( ( X2 @ X3 )
                                                                                                 => ~ ! [X4: $i] :
                                                                                                        ( ( X2 @ X4 )
                                                                                                       => ( X3 = X4 ) ) )
                                                                                           => ( ( descr @ X1 )
                                                                                              = ( descr @ X2 ) ) ) ) )
                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                          ( ( X1 = X2 )
                                                                                         => ! [X3: $i > $o,X4: $i > $o] :
                                                                                              ( ! [X5: $i] :
                                                                                                  ( ( in @ X5 @ X1 )
                                                                                                 => ! [X6: $i] :
                                                                                                      ( ( in @ X6 @ X2 )
                                                                                                     => ( ( X5 = X6 )
                                                                                                       => ( ( X3 @ X5 )
                                                                                                          = ( X4 @ X6 ) ) ) ) )
                                                                                             => ( ( dsetconstr @ X1 @ X3 )
                                                                                                = ( dsetconstr @ X2 @ X4 ) ) ) )
                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                            ( ! [X3: $i] :
                                                                                                ( ( in @ X3 @ X1 )
                                                                                               => ( in @ X3 @ X2 ) )
                                                                                           => ( subset @ X1 @ X2 ) )
                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                              ( ( X1 = X2 )
                                                                                             => ( subset @ X2 @ X1 ) )
                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                ( ( X1 = X2 )
                                                                                               => ( subset @ X1 @ X2 ) )
                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                  ( ! [X3: $i] :
                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                     => ( in @ X3 @ X2 ) )
                                                                                                 => ( subset @ X1 @ X2 ) )
                                                                                             => ( ! [X1: $i] : ( subset @ emptyset @ X1 )
                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                      ( ( subset @ X1 @ X2 )
                                                                                                     => ( ( in @ X3 @ X1 )
                                                                                                       => ( in @ X3 @ X2 ) ) )
                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                        ( ( subset @ X1 @ X2 )
                                                                                                       => ( ~ ( in @ X3 @ X2 )
                                                                                                         => ~ ( in @ X3 @ X1 ) ) )
                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                         => ( ~ ( in @ X3 @ X2 )
                                                                                                           => ~ ( subset @ X1 @ X2 ) ) )
                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                            ( ~ ( subset @ X1 @ X2 )
                                                                                                           => ( X1 != X2 ) )
                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                             => ( ~ ( in @ X3 @ X2 )
                                                                                                               => ( X1 != X2 ) ) )
                                                                                                         => ( ! [X1: $i] : ( subset @ X1 @ X1 )
                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                  ( ( subset @ X1 @ X2 )
                                                                                                                 => ( ( subset @ X2 @ X3 )
                                                                                                                   => ( subset @ X1 @ X3 ) ) )
                                                                                                             => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) )
                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                      ( ( subset @ X1 @ X3 )
                                                                                                                     => ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                        ( ( subset @ X1 @ X2 )
                                                                                                                       => ( in @ X1 @ ( powerset @ X2 ) ) )
                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                          ( ( subset @ X1 @ X2 )
                                                                                                                         => ( ( subset @ X2 @ X1 )
                                                                                                                           => ( X1 = X2 ) ) )
                                                                                                                     => ( ! [X1: $i] :
                                                                                                                            ( ( subset @ X1 @ emptyset )
                                                                                                                           => ( X1 = emptyset ) )
                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                              ( ( subset @ X2 @ X1 )
                                                                                                                             => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                ( ( in @ X2 @ ( powerset @ X1 ) )
                                                                                                                               => ( subset @ X2 @ X1 ) )
                                                                                                                           => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                    ( ( subset @ X1 @ X2 )
                                                                                                                                   => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
                                                                                                                               => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                         => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                              ( ( in @ X3 @ X2 )
                                                                                                                                             => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                                                                                                                                ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                               => ( ( ( in @ X3 @ X1 )
                                                                                                                                                   => X4 )
                                                                                                                                                 => ( ( ( in @ X3 @ X2 )
                                                                                                                                                     => X4 )
                                                                                                                                                   => X4 ) ) )
                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                  ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                 => ( ~ ( in @ X3 @ X1 )
                                                                                                                                                   => ( in @ X3 @ X2 ) ) )
                                                                                                                                             => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                               => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                       => ( ( in @ X3 @ X2 )
                                                                                                                                                         => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                          ( ( subset @ X3 @ X1 )
                                                                                                                                                         => ( ( subset @ X3 @ X2 )
                                                                                                                                                           => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                            ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                                           => ( in @ X3 @ X1 ) )
                                                                                                                                                       => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                ( ( subset @ X1 @ X2 )
                                                                                                                                                               => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                  = X1 ) )
                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                  ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                    = X2 )
                                                                                                                                                                 => ( subset @ X2 @ X1 ) )
                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                    ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                                                   => ( in @ X3 @ X2 ) )
                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                      ( ! [X3: $i] :
                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                         => ~ ( in @ X3 @ X2 ) )
                                                                                                                                                                     => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                        = emptyset ) )
                                                                                                                                                                 => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                          ( ( subset @ X2 @ X1 )
                                                                                                                                                                         => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                            = X2 ) )
                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                            ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                              = X1 )
                                                                                                                                                                           => ( subset @ X1 @ X2 ) )
                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                              ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                                                                                                                                              = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                               => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                 => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                  ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                 => ( in @ X3 @ X1 ) )
                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                    ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                   => ~ ( in @ X3 @ X2 ) )
                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                      ( ( subset @ X1 @ X2 )
                                                                                                                                                                                     => ( ( setminus @ X1 @ X2 )
                                                                                                                                                                                        = emptyset ) )
                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                        ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                       => ( ( in @ X3 @ X1 )
                                                                                                                                                                                         => ( in @ X3 @ X2 ) ) )
                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                          ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                         => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                           => ~ ( in @ X3 @ X1 ) ) )
                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                            ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                           => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                              ( ( in @ X3 @ X2 )
                                                                                                                                                                                             => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                  ( ( ( setminus @ X1 @ X2 )
                                                                                                                                                                                                    = emptyset )
                                                                                                                                                                                                 => ( subset @ X1 @ X2 ) )
                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                    ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                                                                                                                                   => ! [X4: $o] :
                                                                                                                                                                                                        ( ( ( in @ X3 @ X1 )
                                                                                                                                                                                                         => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                           => X4 ) )
                                                                                                                                                                                                       => ( ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                           => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                             => X4 ) )
                                                                                                                                                                                                         => X4 ) ) )
                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                     => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                       => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                        ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                       => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                         => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                         => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                           => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                            ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                           => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                             => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                        ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                       => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                          ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                         => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                           => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                              ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                             => ( ( X3 != X1 )
                                                                                                                                                                                                                               => ( X3 = X2 ) ) )
                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                   => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                     => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                       => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                         => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                           => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                             => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                            ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                           => ~ ! [X4: $i] :
                                                                                                                                                                                                                                                  ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                 => ! [X5: $i] :
                                                                                                                                                                                                                                                      ( ( in @ X5 @ X2 )
                                                                                                                                                                                                                                                     => ( X3
                                                                                                                                                                                                                                                       != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                                                                                                                                       => ( sP5
                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                                                                                                                                               => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                     => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                                                                                                                                           => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                                                                                                                                             => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                                               => ( ! [X1: $i] :
                                                                                                                                                                                                                                                      ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                                                                                                                                      = X1 )
                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                        ( ! [X3: $i] :
                                                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                                                                                                                ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                               => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                                 => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                   => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                                                       => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                               => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                                                         => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                               => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                 != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                          ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                               => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                 != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                                                                                                                                         => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                               => ~ ( X2 @ X3 ) ) )
                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                           => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                             => ( ! [X4: $i] :
                                                                                                                                                                                                                                                                    ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                   => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                     => ( X4 = X3 ) ) )
                                                                                                                                                                                                                                                               => ~ ! [X4: $i] :
                                                                                                                                                                                                                                                                      ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                     => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                       != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                              ( ! [X3: $i] :
                                                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                                                                                                                      ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                     => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                                       => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                         => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                                                             => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                     => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                                                               => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                      ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                     => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                       != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                                                                                                                                  = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                               => ( X1 = X2 ) )
                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                  ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                 => ( X1 = X3 ) )
                                                                                                                                                                                                                                                             => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                    ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                                   => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                          ( ( in @ X2
                                                                                                                                                                                                                                                                            @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                              @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                                                                                                                                         => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                              @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                                                                           != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                                               => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                      ( ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                            ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                                                           => ( X1
                                                                                                                                                                                                                                                                             != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                                                     => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                        ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                        = X1 )
                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                         => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                            ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                              = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                           => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                              ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                                                = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                             => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                ( ( X1 = X2 )
                                                                                                                                                                                                                                                                               => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                                  = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                  ( ( X1 = X2 )
                                                                                                                                                                                                                                                                                 => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                    = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                    ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                      = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                   => ( ( X3 = X4 )
                                                                                                                                                                                                                                                                                     => ( X2 = X4 ) ) )
                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                      ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                                        = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                                                                                                                                     => ( X1 = X2 ) )
                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                        ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                          = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                       => ( X2 = X4 ) )
                                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                          ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                                                            = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                         => ( X2 = X4 ) )
                                                                                                                                                                                                                                                                                     => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                            ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                                                           => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                                  ( ( in @ X2
                                                                                                                                                                                                                                                                                                    @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                      @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                                                          ( X1
                                                                                                                                                                                                                                                                                                          = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                                                                                                                                 => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                      @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                                                          ( X1
                                                                                                                                                                                                                                                                                                          = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                                                                                                                                   != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                              ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                              = X2 )
                                                                                                                                                                                                                                                                                         => ( sP8
                                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                  ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                 => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                    ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                   => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                      ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                     => ( in @ X4 @ X2 ) )
                                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                                           => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                              = X3 ) ) )
                                                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                                             => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                                = X4 ) ) )
                                                                                                                                                                                                                                                                                                     => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                         => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                                                                                                                                            = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h46,assumption,
    ! [X1: $i] :
      ( ( X1 != emptyset )
     => ~ ! [X2: $i] :
            ~ ( in @ X2 @ X1 ) ),
    introduced(assumption,[]) ).

thf(h47,assumption,
    ~ ( ! [X1: $i,X2: $i > $o,X3: $i] :
          ( ( in @ X3 @ X1 )
         => ( ( X2 @ X3 )
           => ( ( dsetconstr @ X1 @ X2 )
             != emptyset ) ) )
     => ( ! [X1: $i] :
            ( ~ ! [X2: $i] :
                  ~ ( in @ X2 @ X1 )
           => ( X1 != emptyset ) )
       => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) )
         => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
           => ( ! [X1: $i,X2: $i,X3: $i] :
                  ( ( in @ X3 @ X2 )
                 => ( in @ X3 @ ( setadjoin @ X1 @ X2 ) ) )
             => ( ! [X1: $i,X2: $i,X3: $i] :
                    ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                   => ! [X4: $o] :
                        ( ( ( X3 = X1 )
                         => X4 )
                       => ( ( ( in @ X3 @ X2 )
                           => X4 )
                         => X4 ) ) )
               => ( ! [X1: $i,X2: $i,X3: $i] :
                      ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                     => ( ( X3 != X1 )
                       => ( in @ X3 @ X2 ) ) )
                 => ( ! [X1: $i] :
                        ( ( dsetconstr @ X1
                          @ ^ [X2: $i] : ~ $false )
                        = X1 )
                   => ( ! [X1: $i,X2: $i] :
                          ( ! [X3: $i] :
                              ( ( in @ X3 @ X2 )
                             => ( in @ X3 @ X1 ) )
                         => ( in @ X2 @ ( powerset @ X1 ) ) )
                     => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                       => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                ( ( in @ X2 @ ( powerset @ X1 ) )
                               => ( ( in @ X3 @ X2 )
                                 => ( in @ X3 @ X1 ) ) )
                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                  ( ( in @ X2 @ X3 )
                                 => ( ( in @ X3 @ X1 )
                                   => ( in @ X2 @ ( setunion @ X1 ) ) ) )
                             => ( ! [X1: $i,X2: $i] :
                                    ( ( in @ X2 @ ( setunion @ X1 ) )
                                   => ! [X3: $o] :
                                        ( ! [X4: $i] :
                                            ( ( in @ X2 @ X4 )
                                           => ( ( in @ X4 @ X1 )
                                             => X3 ) )
                                       => X3 ) )
                               => ( ! [X1: $i,X2: $i] :
                                      ( ( in @ X2 @ X1 )
                                     => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
                                 => ( ! [X1: $i > $o] :
                                        ( ~ ! [X2: $i] :
                                              ( ( X1 @ X2 )
                                             => ~ ! [X3: $i] :
                                                    ( ( X1 @ X3 )
                                                   => ( X2 = X3 ) ) )
                                       => ~ ! [X2: $i] :
                                              ~ ! [X3: $i] :
                                                  ( ( X1 @ X3 )
                                                  = ( X3 = X2 ) ) )
                                   => ( ! [X1: $i] :
                                          ( ( X1 != emptyset )
                                         => ~ ! [X2: $i] :
                                                ~ ( in @ X2 @ X1 ) )
                                     => ( ! [X1: $i,X2: $i] :
                                            ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                           => ( X1 = X2 ) )
                                       => ( ! [X1: $i,X2: $i] :
                                              ( ( X1 != X2 )
                                             => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                         => ( ! [X1: $i,X2: $i] :
                                                ( ( X1 = X2 )
                                               => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                           => ( ! [X1: $i,X2: $i] :
                                                  ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                 => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                    ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                   => ( ( X3 != X1 )
                                                     => ( X3 = X2 ) ) )
                                               => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                 => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                          ( ~ ! [X3: $i] :
                                                                ( ( in @ X3 @ X1 )
                                                               => ~ ( X2 @ X3 ) )
                                                         => ( ( dsetconstr @ X1 @ X2 )
                                                           != emptyset ) )
                                                     => ( ! [X1: $i > $o,X2: $i] :
                                                            ( ( in @ X2 @ emptyset )
                                                           => ( X1 @ X2 ) )
                                                       => ( ! [X1: $o] :
                                                              ( X1
                                                             => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                                         => ( ! [X1: $o] :
                                                                ( X1
                                                               => ( set2prop @ ( prop2set @ X1 ) ) )
                                                           => ( ! [X1: $i > $o] :
                                                                  ( ~ ! [X2: $i] :
                                                                        ~ ( X1 @ X2 )
                                                                 => ( ! [X2: $i,X3: $i] :
                                                                        ( ( X1 @ X2 )
                                                                       => ( ( X1 @ X3 )
                                                                         => ( X2 = X3 ) ) )
                                                                   => ~ ! [X2: $i] :
                                                                          ( ( X1 @ X2 )
                                                                         => ~ ! [X3: $i] :
                                                                                ( ( X1 @ X3 )
                                                                               => ( X2 = X3 ) ) ) ) )
                                                             => ( ! [X1: $i > $o] :
                                                                    ( ~ ! [X2: $i] :
                                                                          ~ ! [X3: $i] :
                                                                              ( ( X1 @ X3 )
                                                                              = ( X3 = X2 ) )
                                                                   => ~ ! [X2: $i] :
                                                                          ( ( X1 @ X2 )
                                                                         => ~ ! [X3: $i] :
                                                                                ( ( X1 @ X3 )
                                                                               => ( X2 = X3 ) ) ) )
                                                               => ( ! [X1: $i,X2: $i] :
                                                                      ( ( X1 = X2 )
                                                                     => ! [X3: $i,X4: $i] :
                                                                          ( ( X3 = X4 )
                                                                         => ( ( in @ X3 @ X1 )
                                                                           => ( in @ X4 @ X2 ) ) ) )
                                                                 => ( ! [X1: $i,X2: $i] :
                                                                        ( ( X1 = X2 )
                                                                       => ! [X3: $i,X4: $i] :
                                                                            ( ( X3 = X4 )
                                                                           => ( ( in @ X3 @ X1 )
                                                                              = ( in @ X4 @ X2 ) ) ) )
                                                                   => ( ! [X1: $i > $o] :
                                                                          ( ~ ! [X2: $i] :
                                                                                ( ( X1 @ X2 )
                                                                               => ~ ! [X3: $i] :
                                                                                      ( ( X1 @ X3 )
                                                                                     => ( X2 = X3 ) ) )
                                                                         => ! [X2: $i,X3: $i] :
                                                                              ( ( X1 @ X2 )
                                                                             => ( ( X1 @ X3 )
                                                                               => ( X2 = X3 ) ) ) )
                                                                     => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                            ( ! [X3: $i,X4: $i] :
                                                                                ( ( X3 = X4 )
                                                                               => ( ( X1 @ X3 )
                                                                                  = ( X2 @ X4 ) ) )
                                                                           => ( ( ~ ! [X3: $i] :
                                                                                      ( ( X1 @ X3 )
                                                                                     => ~ ! [X4: $i] :
                                                                                            ( ( X1 @ X4 )
                                                                                           => ( X3 = X4 ) ) ) )
                                                                              = ( ~ ! [X3: $i] :
                                                                                      ( ( X2 @ X3 )
                                                                                     => ~ ! [X4: $i] :
                                                                                            ( ( X2 @ X4 )
                                                                                           => ( X3 = X4 ) ) ) ) ) )
                                                                       => ( ! [X1: $i,X2: $i] :
                                                                              ( ( X1 = X2 )
                                                                             => ! [X3: $i,X4: $i] :
                                                                                  ( ( X3 = X4 )
                                                                                 => ( ( setadjoin @ X1 @ X3 )
                                                                                    = ( setadjoin @ X2 @ X4 ) ) ) )
                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                ( ( X1 = X2 )
                                                                               => ( ( powerset @ X1 )
                                                                                  = ( powerset @ X2 ) ) )
                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                  ( ( X1 = X2 )
                                                                                 => ( ( setunion @ X1 )
                                                                                    = ( setunion @ X2 ) ) )
                                                                             => ( ! [X1: $i > $o] :
                                                                                    ( ~ ! [X2: $i] :
                                                                                          ( ( X1 @ X2 )
                                                                                         => ~ ! [X3: $i] :
                                                                                                ( ( X1 @ X3 )
                                                                                               => ( X2 = X3 ) ) )
                                                                                   => ! [X2: $i,X3: $i] :
                                                                                        ( ( X1 @ X2 )
                                                                                       => ( ( X1 @ X3 )
                                                                                         => ( X2 = X3 ) ) ) )
                                                                               => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                      ( ! [X3: $i,X4: $i] :
                                                                                          ( ( X3 = X4 )
                                                                                         => ( ( X1 @ X3 )
                                                                                            = ( X2 @ X4 ) ) )
                                                                                     => ( ~ ! [X3: $i] :
                                                                                              ( ( X1 @ X3 )
                                                                                             => ~ ! [X4: $i] :
                                                                                                    ( ( X1 @ X4 )
                                                                                                   => ( X3 = X4 ) ) )
                                                                                       => ( ~ ! [X3: $i] :
                                                                                                ( ( X2 @ X3 )
                                                                                               => ~ ! [X4: $i] :
                                                                                                      ( ( X2 @ X4 )
                                                                                                     => ( X3 = X4 ) ) )
                                                                                         => ( ( descr @ X1 )
                                                                                            = ( descr @ X2 ) ) ) ) )
                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                        ( ( X1 = X2 )
                                                                                       => ! [X3: $i > $o,X4: $i > $o] :
                                                                                            ( ! [X5: $i] :
                                                                                                ( ( in @ X5 @ X1 )
                                                                                               => ! [X6: $i] :
                                                                                                    ( ( in @ X6 @ X2 )
                                                                                                   => ( ( X5 = X6 )
                                                                                                     => ( ( X3 @ X5 )
                                                                                                        = ( X4 @ X6 ) ) ) ) )
                                                                                           => ( ( dsetconstr @ X1 @ X3 )
                                                                                              = ( dsetconstr @ X2 @ X4 ) ) ) )
                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                          ( ! [X3: $i] :
                                                                                              ( ( in @ X3 @ X1 )
                                                                                             => ( in @ X3 @ X2 ) )
                                                                                         => ( subset @ X1 @ X2 ) )
                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                            ( ( X1 = X2 )
                                                                                           => ( subset @ X2 @ X1 ) )
                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                              ( ( X1 = X2 )
                                                                                             => ( subset @ X1 @ X2 ) )
                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                ( ! [X3: $i] :
                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                   => ( in @ X3 @ X2 ) )
                                                                                               => ( subset @ X1 @ X2 ) )
                                                                                           => ( ! [X1: $i] : ( subset @ emptyset @ X1 )
                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                    ( ( subset @ X1 @ X2 )
                                                                                                   => ( ( in @ X3 @ X1 )
                                                                                                     => ( in @ X3 @ X2 ) ) )
                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                      ( ( subset @ X1 @ X2 )
                                                                                                     => ( ~ ( in @ X3 @ X2 )
                                                                                                       => ~ ( in @ X3 @ X1 ) ) )
                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                       => ( ~ ( in @ X3 @ X2 )
                                                                                                         => ~ ( subset @ X1 @ X2 ) ) )
                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                          ( ~ ( subset @ X1 @ X2 )
                                                                                                         => ( X1 != X2 ) )
                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                           => ( ~ ( in @ X3 @ X2 )
                                                                                                             => ( X1 != X2 ) ) )
                                                                                                       => ( ! [X1: $i] : ( subset @ X1 @ X1 )
                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                ( ( subset @ X1 @ X2 )
                                                                                                               => ( ( subset @ X2 @ X3 )
                                                                                                                 => ( subset @ X1 @ X3 ) ) )
                                                                                                           => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) )
                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                    ( ( subset @ X1 @ X3 )
                                                                                                                   => ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                      ( ( subset @ X1 @ X2 )
                                                                                                                     => ( in @ X1 @ ( powerset @ X2 ) ) )
                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                        ( ( subset @ X1 @ X2 )
                                                                                                                       => ( ( subset @ X2 @ X1 )
                                                                                                                         => ( X1 = X2 ) ) )
                                                                                                                   => ( ! [X1: $i] :
                                                                                                                          ( ( subset @ X1 @ emptyset )
                                                                                                                         => ( X1 = emptyset ) )
                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                            ( ( subset @ X2 @ X1 )
                                                                                                                           => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                              ( ( in @ X2 @ ( powerset @ X1 ) )
                                                                                                                             => ( subset @ X2 @ X1 ) )
                                                                                                                         => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                  ( ( subset @ X1 @ X2 )
                                                                                                                                 => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
                                                                                                                             => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                                                                                                                               => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                       => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                            ( ( in @ X3 @ X2 )
                                                                                                                                           => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                                                                                                                              ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                             => ( ( ( in @ X3 @ X1 )
                                                                                                                                                 => X4 )
                                                                                                                                               => ( ( ( in @ X3 @ X2 )
                                                                                                                                                   => X4 )
                                                                                                                                                 => X4 ) ) )
                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                               => ( ~ ( in @ X3 @ X1 )
                                                                                                                                                 => ( in @ X3 @ X2 ) ) )
                                                                                                                                           => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                             => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                     => ( ( in @ X3 @ X2 )
                                                                                                                                                       => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                        ( ( subset @ X3 @ X1 )
                                                                                                                                                       => ( ( subset @ X3 @ X2 )
                                                                                                                                                         => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                          ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                                         => ( in @ X3 @ X1 ) )
                                                                                                                                                     => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                              ( ( subset @ X1 @ X2 )
                                                                                                                                                             => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                = X1 ) )
                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                  = X2 )
                                                                                                                                                               => ( subset @ X2 @ X1 ) )
                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                  ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                                                 => ( in @ X3 @ X2 ) )
                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                    ( ! [X3: $i] :
                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                       => ~ ( in @ X3 @ X2 ) )
                                                                                                                                                                   => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                      = emptyset ) )
                                                                                                                                                               => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                        ( ( subset @ X2 @ X1 )
                                                                                                                                                                       => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                          = X2 ) )
                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                          ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                            = X1 )
                                                                                                                                                                         => ( subset @ X1 @ X2 ) )
                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                            ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                                                                                                                                            = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                             => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                               => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                               => ( in @ X3 @ X1 ) )
                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                  ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                 => ~ ( in @ X3 @ X2 ) )
                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                    ( ( subset @ X1 @ X2 )
                                                                                                                                                                                   => ( ( setminus @ X1 @ X2 )
                                                                                                                                                                                      = emptyset ) )
                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                      ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                     => ( ( in @ X3 @ X1 )
                                                                                                                                                                                       => ( in @ X3 @ X2 ) ) )
                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                        ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                       => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                         => ~ ( in @ X3 @ X1 ) ) )
                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                          ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                         => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                            ( ( in @ X3 @ X2 )
                                                                                                                                                                                           => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                ( ( ( setminus @ X1 @ X2 )
                                                                                                                                                                                                  = emptyset )
                                                                                                                                                                                               => ( subset @ X1 @ X2 ) )
                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                  ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                                                                                                                                 => ! [X4: $o] :
                                                                                                                                                                                                      ( ( ( in @ X3 @ X1 )
                                                                                                                                                                                                       => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                         => X4 ) )
                                                                                                                                                                                                     => ( ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                         => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                           => X4 ) )
                                                                                                                                                                                                       => X4 ) ) )
                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                   => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                     => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                      ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                     => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                       => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                       => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                         => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                          ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                         => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                           => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                      ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                     => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                        ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                       => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                         => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                            ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                           => ( ( X3 != X1 )
                                                                                                                                                                                                                             => ( X3 = X2 ) ) )
                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                 => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                   => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                     => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                       => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                         => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                           => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                         => ~ ! [X4: $i] :
                                                                                                                                                                                                                                                ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                               => ! [X5: $i] :
                                                                                                                                                                                                                                                    ( ( in @ X5 @ X2 )
                                                                                                                                                                                                                                                   => ( X3
                                                                                                                                                                                                                                                     != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                                                                                                                                     => ( sP5
                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                              ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                                                                                                                                             => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                   => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                                                                                                                                         => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                                                                                                                                           => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                                             => ( ! [X1: $i] :
                                                                                                                                                                                                                                                    ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                                                                                                                                    = X1 )
                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                      ( ! [X3: $i] :
                                                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                                                                                                              ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                             => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                               => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                 => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                                                     => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                             => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                                                       => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                              ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                             => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                               != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                        ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                              ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                             => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                               != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                                                                                                                                       => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                             => ~ ( X2 @ X3 ) ) )
                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                         => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                           => ( ! [X4: $i] :
                                                                                                                                                                                                                                                                  ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                 => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                   => ( X4 = X3 ) ) )
                                                                                                                                                                                                                                                             => ~ ! [X4: $i] :
                                                                                                                                                                                                                                                                    ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                   => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                     != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                            ( ! [X3: $i] :
                                                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                                                                                                    ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                   => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                                     => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                       => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                                                           => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                   => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                                                             => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                    ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                   => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                     != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                              ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                                                                                                                                = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                             => ( X1 = X2 ) )
                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                               => ( X1 = X3 ) )
                                                                                                                                                                                                                                                           => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                  ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                                 => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                        ( ( in @ X2
                                                                                                                                                                                                                                                                          @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                            @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                                                                                                                                       => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                            @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                                                                         != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                                             => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                    ( ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                          ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                                                         => ( X1
                                                                                                                                                                                                                                                                           != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                                                   => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                      ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                      = X1 )
                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                       => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                          ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                            = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                         => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                            ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                                              = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                           => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                              ( ( X1 = X2 )
                                                                                                                                                                                                                                                                             => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                                = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                ( ( X1 = X2 )
                                                                                                                                                                                                                                                                               => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                  = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                  ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                    = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                 => ( ( X3 = X4 )
                                                                                                                                                                                                                                                                                   => ( X2 = X4 ) ) )
                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                    ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                                      = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                                                                                                                                   => ( X1 = X2 ) )
                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                      ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                        = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                     => ( X2 = X4 ) )
                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                        ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                                                          = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                       => ( X2 = X4 ) )
                                                                                                                                                                                                                                                                                   => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                          ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                                                         => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                                ( ( in @ X2
                                                                                                                                                                                                                                                                                                  @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                    @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                                                        ( X1
                                                                                                                                                                                                                                                                                                        = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                                                                                                                               => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                    @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                                                        ( X1
                                                                                                                                                                                                                                                                                                        = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                                                                                                                                 != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                            ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                            = X2 )
                                                                                                                                                                                                                                                                                       => ( sP8
                                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                               => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                  ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                 => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                    ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                   => ( in @ X4 @ X2 ) )
                                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                                         => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                            = X3 ) ) )
                                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                                           => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                              = X4 ) ) )
                                                                                                                                                                                                                                                                                                   => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                       => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                                                                                                                                          = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h48,assumption,
    ! [X1: $i,X2: $i > $o,X3: $i] :
      ( ( in @ X3 @ X1 )
     => ( ( X2 @ X3 )
       => ( ( dsetconstr @ X1 @ X2 )
         != emptyset ) ) ),
    introduced(assumption,[]) ).

thf(h49,assumption,
    ~ ( ! [X1: $i] :
          ( ~ ! [X2: $i] :
                ~ ( in @ X2 @ X1 )
         => ( X1 != emptyset ) )
     => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) )
       => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
         => ( ! [X1: $i,X2: $i,X3: $i] :
                ( ( in @ X3 @ X2 )
               => ( in @ X3 @ ( setadjoin @ X1 @ X2 ) ) )
           => ( ! [X1: $i,X2: $i,X3: $i] :
                  ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                 => ! [X4: $o] :
                      ( ( ( X3 = X1 )
                       => X4 )
                     => ( ( ( in @ X3 @ X2 )
                         => X4 )
                       => X4 ) ) )
             => ( ! [X1: $i,X2: $i,X3: $i] :
                    ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                   => ( ( X3 != X1 )
                     => ( in @ X3 @ X2 ) ) )
               => ( ! [X1: $i] :
                      ( ( dsetconstr @ X1
                        @ ^ [X2: $i] : ~ $false )
                      = X1 )
                 => ( ! [X1: $i,X2: $i] :
                        ( ! [X3: $i] :
                            ( ( in @ X3 @ X2 )
                           => ( in @ X3 @ X1 ) )
                       => ( in @ X2 @ ( powerset @ X1 ) ) )
                   => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                     => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                       => ( ! [X1: $i,X2: $i,X3: $i] :
                              ( ( in @ X2 @ ( powerset @ X1 ) )
                             => ( ( in @ X3 @ X2 )
                               => ( in @ X3 @ X1 ) ) )
                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                ( ( in @ X2 @ X3 )
                               => ( ( in @ X3 @ X1 )
                                 => ( in @ X2 @ ( setunion @ X1 ) ) ) )
                           => ( ! [X1: $i,X2: $i] :
                                  ( ( in @ X2 @ ( setunion @ X1 ) )
                                 => ! [X3: $o] :
                                      ( ! [X4: $i] :
                                          ( ( in @ X2 @ X4 )
                                         => ( ( in @ X4 @ X1 )
                                           => X3 ) )
                                     => X3 ) )
                             => ( ! [X1: $i,X2: $i] :
                                    ( ( in @ X2 @ X1 )
                                   => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
                               => ( ! [X1: $i > $o] :
                                      ( ~ ! [X2: $i] :
                                            ( ( X1 @ X2 )
                                           => ~ ! [X3: $i] :
                                                  ( ( X1 @ X3 )
                                                 => ( X2 = X3 ) ) )
                                     => ~ ! [X2: $i] :
                                            ~ ! [X3: $i] :
                                                ( ( X1 @ X3 )
                                                = ( X3 = X2 ) ) )
                                 => ( ! [X1: $i] :
                                        ( ( X1 != emptyset )
                                       => ~ ! [X2: $i] :
                                              ~ ( in @ X2 @ X1 ) )
                                   => ( ! [X1: $i,X2: $i] :
                                          ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                         => ( X1 = X2 ) )
                                     => ( ! [X1: $i,X2: $i] :
                                            ( ( X1 != X2 )
                                           => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                       => ( ! [X1: $i,X2: $i] :
                                              ( ( X1 = X2 )
                                             => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                         => ( ! [X1: $i,X2: $i] :
                                                ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                               => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                  ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                 => ( ( X3 != X1 )
                                                   => ( X3 = X2 ) ) )
                                             => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                               => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                        ( ~ ! [X3: $i] :
                                                              ( ( in @ X3 @ X1 )
                                                             => ~ ( X2 @ X3 ) )
                                                       => ( ( dsetconstr @ X1 @ X2 )
                                                         != emptyset ) )
                                                   => ( ! [X1: $i > $o,X2: $i] :
                                                          ( ( in @ X2 @ emptyset )
                                                         => ( X1 @ X2 ) )
                                                     => ( ! [X1: $o] :
                                                            ( X1
                                                           => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                                       => ( ! [X1: $o] :
                                                              ( X1
                                                             => ( set2prop @ ( prop2set @ X1 ) ) )
                                                         => ( ! [X1: $i > $o] :
                                                                ( ~ ! [X2: $i] :
                                                                      ~ ( X1 @ X2 )
                                                               => ( ! [X2: $i,X3: $i] :
                                                                      ( ( X1 @ X2 )
                                                                     => ( ( X1 @ X3 )
                                                                       => ( X2 = X3 ) ) )
                                                                 => ~ ! [X2: $i] :
                                                                        ( ( X1 @ X2 )
                                                                       => ~ ! [X3: $i] :
                                                                              ( ( X1 @ X3 )
                                                                             => ( X2 = X3 ) ) ) ) )
                                                           => ( ! [X1: $i > $o] :
                                                                  ( ~ ! [X2: $i] :
                                                                        ~ ! [X3: $i] :
                                                                            ( ( X1 @ X3 )
                                                                            = ( X3 = X2 ) )
                                                                 => ~ ! [X2: $i] :
                                                                        ( ( X1 @ X2 )
                                                                       => ~ ! [X3: $i] :
                                                                              ( ( X1 @ X3 )
                                                                             => ( X2 = X3 ) ) ) )
                                                             => ( ! [X1: $i,X2: $i] :
                                                                    ( ( X1 = X2 )
                                                                   => ! [X3: $i,X4: $i] :
                                                                        ( ( X3 = X4 )
                                                                       => ( ( in @ X3 @ X1 )
                                                                         => ( in @ X4 @ X2 ) ) ) )
                                                               => ( ! [X1: $i,X2: $i] :
                                                                      ( ( X1 = X2 )
                                                                     => ! [X3: $i,X4: $i] :
                                                                          ( ( X3 = X4 )
                                                                         => ( ( in @ X3 @ X1 )
                                                                            = ( in @ X4 @ X2 ) ) ) )
                                                                 => ( ! [X1: $i > $o] :
                                                                        ( ~ ! [X2: $i] :
                                                                              ( ( X1 @ X2 )
                                                                             => ~ ! [X3: $i] :
                                                                                    ( ( X1 @ X3 )
                                                                                   => ( X2 = X3 ) ) )
                                                                       => ! [X2: $i,X3: $i] :
                                                                            ( ( X1 @ X2 )
                                                                           => ( ( X1 @ X3 )
                                                                             => ( X2 = X3 ) ) ) )
                                                                   => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                          ( ! [X3: $i,X4: $i] :
                                                                              ( ( X3 = X4 )
                                                                             => ( ( X1 @ X3 )
                                                                                = ( X2 @ X4 ) ) )
                                                                         => ( ( ~ ! [X3: $i] :
                                                                                    ( ( X1 @ X3 )
                                                                                   => ~ ! [X4: $i] :
                                                                                          ( ( X1 @ X4 )
                                                                                         => ( X3 = X4 ) ) ) )
                                                                            = ( ~ ! [X3: $i] :
                                                                                    ( ( X2 @ X3 )
                                                                                   => ~ ! [X4: $i] :
                                                                                          ( ( X2 @ X4 )
                                                                                         => ( X3 = X4 ) ) ) ) ) )
                                                                     => ( ! [X1: $i,X2: $i] :
                                                                            ( ( X1 = X2 )
                                                                           => ! [X3: $i,X4: $i] :
                                                                                ( ( X3 = X4 )
                                                                               => ( ( setadjoin @ X1 @ X3 )
                                                                                  = ( setadjoin @ X2 @ X4 ) ) ) )
                                                                       => ( ! [X1: $i,X2: $i] :
                                                                              ( ( X1 = X2 )
                                                                             => ( ( powerset @ X1 )
                                                                                = ( powerset @ X2 ) ) )
                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                ( ( X1 = X2 )
                                                                               => ( ( setunion @ X1 )
                                                                                  = ( setunion @ X2 ) ) )
                                                                           => ( ! [X1: $i > $o] :
                                                                                  ( ~ ! [X2: $i] :
                                                                                        ( ( X1 @ X2 )
                                                                                       => ~ ! [X3: $i] :
                                                                                              ( ( X1 @ X3 )
                                                                                             => ( X2 = X3 ) ) )
                                                                                 => ! [X2: $i,X3: $i] :
                                                                                      ( ( X1 @ X2 )
                                                                                     => ( ( X1 @ X3 )
                                                                                       => ( X2 = X3 ) ) ) )
                                                                             => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                    ( ! [X3: $i,X4: $i] :
                                                                                        ( ( X3 = X4 )
                                                                                       => ( ( X1 @ X3 )
                                                                                          = ( X2 @ X4 ) ) )
                                                                                   => ( ~ ! [X3: $i] :
                                                                                            ( ( X1 @ X3 )
                                                                                           => ~ ! [X4: $i] :
                                                                                                  ( ( X1 @ X4 )
                                                                                                 => ( X3 = X4 ) ) )
                                                                                     => ( ~ ! [X3: $i] :
                                                                                              ( ( X2 @ X3 )
                                                                                             => ~ ! [X4: $i] :
                                                                                                    ( ( X2 @ X4 )
                                                                                                   => ( X3 = X4 ) ) )
                                                                                       => ( ( descr @ X1 )
                                                                                          = ( descr @ X2 ) ) ) ) )
                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                      ( ( X1 = X2 )
                                                                                     => ! [X3: $i > $o,X4: $i > $o] :
                                                                                          ( ! [X5: $i] :
                                                                                              ( ( in @ X5 @ X1 )
                                                                                             => ! [X6: $i] :
                                                                                                  ( ( in @ X6 @ X2 )
                                                                                                 => ( ( X5 = X6 )
                                                                                                   => ( ( X3 @ X5 )
                                                                                                      = ( X4 @ X6 ) ) ) ) )
                                                                                         => ( ( dsetconstr @ X1 @ X3 )
                                                                                            = ( dsetconstr @ X2 @ X4 ) ) ) )
                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                        ( ! [X3: $i] :
                                                                                            ( ( in @ X3 @ X1 )
                                                                                           => ( in @ X3 @ X2 ) )
                                                                                       => ( subset @ X1 @ X2 ) )
                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                          ( ( X1 = X2 )
                                                                                         => ( subset @ X2 @ X1 ) )
                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                            ( ( X1 = X2 )
                                                                                           => ( subset @ X1 @ X2 ) )
                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                              ( ! [X3: $i] :
                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                 => ( in @ X3 @ X2 ) )
                                                                                             => ( subset @ X1 @ X2 ) )
                                                                                         => ( ! [X1: $i] : ( subset @ emptyset @ X1 )
                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                  ( ( subset @ X1 @ X2 )
                                                                                                 => ( ( in @ X3 @ X1 )
                                                                                                   => ( in @ X3 @ X2 ) ) )
                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                    ( ( subset @ X1 @ X2 )
                                                                                                   => ( ~ ( in @ X3 @ X2 )
                                                                                                     => ~ ( in @ X3 @ X1 ) ) )
                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                     => ( ~ ( in @ X3 @ X2 )
                                                                                                       => ~ ( subset @ X1 @ X2 ) ) )
                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                        ( ~ ( subset @ X1 @ X2 )
                                                                                                       => ( X1 != X2 ) )
                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                         => ( ~ ( in @ X3 @ X2 )
                                                                                                           => ( X1 != X2 ) ) )
                                                                                                     => ( ! [X1: $i] : ( subset @ X1 @ X1 )
                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                              ( ( subset @ X1 @ X2 )
                                                                                                             => ( ( subset @ X2 @ X3 )
                                                                                                               => ( subset @ X1 @ X3 ) ) )
                                                                                                         => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) )
                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                  ( ( subset @ X1 @ X3 )
                                                                                                                 => ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                    ( ( subset @ X1 @ X2 )
                                                                                                                   => ( in @ X1 @ ( powerset @ X2 ) ) )
                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                      ( ( subset @ X1 @ X2 )
                                                                                                                     => ( ( subset @ X2 @ X1 )
                                                                                                                       => ( X1 = X2 ) ) )
                                                                                                                 => ( ! [X1: $i] :
                                                                                                                        ( ( subset @ X1 @ emptyset )
                                                                                                                       => ( X1 = emptyset ) )
                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                          ( ( subset @ X2 @ X1 )
                                                                                                                         => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                            ( ( in @ X2 @ ( powerset @ X1 ) )
                                                                                                                           => ( subset @ X2 @ X1 ) )
                                                                                                                       => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                ( ( subset @ X1 @ X2 )
                                                                                                                               => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
                                                                                                                           => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                                                                                                                             => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                     => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                          ( ( in @ X3 @ X2 )
                                                                                                                                         => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                                                                                                                            ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                           => ( ( ( in @ X3 @ X1 )
                                                                                                                                               => X4 )
                                                                                                                                             => ( ( ( in @ X3 @ X2 )
                                                                                                                                                 => X4 )
                                                                                                                                               => X4 ) ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                              ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                             => ( ~ ( in @ X3 @ X1 )
                                                                                                                                               => ( in @ X3 @ X2 ) ) )
                                                                                                                                         => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                           => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                   => ( ( in @ X3 @ X2 )
                                                                                                                                                     => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                      ( ( subset @ X3 @ X1 )
                                                                                                                                                     => ( ( subset @ X3 @ X2 )
                                                                                                                                                       => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                        ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                                       => ( in @ X3 @ X1 ) )
                                                                                                                                                   => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                            ( ( subset @ X1 @ X2 )
                                                                                                                                                           => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                              = X1 ) )
                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                              ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                = X2 )
                                                                                                                                                             => ( subset @ X2 @ X1 ) )
                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                                               => ( in @ X3 @ X2 ) )
                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                  ( ! [X3: $i] :
                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                     => ~ ( in @ X3 @ X2 ) )
                                                                                                                                                                 => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                    = emptyset ) )
                                                                                                                                                             => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                      ( ( subset @ X2 @ X1 )
                                                                                                                                                                     => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                        = X2 ) )
                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                        ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                          = X1 )
                                                                                                                                                                       => ( subset @ X1 @ X2 ) )
                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                          ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                                                                                                                                          = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                           => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                             => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                              ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                             => ( in @ X3 @ X1 ) )
                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                               => ~ ( in @ X3 @ X2 ) )
                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                  ( ( subset @ X1 @ X2 )
                                                                                                                                                                                 => ( ( setminus @ X1 @ X2 )
                                                                                                                                                                                    = emptyset ) )
                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                    ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                   => ( ( in @ X3 @ X1 )
                                                                                                                                                                                     => ( in @ X3 @ X2 ) ) )
                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                      ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                     => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                       => ~ ( in @ X3 @ X1 ) ) )
                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                        ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                       => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                          ( ( in @ X3 @ X2 )
                                                                                                                                                                                         => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                              ( ( ( setminus @ X1 @ X2 )
                                                                                                                                                                                                = emptyset )
                                                                                                                                                                                             => ( subset @ X1 @ X2 ) )
                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                                                                                                                               => ! [X4: $o] :
                                                                                                                                                                                                    ( ( ( in @ X3 @ X1 )
                                                                                                                                                                                                     => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                       => X4 ) )
                                                                                                                                                                                                   => ( ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                       => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                         => X4 ) )
                                                                                                                                                                                                     => X4 ) ) )
                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                 => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                   => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                    ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                   => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                     => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                     => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                       => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                        ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                       => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                         => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                    ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                   => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                      ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                     => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                       => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                          ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                         => ( ( X3 != X1 )
                                                                                                                                                                                                                           => ( X3 = X2 ) ) )
                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                               => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                 => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                   => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                     => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                       => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                         => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                       => ~ ! [X4: $i] :
                                                                                                                                                                                                                                              ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                             => ! [X5: $i] :
                                                                                                                                                                                                                                                  ( ( in @ X5 @ X2 )
                                                                                                                                                                                                                                                 => ( X3
                                                                                                                                                                                                                                                   != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                                                                                                                                   => ( sP5
                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                            ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                                                                                                                                           => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                 => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                                                                                                                                       => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                                                                                                                                         => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                                           => ( ! [X1: $i] :
                                                                                                                                                                                                                                                  ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                                                                                                                                  = X1 )
                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                    ( ! [X3: $i] :
                                                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                                                                                                            ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                           => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                             => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                               => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                                                   => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                           => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                                                     => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                            ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                           => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                             != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                      ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                            ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                           => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                             != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                                                                                                                                     => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                           => ~ ( X2 @ X3 ) ) )
                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                       => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                         => ( ! [X4: $i] :
                                                                                                                                                                                                                                                                ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                               => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                 => ( X4 = X3 ) ) )
                                                                                                                                                                                                                                                           => ~ ! [X4: $i] :
                                                                                                                                                                                                                                                                  ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                 => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                   != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                          ( ! [X3: $i] :
                                                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                                                                                                  ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                 => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                                   => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                     => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                                                         => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                 => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                                                           => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                  ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                 => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                   != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                            ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                                                                                                                              = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                           => ( X1 = X2 ) )
                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                              ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                             => ( X1 = X3 ) )
                                                                                                                                                                                                                                                         => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                               => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                      ( ( in @ X2
                                                                                                                                                                                                                                                                        @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                          @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                                                                                                                                     => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                          @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                                                                       != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                                           => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                  ( ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                        ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                                                       => ( X1
                                                                                                                                                                                                                                                                         != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                                                 => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                    ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                    = X1 )
                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                      ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                     => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                        ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                          = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                       => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                          ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                                            = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                         => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                            ( ( X1 = X2 )
                                                                                                                                                                                                                                                                           => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                              = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                              ( ( X1 = X2 )
                                                                                                                                                                                                                                                                             => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                  = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                               => ( ( X3 = X4 )
                                                                                                                                                                                                                                                                                 => ( X2 = X4 ) ) )
                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                  ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                                    = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                                                                                                                                 => ( X1 = X2 ) )
                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                    ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                      = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                   => ( X2 = X4 ) )
                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                      ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                                                        = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                     => ( X2 = X4 ) )
                                                                                                                                                                                                                                                                                 => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                        ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                                                       => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                              ( ( in @ X2
                                                                                                                                                                                                                                                                                                @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                  @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                                                      ( X1
                                                                                                                                                                                                                                                                                                      = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                                                                                                                             => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                  @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                                                      ( X1
                                                                                                                                                                                                                                                                                                      = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                                                                                                                               != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                          ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                          = X2 )
                                                                                                                                                                                                                                                                                     => ( sP8
                                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                              ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                             => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                               => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                  ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                 => ( in @ X4 @ X2 ) )
                                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                                       => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                          = X3 ) ) )
                                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                                         => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                            = X4 ) ) )
                                                                                                                                                                                                                                                                                                 => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                      ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                     => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                                                                                                                                        = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h50,assumption,
    ! [X1: $i] :
      ( ~ ! [X2: $i] :
            ~ ( in @ X2 @ X1 )
     => ( X1 != emptyset ) ),
    introduced(assumption,[]) ).

thf(h51,assumption,
    ~ ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) )
     => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
       => ( ! [X1: $i,X2: $i,X3: $i] :
              ( ( in @ X3 @ X2 )
             => ( in @ X3 @ ( setadjoin @ X1 @ X2 ) ) )
         => ( ! [X1: $i,X2: $i,X3: $i] :
                ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
               => ! [X4: $o] :
                    ( ( ( X3 = X1 )
                     => X4 )
                   => ( ( ( in @ X3 @ X2 )
                       => X4 )
                     => X4 ) ) )
           => ( ! [X1: $i,X2: $i,X3: $i] :
                  ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                 => ( ( X3 != X1 )
                   => ( in @ X3 @ X2 ) ) )
             => ( ! [X1: $i] :
                    ( ( dsetconstr @ X1
                      @ ^ [X2: $i] : ~ $false )
                    = X1 )
               => ( ! [X1: $i,X2: $i] :
                      ( ! [X3: $i] :
                          ( ( in @ X3 @ X2 )
                         => ( in @ X3 @ X1 ) )
                     => ( in @ X2 @ ( powerset @ X1 ) ) )
                 => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                   => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                     => ( ! [X1: $i,X2: $i,X3: $i] :
                            ( ( in @ X2 @ ( powerset @ X1 ) )
                           => ( ( in @ X3 @ X2 )
                             => ( in @ X3 @ X1 ) ) )
                       => ( ! [X1: $i,X2: $i,X3: $i] :
                              ( ( in @ X2 @ X3 )
                             => ( ( in @ X3 @ X1 )
                               => ( in @ X2 @ ( setunion @ X1 ) ) ) )
                         => ( ! [X1: $i,X2: $i] :
                                ( ( in @ X2 @ ( setunion @ X1 ) )
                               => ! [X3: $o] :
                                    ( ! [X4: $i] :
                                        ( ( in @ X2 @ X4 )
                                       => ( ( in @ X4 @ X1 )
                                         => X3 ) )
                                   => X3 ) )
                           => ( ! [X1: $i,X2: $i] :
                                  ( ( in @ X2 @ X1 )
                                 => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
                             => ( ! [X1: $i > $o] :
                                    ( ~ ! [X2: $i] :
                                          ( ( X1 @ X2 )
                                         => ~ ! [X3: $i] :
                                                ( ( X1 @ X3 )
                                               => ( X2 = X3 ) ) )
                                   => ~ ! [X2: $i] :
                                          ~ ! [X3: $i] :
                                              ( ( X1 @ X3 )
                                              = ( X3 = X2 ) ) )
                               => ( ! [X1: $i] :
                                      ( ( X1 != emptyset )
                                     => ~ ! [X2: $i] :
                                            ~ ( in @ X2 @ X1 ) )
                                 => ( ! [X1: $i,X2: $i] :
                                        ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                       => ( X1 = X2 ) )
                                   => ( ! [X1: $i,X2: $i] :
                                          ( ( X1 != X2 )
                                         => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                     => ( ! [X1: $i,X2: $i] :
                                            ( ( X1 = X2 )
                                           => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                       => ( ! [X1: $i,X2: $i] :
                                              ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                             => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                               => ( ( X3 != X1 )
                                                 => ( X3 = X2 ) ) )
                                           => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                             => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                               => ( ! [X1: $i,X2: $i > $o] :
                                                      ( ~ ! [X3: $i] :
                                                            ( ( in @ X3 @ X1 )
                                                           => ~ ( X2 @ X3 ) )
                                                     => ( ( dsetconstr @ X1 @ X2 )
                                                       != emptyset ) )
                                                 => ( ! [X1: $i > $o,X2: $i] :
                                                        ( ( in @ X2 @ emptyset )
                                                       => ( X1 @ X2 ) )
                                                   => ( ! [X1: $o] :
                                                          ( X1
                                                         => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                                     => ( ! [X1: $o] :
                                                            ( X1
                                                           => ( set2prop @ ( prop2set @ X1 ) ) )
                                                       => ( ! [X1: $i > $o] :
                                                              ( ~ ! [X2: $i] :
                                                                    ~ ( X1 @ X2 )
                                                             => ( ! [X2: $i,X3: $i] :
                                                                    ( ( X1 @ X2 )
                                                                   => ( ( X1 @ X3 )
                                                                     => ( X2 = X3 ) ) )
                                                               => ~ ! [X2: $i] :
                                                                      ( ( X1 @ X2 )
                                                                     => ~ ! [X3: $i] :
                                                                            ( ( X1 @ X3 )
                                                                           => ( X2 = X3 ) ) ) ) )
                                                         => ( ! [X1: $i > $o] :
                                                                ( ~ ! [X2: $i] :
                                                                      ~ ! [X3: $i] :
                                                                          ( ( X1 @ X3 )
                                                                          = ( X3 = X2 ) )
                                                               => ~ ! [X2: $i] :
                                                                      ( ( X1 @ X2 )
                                                                     => ~ ! [X3: $i] :
                                                                            ( ( X1 @ X3 )
                                                                           => ( X2 = X3 ) ) ) )
                                                           => ( ! [X1: $i,X2: $i] :
                                                                  ( ( X1 = X2 )
                                                                 => ! [X3: $i,X4: $i] :
                                                                      ( ( X3 = X4 )
                                                                     => ( ( in @ X3 @ X1 )
                                                                       => ( in @ X4 @ X2 ) ) ) )
                                                             => ( ! [X1: $i,X2: $i] :
                                                                    ( ( X1 = X2 )
                                                                   => ! [X3: $i,X4: $i] :
                                                                        ( ( X3 = X4 )
                                                                       => ( ( in @ X3 @ X1 )
                                                                          = ( in @ X4 @ X2 ) ) ) )
                                                               => ( ! [X1: $i > $o] :
                                                                      ( ~ ! [X2: $i] :
                                                                            ( ( X1 @ X2 )
                                                                           => ~ ! [X3: $i] :
                                                                                  ( ( X1 @ X3 )
                                                                                 => ( X2 = X3 ) ) )
                                                                     => ! [X2: $i,X3: $i] :
                                                                          ( ( X1 @ X2 )
                                                                         => ( ( X1 @ X3 )
                                                                           => ( X2 = X3 ) ) ) )
                                                                 => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                        ( ! [X3: $i,X4: $i] :
                                                                            ( ( X3 = X4 )
                                                                           => ( ( X1 @ X3 )
                                                                              = ( X2 @ X4 ) ) )
                                                                       => ( ( ~ ! [X3: $i] :
                                                                                  ( ( X1 @ X3 )
                                                                                 => ~ ! [X4: $i] :
                                                                                        ( ( X1 @ X4 )
                                                                                       => ( X3 = X4 ) ) ) )
                                                                          = ( ~ ! [X3: $i] :
                                                                                  ( ( X2 @ X3 )
                                                                                 => ~ ! [X4: $i] :
                                                                                        ( ( X2 @ X4 )
                                                                                       => ( X3 = X4 ) ) ) ) ) )
                                                                   => ( ! [X1: $i,X2: $i] :
                                                                          ( ( X1 = X2 )
                                                                         => ! [X3: $i,X4: $i] :
                                                                              ( ( X3 = X4 )
                                                                             => ( ( setadjoin @ X1 @ X3 )
                                                                                = ( setadjoin @ X2 @ X4 ) ) ) )
                                                                     => ( ! [X1: $i,X2: $i] :
                                                                            ( ( X1 = X2 )
                                                                           => ( ( powerset @ X1 )
                                                                              = ( powerset @ X2 ) ) )
                                                                       => ( ! [X1: $i,X2: $i] :
                                                                              ( ( X1 = X2 )
                                                                             => ( ( setunion @ X1 )
                                                                                = ( setunion @ X2 ) ) )
                                                                         => ( ! [X1: $i > $o] :
                                                                                ( ~ ! [X2: $i] :
                                                                                      ( ( X1 @ X2 )
                                                                                     => ~ ! [X3: $i] :
                                                                                            ( ( X1 @ X3 )
                                                                                           => ( X2 = X3 ) ) )
                                                                               => ! [X2: $i,X3: $i] :
                                                                                    ( ( X1 @ X2 )
                                                                                   => ( ( X1 @ X3 )
                                                                                     => ( X2 = X3 ) ) ) )
                                                                           => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                  ( ! [X3: $i,X4: $i] :
                                                                                      ( ( X3 = X4 )
                                                                                     => ( ( X1 @ X3 )
                                                                                        = ( X2 @ X4 ) ) )
                                                                                 => ( ~ ! [X3: $i] :
                                                                                          ( ( X1 @ X3 )
                                                                                         => ~ ! [X4: $i] :
                                                                                                ( ( X1 @ X4 )
                                                                                               => ( X3 = X4 ) ) )
                                                                                   => ( ~ ! [X3: $i] :
                                                                                            ( ( X2 @ X3 )
                                                                                           => ~ ! [X4: $i] :
                                                                                                  ( ( X2 @ X4 )
                                                                                                 => ( X3 = X4 ) ) )
                                                                                     => ( ( descr @ X1 )
                                                                                        = ( descr @ X2 ) ) ) ) )
                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                    ( ( X1 = X2 )
                                                                                   => ! [X3: $i > $o,X4: $i > $o] :
                                                                                        ( ! [X5: $i] :
                                                                                            ( ( in @ X5 @ X1 )
                                                                                           => ! [X6: $i] :
                                                                                                ( ( in @ X6 @ X2 )
                                                                                               => ( ( X5 = X6 )
                                                                                                 => ( ( X3 @ X5 )
                                                                                                    = ( X4 @ X6 ) ) ) ) )
                                                                                       => ( ( dsetconstr @ X1 @ X3 )
                                                                                          = ( dsetconstr @ X2 @ X4 ) ) ) )
                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                      ( ! [X3: $i] :
                                                                                          ( ( in @ X3 @ X1 )
                                                                                         => ( in @ X3 @ X2 ) )
                                                                                     => ( subset @ X1 @ X2 ) )
                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                        ( ( X1 = X2 )
                                                                                       => ( subset @ X2 @ X1 ) )
                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                          ( ( X1 = X2 )
                                                                                         => ( subset @ X1 @ X2 ) )
                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                            ( ! [X3: $i] :
                                                                                                ( ( in @ X3 @ X1 )
                                                                                               => ( in @ X3 @ X2 ) )
                                                                                           => ( subset @ X1 @ X2 ) )
                                                                                       => ( ! [X1: $i] : ( subset @ emptyset @ X1 )
                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                ( ( subset @ X1 @ X2 )
                                                                                               => ( ( in @ X3 @ X1 )
                                                                                                 => ( in @ X3 @ X2 ) ) )
                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                  ( ( subset @ X1 @ X2 )
                                                                                                 => ( ~ ( in @ X3 @ X2 )
                                                                                                   => ~ ( in @ X3 @ X1 ) ) )
                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                   => ( ~ ( in @ X3 @ X2 )
                                                                                                     => ~ ( subset @ X1 @ X2 ) ) )
                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                      ( ~ ( subset @ X1 @ X2 )
                                                                                                     => ( X1 != X2 ) )
                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                       => ( ~ ( in @ X3 @ X2 )
                                                                                                         => ( X1 != X2 ) ) )
                                                                                                   => ( ! [X1: $i] : ( subset @ X1 @ X1 )
                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                            ( ( subset @ X1 @ X2 )
                                                                                                           => ( ( subset @ X2 @ X3 )
                                                                                                             => ( subset @ X1 @ X3 ) ) )
                                                                                                       => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) )
                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                ( ( subset @ X1 @ X3 )
                                                                                                               => ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                  ( ( subset @ X1 @ X2 )
                                                                                                                 => ( in @ X1 @ ( powerset @ X2 ) ) )
                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                    ( ( subset @ X1 @ X2 )
                                                                                                                   => ( ( subset @ X2 @ X1 )
                                                                                                                     => ( X1 = X2 ) ) )
                                                                                                               => ( ! [X1: $i] :
                                                                                                                      ( ( subset @ X1 @ emptyset )
                                                                                                                     => ( X1 = emptyset ) )
                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                        ( ( subset @ X2 @ X1 )
                                                                                                                       => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                          ( ( in @ X2 @ ( powerset @ X1 ) )
                                                                                                                         => ( subset @ X2 @ X1 ) )
                                                                                                                     => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                              ( ( subset @ X1 @ X2 )
                                                                                                                             => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
                                                                                                                         => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                                                                                                                           => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                   => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                                               => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                        ( ( in @ X3 @ X2 )
                                                                                                                                       => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                                                                                                                          ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                         => ( ( ( in @ X3 @ X1 )
                                                                                                                                             => X4 )
                                                                                                                                           => ( ( ( in @ X3 @ X2 )
                                                                                                                                               => X4 )
                                                                                                                                             => X4 ) ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                            ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                           => ( ~ ( in @ X3 @ X1 )
                                                                                                                                             => ( in @ X3 @ X2 ) ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                         => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                 => ( ( in @ X3 @ X2 )
                                                                                                                                                   => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                    ( ( subset @ X3 @ X1 )
                                                                                                                                                   => ( ( subset @ X3 @ X2 )
                                                                                                                                                     => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                      ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                                     => ( in @ X3 @ X1 ) )
                                                                                                                                                 => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                          ( ( subset @ X1 @ X2 )
                                                                                                                                                         => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                            = X1 ) )
                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                            ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                                              = X2 )
                                                                                                                                                           => ( subset @ X2 @ X1 ) )
                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                              ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                                             => ( in @ X3 @ X2 ) )
                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                ( ! [X3: $i] :
                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                   => ~ ( in @ X3 @ X2 ) )
                                                                                                                                                               => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                  = emptyset ) )
                                                                                                                                                           => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                    ( ( subset @ X2 @ X1 )
                                                                                                                                                                   => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                      = X2 ) )
                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                      ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                        = X1 )
                                                                                                                                                                     => ( subset @ X1 @ X2 ) )
                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                        ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                                                                                                                                        = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                         => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                           => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                            ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                           => ( in @ X3 @ X1 ) )
                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                              ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                             => ~ ( in @ X3 @ X2 ) )
                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                ( ( subset @ X1 @ X2 )
                                                                                                                                                                               => ( ( setminus @ X1 @ X2 )
                                                                                                                                                                                  = emptyset ) )
                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                  ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                 => ( ( in @ X3 @ X1 )
                                                                                                                                                                                   => ( in @ X3 @ X2 ) ) )
                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                    ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                   => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                     => ~ ( in @ X3 @ X1 ) ) )
                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                      ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                     => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                        ( ( in @ X3 @ X2 )
                                                                                                                                                                                       => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                            ( ( ( setminus @ X1 @ X2 )
                                                                                                                                                                                              = emptyset )
                                                                                                                                                                                           => ( subset @ X1 @ X2 ) )
                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                              ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                                                                                                                             => ! [X4: $o] :
                                                                                                                                                                                                  ( ( ( in @ X3 @ X1 )
                                                                                                                                                                                                   => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                     => X4 ) )
                                                                                                                                                                                                 => ( ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                     => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                       => X4 ) )
                                                                                                                                                                                                   => X4 ) ) )
                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                               => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                 => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                  ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                 => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                   => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                   => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                     => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                      ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                     => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                       => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                  ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                 => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                    ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                   => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                     => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                        ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                       => ( ( X3 != X1 )
                                                                                                                                                                                                                         => ( X3 = X2 ) ) )
                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                             => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                               => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                 => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                   => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                     => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                       => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                      ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                     => ~ ! [X4: $i] :
                                                                                                                                                                                                                                            ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                           => ! [X5: $i] :
                                                                                                                                                                                                                                                ( ( in @ X5 @ X2 )
                                                                                                                                                                                                                                               => ( X3
                                                                                                                                                                                                                                                 != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                                                                                                                                 => ( sP5
                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                          ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                                                                                                                                         => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                               => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                                                                                                                                     => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                                                                                                                                       => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                                         => ( ! [X1: $i] :
                                                                                                                                                                                                                                                ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                                                                                                                                = X1 )
                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                  ( ! [X3: $i] :
                                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                                                                                                          ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                         => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                           => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                             => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                                                 => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                         => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                                                   => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                          ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                         => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                           != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                    ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                          ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                         => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                           != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                                                                                                                                   => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                         => ~ ( X2 @ X3 ) ) )
                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                     => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                       => ( ! [X4: $i] :
                                                                                                                                                                                                                                                              ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                             => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                               => ( X4 = X3 ) ) )
                                                                                                                                                                                                                                                         => ~ ! [X4: $i] :
                                                                                                                                                                                                                                                                ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                               => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                 != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                        ( ! [X3: $i] :
                                                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                                                                                                                ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                               => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                                 => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                   => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                                                       => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                               => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                                                         => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                               => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                 != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                          ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                                                                                                                            = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                         => ( X1 = X2 ) )
                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                            ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                           => ( X1 = X3 ) )
                                                                                                                                                                                                                                                       => ( ! [X1: $i] :
                                                                                                                                                                                                                                                              ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                             => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                    ( ( in @ X2
                                                                                                                                                                                                                                                                      @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                        @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                                                                                                                                   => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                        @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                                                                     != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                                         => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                ( ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                      ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                                                     => ( X1
                                                                                                                                                                                                                                                                       != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                                               => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                  ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                  = X1 )
                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                    ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                   => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                      ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                        = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                     => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                        ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                                          = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                       => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                          ( ( X1 = X2 )
                                                                                                                                                                                                                                                                         => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                            = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                            ( ( X1 = X2 )
                                                                                                                                                                                                                                                                           => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                              = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                              ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                             => ( ( X3 = X4 )
                                                                                                                                                                                                                                                                               => ( X2 = X4 ) ) )
                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                                  = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                                                                                                                               => ( X1 = X2 ) )
                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                  ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                    = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                 => ( X2 = X4 ) )
                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                    ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                                                      = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                   => ( X2 = X4 ) )
                                                                                                                                                                                                                                                                               => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                      ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                                                     => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                            ( ( in @ X2
                                                                                                                                                                                                                                                                                              @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                                                    ( X1
                                                                                                                                                                                                                                                                                                    = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                                                                                                                           => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                                                    ( X1
                                                                                                                                                                                                                                                                                                    = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                                                                                                                             != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                        ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                        = X2 )
                                                                                                                                                                                                                                                                                   => ( sP8
                                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                            ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                           => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                              ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                             => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                               => ( in @ X4 @ X2 ) )
                                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                                     => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                        = X3 ) ) )
                                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                                       => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                          = X4 ) ) )
                                                                                                                                                                                                                                                                                               => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                    ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                   => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                                                                                                                                      = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h52,assumption,
    ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) ),
    introduced(assumption,[]) ).

thf(h53,assumption,
    ~ ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
     => ( ! [X1: $i,X2: $i,X3: $i] :
            ( ( in @ X3 @ X2 )
           => ( in @ X3 @ ( setadjoin @ X1 @ X2 ) ) )
       => ( ! [X1: $i,X2: $i,X3: $i] :
              ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
             => ! [X4: $o] :
                  ( ( ( X3 = X1 )
                   => X4 )
                 => ( ( ( in @ X3 @ X2 )
                     => X4 )
                   => X4 ) ) )
         => ( ! [X1: $i,X2: $i,X3: $i] :
                ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
               => ( ( X3 != X1 )
                 => ( in @ X3 @ X2 ) ) )
           => ( ! [X1: $i] :
                  ( ( dsetconstr @ X1
                    @ ^ [X2: $i] : ~ $false )
                  = X1 )
             => ( ! [X1: $i,X2: $i] :
                    ( ! [X3: $i] :
                        ( ( in @ X3 @ X2 )
                       => ( in @ X3 @ X1 ) )
                   => ( in @ X2 @ ( powerset @ X1 ) ) )
               => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                 => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                   => ( ! [X1: $i,X2: $i,X3: $i] :
                          ( ( in @ X2 @ ( powerset @ X1 ) )
                         => ( ( in @ X3 @ X2 )
                           => ( in @ X3 @ X1 ) ) )
                     => ( ! [X1: $i,X2: $i,X3: $i] :
                            ( ( in @ X2 @ X3 )
                           => ( ( in @ X3 @ X1 )
                             => ( in @ X2 @ ( setunion @ X1 ) ) ) )
                       => ( ! [X1: $i,X2: $i] :
                              ( ( in @ X2 @ ( setunion @ X1 ) )
                             => ! [X3: $o] :
                                  ( ! [X4: $i] :
                                      ( ( in @ X2 @ X4 )
                                     => ( ( in @ X4 @ X1 )
                                       => X3 ) )
                                 => X3 ) )
                         => ( ! [X1: $i,X2: $i] :
                                ( ( in @ X2 @ X1 )
                               => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
                           => ( ! [X1: $i > $o] :
                                  ( ~ ! [X2: $i] :
                                        ( ( X1 @ X2 )
                                       => ~ ! [X3: $i] :
                                              ( ( X1 @ X3 )
                                             => ( X2 = X3 ) ) )
                                 => ~ ! [X2: $i] :
                                        ~ ! [X3: $i] :
                                            ( ( X1 @ X3 )
                                            = ( X3 = X2 ) ) )
                             => ( ! [X1: $i] :
                                    ( ( X1 != emptyset )
                                   => ~ ! [X2: $i] :
                                          ~ ( in @ X2 @ X1 ) )
                               => ( ! [X1: $i,X2: $i] :
                                      ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                     => ( X1 = X2 ) )
                                 => ( ! [X1: $i,X2: $i] :
                                        ( ( X1 != X2 )
                                       => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                   => ( ! [X1: $i,X2: $i] :
                                          ( ( X1 = X2 )
                                         => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                     => ( ! [X1: $i,X2: $i] :
                                            ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                           => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                              ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                             => ( ( X3 != X1 )
                                               => ( X3 = X2 ) ) )
                                         => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                           => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                             => ( ! [X1: $i,X2: $i > $o] :
                                                    ( ~ ! [X3: $i] :
                                                          ( ( in @ X3 @ X1 )
                                                         => ~ ( X2 @ X3 ) )
                                                   => ( ( dsetconstr @ X1 @ X2 )
                                                     != emptyset ) )
                                               => ( ! [X1: $i > $o,X2: $i] :
                                                      ( ( in @ X2 @ emptyset )
                                                     => ( X1 @ X2 ) )
                                                 => ( ! [X1: $o] :
                                                        ( X1
                                                       => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                                   => ( ! [X1: $o] :
                                                          ( X1
                                                         => ( set2prop @ ( prop2set @ X1 ) ) )
                                                     => ( ! [X1: $i > $o] :
                                                            ( ~ ! [X2: $i] :
                                                                  ~ ( X1 @ X2 )
                                                           => ( ! [X2: $i,X3: $i] :
                                                                  ( ( X1 @ X2 )
                                                                 => ( ( X1 @ X3 )
                                                                   => ( X2 = X3 ) ) )
                                                             => ~ ! [X2: $i] :
                                                                    ( ( X1 @ X2 )
                                                                   => ~ ! [X3: $i] :
                                                                          ( ( X1 @ X3 )
                                                                         => ( X2 = X3 ) ) ) ) )
                                                       => ( ! [X1: $i > $o] :
                                                              ( ~ ! [X2: $i] :
                                                                    ~ ! [X3: $i] :
                                                                        ( ( X1 @ X3 )
                                                                        = ( X3 = X2 ) )
                                                             => ~ ! [X2: $i] :
                                                                    ( ( X1 @ X2 )
                                                                   => ~ ! [X3: $i] :
                                                                          ( ( X1 @ X3 )
                                                                         => ( X2 = X3 ) ) ) )
                                                         => ( ! [X1: $i,X2: $i] :
                                                                ( ( X1 = X2 )
                                                               => ! [X3: $i,X4: $i] :
                                                                    ( ( X3 = X4 )
                                                                   => ( ( in @ X3 @ X1 )
                                                                     => ( in @ X4 @ X2 ) ) ) )
                                                           => ( ! [X1: $i,X2: $i] :
                                                                  ( ( X1 = X2 )
                                                                 => ! [X3: $i,X4: $i] :
                                                                      ( ( X3 = X4 )
                                                                     => ( ( in @ X3 @ X1 )
                                                                        = ( in @ X4 @ X2 ) ) ) )
                                                             => ( ! [X1: $i > $o] :
                                                                    ( ~ ! [X2: $i] :
                                                                          ( ( X1 @ X2 )
                                                                         => ~ ! [X3: $i] :
                                                                                ( ( X1 @ X3 )
                                                                               => ( X2 = X3 ) ) )
                                                                   => ! [X2: $i,X3: $i] :
                                                                        ( ( X1 @ X2 )
                                                                       => ( ( X1 @ X3 )
                                                                         => ( X2 = X3 ) ) ) )
                                                               => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                      ( ! [X3: $i,X4: $i] :
                                                                          ( ( X3 = X4 )
                                                                         => ( ( X1 @ X3 )
                                                                            = ( X2 @ X4 ) ) )
                                                                     => ( ( ~ ! [X3: $i] :
                                                                                ( ( X1 @ X3 )
                                                                               => ~ ! [X4: $i] :
                                                                                      ( ( X1 @ X4 )
                                                                                     => ( X3 = X4 ) ) ) )
                                                                        = ( ~ ! [X3: $i] :
                                                                                ( ( X2 @ X3 )
                                                                               => ~ ! [X4: $i] :
                                                                                      ( ( X2 @ X4 )
                                                                                     => ( X3 = X4 ) ) ) ) ) )
                                                                 => ( ! [X1: $i,X2: $i] :
                                                                        ( ( X1 = X2 )
                                                                       => ! [X3: $i,X4: $i] :
                                                                            ( ( X3 = X4 )
                                                                           => ( ( setadjoin @ X1 @ X3 )
                                                                              = ( setadjoin @ X2 @ X4 ) ) ) )
                                                                   => ( ! [X1: $i,X2: $i] :
                                                                          ( ( X1 = X2 )
                                                                         => ( ( powerset @ X1 )
                                                                            = ( powerset @ X2 ) ) )
                                                                     => ( ! [X1: $i,X2: $i] :
                                                                            ( ( X1 = X2 )
                                                                           => ( ( setunion @ X1 )
                                                                              = ( setunion @ X2 ) ) )
                                                                       => ( ! [X1: $i > $o] :
                                                                              ( ~ ! [X2: $i] :
                                                                                    ( ( X1 @ X2 )
                                                                                   => ~ ! [X3: $i] :
                                                                                          ( ( X1 @ X3 )
                                                                                         => ( X2 = X3 ) ) )
                                                                             => ! [X2: $i,X3: $i] :
                                                                                  ( ( X1 @ X2 )
                                                                                 => ( ( X1 @ X3 )
                                                                                   => ( X2 = X3 ) ) ) )
                                                                         => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                ( ! [X3: $i,X4: $i] :
                                                                                    ( ( X3 = X4 )
                                                                                   => ( ( X1 @ X3 )
                                                                                      = ( X2 @ X4 ) ) )
                                                                               => ( ~ ! [X3: $i] :
                                                                                        ( ( X1 @ X3 )
                                                                                       => ~ ! [X4: $i] :
                                                                                              ( ( X1 @ X4 )
                                                                                             => ( X3 = X4 ) ) )
                                                                                 => ( ~ ! [X3: $i] :
                                                                                          ( ( X2 @ X3 )
                                                                                         => ~ ! [X4: $i] :
                                                                                                ( ( X2 @ X4 )
                                                                                               => ( X3 = X4 ) ) )
                                                                                   => ( ( descr @ X1 )
                                                                                      = ( descr @ X2 ) ) ) ) )
                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                  ( ( X1 = X2 )
                                                                                 => ! [X3: $i > $o,X4: $i > $o] :
                                                                                      ( ! [X5: $i] :
                                                                                          ( ( in @ X5 @ X1 )
                                                                                         => ! [X6: $i] :
                                                                                              ( ( in @ X6 @ X2 )
                                                                                             => ( ( X5 = X6 )
                                                                                               => ( ( X3 @ X5 )
                                                                                                  = ( X4 @ X6 ) ) ) ) )
                                                                                     => ( ( dsetconstr @ X1 @ X3 )
                                                                                        = ( dsetconstr @ X2 @ X4 ) ) ) )
                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                    ( ! [X3: $i] :
                                                                                        ( ( in @ X3 @ X1 )
                                                                                       => ( in @ X3 @ X2 ) )
                                                                                   => ( subset @ X1 @ X2 ) )
                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                      ( ( X1 = X2 )
                                                                                     => ( subset @ X2 @ X1 ) )
                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                        ( ( X1 = X2 )
                                                                                       => ( subset @ X1 @ X2 ) )
                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                          ( ! [X3: $i] :
                                                                                              ( ( in @ X3 @ X1 )
                                                                                             => ( in @ X3 @ X2 ) )
                                                                                         => ( subset @ X1 @ X2 ) )
                                                                                     => ( ! [X1: $i] : ( subset @ emptyset @ X1 )
                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                              ( ( subset @ X1 @ X2 )
                                                                                             => ( ( in @ X3 @ X1 )
                                                                                               => ( in @ X3 @ X2 ) ) )
                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                ( ( subset @ X1 @ X2 )
                                                                                               => ( ~ ( in @ X3 @ X2 )
                                                                                                 => ~ ( in @ X3 @ X1 ) ) )
                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                 => ( ~ ( in @ X3 @ X2 )
                                                                                                   => ~ ( subset @ X1 @ X2 ) ) )
                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                    ( ~ ( subset @ X1 @ X2 )
                                                                                                   => ( X1 != X2 ) )
                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                     => ( ~ ( in @ X3 @ X2 )
                                                                                                       => ( X1 != X2 ) ) )
                                                                                                 => ( ! [X1: $i] : ( subset @ X1 @ X1 )
                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                          ( ( subset @ X1 @ X2 )
                                                                                                         => ( ( subset @ X2 @ X3 )
                                                                                                           => ( subset @ X1 @ X3 ) ) )
                                                                                                     => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) )
                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                              ( ( subset @ X1 @ X3 )
                                                                                                             => ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                ( ( subset @ X1 @ X2 )
                                                                                                               => ( in @ X1 @ ( powerset @ X2 ) ) )
                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                  ( ( subset @ X1 @ X2 )
                                                                                                                 => ( ( subset @ X2 @ X1 )
                                                                                                                   => ( X1 = X2 ) ) )
                                                                                                             => ( ! [X1: $i] :
                                                                                                                    ( ( subset @ X1 @ emptyset )
                                                                                                                   => ( X1 = emptyset ) )
                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                      ( ( subset @ X2 @ X1 )
                                                                                                                     => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                        ( ( in @ X2 @ ( powerset @ X1 ) )
                                                                                                                       => ( subset @ X2 @ X1 ) )
                                                                                                                   => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                            ( ( subset @ X1 @ X2 )
                                                                                                                           => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
                                                                                                                       => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                                                                                                                         => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                 => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                                             => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                      ( ( in @ X3 @ X2 )
                                                                                                                                     => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                                                                                                                        ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                       => ( ( ( in @ X3 @ X1 )
                                                                                                                                           => X4 )
                                                                                                                                         => ( ( ( in @ X3 @ X2 )
                                                                                                                                             => X4 )
                                                                                                                                           => X4 ) ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                          ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                         => ( ~ ( in @ X3 @ X1 )
                                                                                                                                           => ( in @ X3 @ X2 ) ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                               => ( ( in @ X3 @ X2 )
                                                                                                                                                 => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                  ( ( subset @ X3 @ X1 )
                                                                                                                                                 => ( ( subset @ X3 @ X2 )
                                                                                                                                                   => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                    ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                                   => ( in @ X3 @ X1 ) )
                                                                                                                                               => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                        ( ( subset @ X1 @ X2 )
                                                                                                                                                       => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                          = X1 ) )
                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                          ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                                            = X2 )
                                                                                                                                                         => ( subset @ X2 @ X1 ) )
                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                            ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                                           => ( in @ X3 @ X2 ) )
                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                              ( ! [X3: $i] :
                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                 => ~ ( in @ X3 @ X2 ) )
                                                                                                                                                             => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                = emptyset ) )
                                                                                                                                                         => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                  ( ( subset @ X2 @ X1 )
                                                                                                                                                                 => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                    = X2 ) )
                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                    ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                      = X1 )
                                                                                                                                                                   => ( subset @ X1 @ X2 ) )
                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                      ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                                                                                                                                      = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                       => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                         => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                          ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                         => ( in @ X3 @ X1 ) )
                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                            ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                           => ~ ( in @ X3 @ X2 ) )
                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                              ( ( subset @ X1 @ X2 )
                                                                                                                                                                             => ( ( setminus @ X1 @ X2 )
                                                                                                                                                                                = emptyset ) )
                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                               => ( ( in @ X3 @ X1 )
                                                                                                                                                                                 => ( in @ X3 @ X2 ) ) )
                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                  ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                 => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                   => ~ ( in @ X3 @ X1 ) ) )
                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                    ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                   => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                      ( ( in @ X3 @ X2 )
                                                                                                                                                                                     => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                          ( ( ( setminus @ X1 @ X2 )
                                                                                                                                                                                            = emptyset )
                                                                                                                                                                                         => ( subset @ X1 @ X2 ) )
                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                            ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                                                                                                                           => ! [X4: $o] :
                                                                                                                                                                                                ( ( ( in @ X3 @ X1 )
                                                                                                                                                                                                 => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                   => X4 ) )
                                                                                                                                                                                               => ( ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                   => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                     => X4 ) )
                                                                                                                                                                                                 => X4 ) ) )
                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                             => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                               => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                               => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                 => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                 => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                   => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                    ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                   => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                     => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                ( ( in @ X2 @ X1 )
                                                                                                                                                                                                               => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                  ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                 => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                   => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                      ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                     => ( ( X3 != X1 )
                                                                                                                                                                                                                       => ( X3 = X2 ) ) )
                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                           => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                             => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                               => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                 => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                   => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                     => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                    ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                   => ~ ! [X4: $i] :
                                                                                                                                                                                                                                          ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                         => ! [X5: $i] :
                                                                                                                                                                                                                                              ( ( in @ X5 @ X2 )
                                                                                                                                                                                                                                             => ( X3
                                                                                                                                                                                                                                               != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                                                                                                                               => ( sP5
                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                        ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                                                                                                                                       => ~ ! [X3: $i] :
                                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                             => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                                                                                                                                   => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                                                                                                                                     => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                                       => ( ! [X1: $i] :
                                                                                                                                                                                                                                              ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                                                                                                                              = X1 )
                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                ( ! [X3: $i] :
                                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                                                                                                        ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                       => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                         => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                           => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                                               => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                       => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                                                 => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                        ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                       => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                         != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                  ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                        ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                       => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                         != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                                                                                                                                 => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                       => ~ ( X2 @ X3 ) ) )
                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                   => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                     => ( ! [X4: $i] :
                                                                                                                                                                                                                                                            ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                           => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                             => ( X4 = X3 ) ) )
                                                                                                                                                                                                                                                       => ~ ! [X4: $i] :
                                                                                                                                                                                                                                                              ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                             => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                               != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                      ( ! [X3: $i] :
                                                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                                                                                                              ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                             => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                               => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                 => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                                                     => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                             => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                                                       => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                              ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                             => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                               != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                        ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                                                                                                                          = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                       => ( X1 = X2 ) )
                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                          ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                         => ( X1 = X3 ) )
                                                                                                                                                                                                                                                     => ( ! [X1: $i] :
                                                                                                                                                                                                                                                            ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                           => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                  ( ( in @ X2
                                                                                                                                                                                                                                                                    @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                      @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                                                                                                                                 => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                      @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                                                                   != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                                       => ( ! [X1: $i] :
                                                                                                                                                                                                                                                              ( ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                    ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                                                   => ( X1
                                                                                                                                                                                                                                                                     != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                                             => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                = X1 )
                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                  ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                 => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                    ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                      = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                   => ( X1 = X3 ) )
                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                      ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                                        = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                     => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                        ( ( X1 = X2 )
                                                                                                                                                                                                                                                                       => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                          = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                          ( ( X1 = X2 )
                                                                                                                                                                                                                                                                         => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                            = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                            ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                              = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                           => ( ( X3 = X4 )
                                                                                                                                                                                                                                                                             => ( X2 = X4 ) ) )
                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                              ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                                = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                                                                                                                             => ( X1 = X2 ) )
                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                  = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                               => ( X2 = X4 ) )
                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                  ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                                                    = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                 => ( X2 = X4 ) )
                                                                                                                                                                                                                                                                             => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                    ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                                                   => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                          ( ( in @ X2
                                                                                                                                                                                                                                                                                            @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                              @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                                                  ( X1
                                                                                                                                                                                                                                                                                                  = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                                                                                                                         => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                              @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                                                  ( X1
                                                                                                                                                                                                                                                                                                  = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                                                                                                                           != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                      ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                      = X2 )
                                                                                                                                                                                                                                                                                 => ( sP8
                                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                         => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                            ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                           => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                              ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                             => ( in @ X4 @ X2 ) )
                                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                                   => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                      = X3 ) ) )
                                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                                     => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                        = X4 ) ) )
                                                                                                                                                                                                                                                                                             => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                  ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                 => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                                                                                                                                    = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h54,assumption,
    in @ emptyset @ ( setadjoin @ emptyset @ emptyset ),
    introduced(assumption,[]) ).

thf(h55,assumption,
    ~ ( ! [X1: $i,X2: $i,X3: $i] :
          ( ( in @ X3 @ X2 )
         => ( in @ X3 @ ( setadjoin @ X1 @ X2 ) ) )
     => ( ! [X1: $i,X2: $i,X3: $i] :
            ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
           => ! [X4: $o] :
                ( ( ( X3 = X1 )
                 => X4 )
               => ( ( ( in @ X3 @ X2 )
                   => X4 )
                 => X4 ) ) )
       => ( ! [X1: $i,X2: $i,X3: $i] :
              ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
             => ( ( X3 != X1 )
               => ( in @ X3 @ X2 ) ) )
         => ( ! [X1: $i] :
                ( ( dsetconstr @ X1
                  @ ^ [X2: $i] : ~ $false )
                = X1 )
           => ( ! [X1: $i,X2: $i] :
                  ( ! [X3: $i] :
                      ( ( in @ X3 @ X2 )
                     => ( in @ X3 @ X1 ) )
                 => ( in @ X2 @ ( powerset @ X1 ) ) )
             => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
               => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                 => ( ! [X1: $i,X2: $i,X3: $i] :
                        ( ( in @ X2 @ ( powerset @ X1 ) )
                       => ( ( in @ X3 @ X2 )
                         => ( in @ X3 @ X1 ) ) )
                   => ( ! [X1: $i,X2: $i,X3: $i] :
                          ( ( in @ X2 @ X3 )
                         => ( ( in @ X3 @ X1 )
                           => ( in @ X2 @ ( setunion @ X1 ) ) ) )
                     => ( ! [X1: $i,X2: $i] :
                            ( ( in @ X2 @ ( setunion @ X1 ) )
                           => ! [X3: $o] :
                                ( ! [X4: $i] :
                                    ( ( in @ X2 @ X4 )
                                   => ( ( in @ X4 @ X1 )
                                     => X3 ) )
                               => X3 ) )
                       => ( ! [X1: $i,X2: $i] :
                              ( ( in @ X2 @ X1 )
                             => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
                         => ( ! [X1: $i > $o] :
                                ( ~ ! [X2: $i] :
                                      ( ( X1 @ X2 )
                                     => ~ ! [X3: $i] :
                                            ( ( X1 @ X3 )
                                           => ( X2 = X3 ) ) )
                               => ~ ! [X2: $i] :
                                      ~ ! [X3: $i] :
                                          ( ( X1 @ X3 )
                                          = ( X3 = X2 ) ) )
                           => ( ! [X1: $i] :
                                  ( ( X1 != emptyset )
                                 => ~ ! [X2: $i] :
                                        ~ ( in @ X2 @ X1 ) )
                             => ( ! [X1: $i,X2: $i] :
                                    ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                   => ( X1 = X2 ) )
                               => ( ! [X1: $i,X2: $i] :
                                      ( ( X1 != X2 )
                                     => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                 => ( ! [X1: $i,X2: $i] :
                                        ( ( X1 = X2 )
                                       => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                   => ( ! [X1: $i,X2: $i] :
                                          ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                         => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                            ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                           => ( ( X3 != X1 )
                                             => ( X3 = X2 ) ) )
                                       => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                         => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                           => ( ! [X1: $i,X2: $i > $o] :
                                                  ( ~ ! [X3: $i] :
                                                        ( ( in @ X3 @ X1 )
                                                       => ~ ( X2 @ X3 ) )
                                                 => ( ( dsetconstr @ X1 @ X2 )
                                                   != emptyset ) )
                                             => ( ! [X1: $i > $o,X2: $i] :
                                                    ( ( in @ X2 @ emptyset )
                                                   => ( X1 @ X2 ) )
                                               => ( ! [X1: $o] :
                                                      ( X1
                                                     => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                                 => ( ! [X1: $o] :
                                                        ( X1
                                                       => ( set2prop @ ( prop2set @ X1 ) ) )
                                                   => ( ! [X1: $i > $o] :
                                                          ( ~ ! [X2: $i] :
                                                                ~ ( X1 @ X2 )
                                                         => ( ! [X2: $i,X3: $i] :
                                                                ( ( X1 @ X2 )
                                                               => ( ( X1 @ X3 )
                                                                 => ( X2 = X3 ) ) )
                                                           => ~ ! [X2: $i] :
                                                                  ( ( X1 @ X2 )
                                                                 => ~ ! [X3: $i] :
                                                                        ( ( X1 @ X3 )
                                                                       => ( X2 = X3 ) ) ) ) )
                                                     => ( ! [X1: $i > $o] :
                                                            ( ~ ! [X2: $i] :
                                                                  ~ ! [X3: $i] :
                                                                      ( ( X1 @ X3 )
                                                                      = ( X3 = X2 ) )
                                                           => ~ ! [X2: $i] :
                                                                  ( ( X1 @ X2 )
                                                                 => ~ ! [X3: $i] :
                                                                        ( ( X1 @ X3 )
                                                                       => ( X2 = X3 ) ) ) )
                                                       => ( ! [X1: $i,X2: $i] :
                                                              ( ( X1 = X2 )
                                                             => ! [X3: $i,X4: $i] :
                                                                  ( ( X3 = X4 )
                                                                 => ( ( in @ X3 @ X1 )
                                                                   => ( in @ X4 @ X2 ) ) ) )
                                                         => ( ! [X1: $i,X2: $i] :
                                                                ( ( X1 = X2 )
                                                               => ! [X3: $i,X4: $i] :
                                                                    ( ( X3 = X4 )
                                                                   => ( ( in @ X3 @ X1 )
                                                                      = ( in @ X4 @ X2 ) ) ) )
                                                           => ( ! [X1: $i > $o] :
                                                                  ( ~ ! [X2: $i] :
                                                                        ( ( X1 @ X2 )
                                                                       => ~ ! [X3: $i] :
                                                                              ( ( X1 @ X3 )
                                                                             => ( X2 = X3 ) ) )
                                                                 => ! [X2: $i,X3: $i] :
                                                                      ( ( X1 @ X2 )
                                                                     => ( ( X1 @ X3 )
                                                                       => ( X2 = X3 ) ) ) )
                                                             => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                    ( ! [X3: $i,X4: $i] :
                                                                        ( ( X3 = X4 )
                                                                       => ( ( X1 @ X3 )
                                                                          = ( X2 @ X4 ) ) )
                                                                   => ( ( ~ ! [X3: $i] :
                                                                              ( ( X1 @ X3 )
                                                                             => ~ ! [X4: $i] :
                                                                                    ( ( X1 @ X4 )
                                                                                   => ( X3 = X4 ) ) ) )
                                                                      = ( ~ ! [X3: $i] :
                                                                              ( ( X2 @ X3 )
                                                                             => ~ ! [X4: $i] :
                                                                                    ( ( X2 @ X4 )
                                                                                   => ( X3 = X4 ) ) ) ) ) )
                                                               => ( ! [X1: $i,X2: $i] :
                                                                      ( ( X1 = X2 )
                                                                     => ! [X3: $i,X4: $i] :
                                                                          ( ( X3 = X4 )
                                                                         => ( ( setadjoin @ X1 @ X3 )
                                                                            = ( setadjoin @ X2 @ X4 ) ) ) )
                                                                 => ( ! [X1: $i,X2: $i] :
                                                                        ( ( X1 = X2 )
                                                                       => ( ( powerset @ X1 )
                                                                          = ( powerset @ X2 ) ) )
                                                                   => ( ! [X1: $i,X2: $i] :
                                                                          ( ( X1 = X2 )
                                                                         => ( ( setunion @ X1 )
                                                                            = ( setunion @ X2 ) ) )
                                                                     => ( ! [X1: $i > $o] :
                                                                            ( ~ ! [X2: $i] :
                                                                                  ( ( X1 @ X2 )
                                                                                 => ~ ! [X3: $i] :
                                                                                        ( ( X1 @ X3 )
                                                                                       => ( X2 = X3 ) ) )
                                                                           => ! [X2: $i,X3: $i] :
                                                                                ( ( X1 @ X2 )
                                                                               => ( ( X1 @ X3 )
                                                                                 => ( X2 = X3 ) ) ) )
                                                                       => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                              ( ! [X3: $i,X4: $i] :
                                                                                  ( ( X3 = X4 )
                                                                                 => ( ( X1 @ X3 )
                                                                                    = ( X2 @ X4 ) ) )
                                                                             => ( ~ ! [X3: $i] :
                                                                                      ( ( X1 @ X3 )
                                                                                     => ~ ! [X4: $i] :
                                                                                            ( ( X1 @ X4 )
                                                                                           => ( X3 = X4 ) ) )
                                                                               => ( ~ ! [X3: $i] :
                                                                                        ( ( X2 @ X3 )
                                                                                       => ~ ! [X4: $i] :
                                                                                              ( ( X2 @ X4 )
                                                                                             => ( X3 = X4 ) ) )
                                                                                 => ( ( descr @ X1 )
                                                                                    = ( descr @ X2 ) ) ) ) )
                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                ( ( X1 = X2 )
                                                                               => ! [X3: $i > $o,X4: $i > $o] :
                                                                                    ( ! [X5: $i] :
                                                                                        ( ( in @ X5 @ X1 )
                                                                                       => ! [X6: $i] :
                                                                                            ( ( in @ X6 @ X2 )
                                                                                           => ( ( X5 = X6 )
                                                                                             => ( ( X3 @ X5 )
                                                                                                = ( X4 @ X6 ) ) ) ) )
                                                                                   => ( ( dsetconstr @ X1 @ X3 )
                                                                                      = ( dsetconstr @ X2 @ X4 ) ) ) )
                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                  ( ! [X3: $i] :
                                                                                      ( ( in @ X3 @ X1 )
                                                                                     => ( in @ X3 @ X2 ) )
                                                                                 => ( subset @ X1 @ X2 ) )
                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                    ( ( X1 = X2 )
                                                                                   => ( subset @ X2 @ X1 ) )
                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                      ( ( X1 = X2 )
                                                                                     => ( subset @ X1 @ X2 ) )
                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                        ( ! [X3: $i] :
                                                                                            ( ( in @ X3 @ X1 )
                                                                                           => ( in @ X3 @ X2 ) )
                                                                                       => ( subset @ X1 @ X2 ) )
                                                                                   => ( ! [X1: $i] : ( subset @ emptyset @ X1 )
                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                            ( ( subset @ X1 @ X2 )
                                                                                           => ( ( in @ X3 @ X1 )
                                                                                             => ( in @ X3 @ X2 ) ) )
                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                              ( ( subset @ X1 @ X2 )
                                                                                             => ( ~ ( in @ X3 @ X2 )
                                                                                               => ~ ( in @ X3 @ X1 ) ) )
                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                ( ( in @ X3 @ X1 )
                                                                                               => ( ~ ( in @ X3 @ X2 )
                                                                                                 => ~ ( subset @ X1 @ X2 ) ) )
                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                  ( ~ ( subset @ X1 @ X2 )
                                                                                                 => ( X1 != X2 ) )
                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                   => ( ~ ( in @ X3 @ X2 )
                                                                                                     => ( X1 != X2 ) ) )
                                                                                               => ( ! [X1: $i] : ( subset @ X1 @ X1 )
                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                        ( ( subset @ X1 @ X2 )
                                                                                                       => ( ( subset @ X2 @ X3 )
                                                                                                         => ( subset @ X1 @ X3 ) ) )
                                                                                                   => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) )
                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                            ( ( subset @ X1 @ X3 )
                                                                                                           => ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                              ( ( subset @ X1 @ X2 )
                                                                                                             => ( in @ X1 @ ( powerset @ X2 ) ) )
                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                ( ( subset @ X1 @ X2 )
                                                                                                               => ( ( subset @ X2 @ X1 )
                                                                                                                 => ( X1 = X2 ) ) )
                                                                                                           => ( ! [X1: $i] :
                                                                                                                  ( ( subset @ X1 @ emptyset )
                                                                                                                 => ( X1 = emptyset ) )
                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                    ( ( subset @ X2 @ X1 )
                                                                                                                   => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                      ( ( in @ X2 @ ( powerset @ X1 ) )
                                                                                                                     => ( subset @ X2 @ X1 ) )
                                                                                                                 => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                          ( ( subset @ X1 @ X2 )
                                                                                                                         => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
                                                                                                                     => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                                                                                                                       => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                               => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                                           => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                    ( ( in @ X3 @ X2 )
                                                                                                                                   => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                                                                                                                      ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                     => ( ( ( in @ X3 @ X1 )
                                                                                                                                         => X4 )
                                                                                                                                       => ( ( ( in @ X3 @ X2 )
                                                                                                                                           => X4 )
                                                                                                                                         => X4 ) ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                        ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                       => ( ~ ( in @ X3 @ X1 )
                                                                                                                                         => ( in @ X3 @ X2 ) ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                             => ( ( in @ X3 @ X2 )
                                                                                                                                               => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                ( ( subset @ X3 @ X1 )
                                                                                                                                               => ( ( subset @ X3 @ X2 )
                                                                                                                                                 => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                  ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                                 => ( in @ X3 @ X1 ) )
                                                                                                                                             => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                      ( ( subset @ X1 @ X2 )
                                                                                                                                                     => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                        = X1 ) )
                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                        ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                                          = X2 )
                                                                                                                                                       => ( subset @ X2 @ X1 ) )
                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                          ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                                         => ( in @ X3 @ X2 ) )
                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                            ( ! [X3: $i] :
                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                               => ~ ( in @ X3 @ X2 ) )
                                                                                                                                                           => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                              = emptyset ) )
                                                                                                                                                       => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                ( ( subset @ X2 @ X1 )
                                                                                                                                                               => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                  = X2 ) )
                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                  ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                    = X1 )
                                                                                                                                                                 => ( subset @ X1 @ X2 ) )
                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                    ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                                                                                                                                    = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                     => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                       => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                        ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                       => ( in @ X3 @ X1 ) )
                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                          ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                         => ~ ( in @ X3 @ X2 ) )
                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                            ( ( subset @ X1 @ X2 )
                                                                                                                                                                           => ( ( setminus @ X1 @ X2 )
                                                                                                                                                                              = emptyset ) )
                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                              ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                             => ( ( in @ X3 @ X1 )
                                                                                                                                                                               => ( in @ X3 @ X2 ) ) )
                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                               => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                 => ~ ( in @ X3 @ X1 ) ) )
                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                  ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                 => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                    ( ( in @ X3 @ X2 )
                                                                                                                                                                                   => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                                               => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                        ( ( ( setminus @ X1 @ X2 )
                                                                                                                                                                                          = emptyset )
                                                                                                                                                                                       => ( subset @ X1 @ X2 ) )
                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                          ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                                                                                                                         => ! [X4: $o] :
                                                                                                                                                                                              ( ( ( in @ X3 @ X1 )
                                                                                                                                                                                               => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                 => X4 ) )
                                                                                                                                                                                             => ( ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                 => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                   => X4 ) )
                                                                                                                                                                                               => X4 ) ) )
                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                           => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                             => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                              ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                             => ( ( in @ X3 @ X2 )
                                                                                                                                                                                               => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                               => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                 => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                  ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                 => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                   => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                              ( ( in @ X2 @ X1 )
                                                                                                                                                                                                             => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                ( ( in @ X2 @ X1 )
                                                                                                                                                                                                               => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                 => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                    ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                   => ( ( X3 != X1 )
                                                                                                                                                                                                                     => ( X3 = X2 ) ) )
                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                         => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                           => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                             => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                               => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                 => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                   => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                  ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                 => ~ ! [X4: $i] :
                                                                                                                                                                                                                                        ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                       => ! [X5: $i] :
                                                                                                                                                                                                                                            ( ( in @ X5 @ X2 )
                                                                                                                                                                                                                                           => ( X3
                                                                                                                                                                                                                                             != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                                                                                                                             => ( sP5
                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                      ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                                                                                                                                     => ~ ! [X3: $i] :
                                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                           => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                                                                                                                                 => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                                                                                                                                   => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                                     => ( ! [X1: $i] :
                                                                                                                                                                                                                                            ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                                                                                                                            = X1 )
                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                              ( ! [X3: $i] :
                                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                                                                                                      ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                     => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                       => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                         => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                                             => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                     => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                                               => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                      ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                     => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                       != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                      ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                     => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                       != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                                                                                                                               => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                     => ~ ( X2 @ X3 ) ) )
                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                 => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                   => ( ! [X4: $i] :
                                                                                                                                                                                                                                                          ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                         => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                           => ( X4 = X3 ) ) )
                                                                                                                                                                                                                                                     => ~ ! [X4: $i] :
                                                                                                                                                                                                                                                            ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                           => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                             != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                    ( ! [X3: $i] :
                                                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                                                                                                            ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                           => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                             => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                               => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                                                   => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                           => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                                                     => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                            ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                           => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                             != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                      ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                                                                                                                        = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                     => ( X1 = X2 ) )
                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                        ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                       => ( X1 = X3 ) )
                                                                                                                                                                                                                                                   => ( ! [X1: $i] :
                                                                                                                                                                                                                                                          ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                         => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                ( ( in @ X2
                                                                                                                                                                                                                                                                  @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                    @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                                                                                                                               => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                    @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                                                                 != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                                     => ( ! [X1: $i] :
                                                                                                                                                                                                                                                            ( ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                  ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                                                 => ( X1
                                                                                                                                                                                                                                                                   != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                                           => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                              ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                              = X1 )
                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                               => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                  ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                    = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                 => ( X1 = X3 ) )
                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                    ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                                      = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                   => ( X1 = X3 ) )
                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                      ( ( X1 = X2 )
                                                                                                                                                                                                                                                                     => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                        = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                        ( ( X1 = X2 )
                                                                                                                                                                                                                                                                       => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                          = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                          ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                            = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                         => ( ( X3 = X4 )
                                                                                                                                                                                                                                                                           => ( X2 = X4 ) ) )
                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                            ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                              = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                                                                                                                           => ( X1 = X2 ) )
                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                              ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                             => ( X2 = X4 ) )
                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                                                  = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                               => ( X2 = X4 ) )
                                                                                                                                                                                                                                                                           => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                  ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                                                 => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                        ( ( in @ X2
                                                                                                                                                                                                                                                                                          @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                            @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                                                ( X1
                                                                                                                                                                                                                                                                                                = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                                                                                                                       => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                            @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                                                ( X1
                                                                                                                                                                                                                                                                                                = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                                                                                                                         != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                    ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                    = X2 )
                                                                                                                                                                                                                                                                               => ( sP8
                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                       => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                          ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                         => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                            ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                           => ( in @ X4 @ X2 ) )
                                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                                 => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                    = X3 ) ) )
                                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                                   => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                      = X4 ) ) )
                                                                                                                                                                                                                                                                                           => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                               => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                                                                                                                                  = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h56,assumption,
    ! [X1: $i,X2: $i,X3: $i] :
      ( ( in @ X3 @ X2 )
     => ( in @ X3 @ ( setadjoin @ X1 @ X2 ) ) ),
    introduced(assumption,[]) ).

thf(h57,assumption,
    ~ ( ! [X1: $i,X2: $i,X3: $i] :
          ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
         => ! [X4: $o] :
              ( ( ( X3 = X1 )
               => X4 )
             => ( ( ( in @ X3 @ X2 )
                 => X4 )
               => X4 ) ) )
     => ( ! [X1: $i,X2: $i,X3: $i] :
            ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
           => ( ( X3 != X1 )
             => ( in @ X3 @ X2 ) ) )
       => ( ! [X1: $i] :
              ( ( dsetconstr @ X1
                @ ^ [X2: $i] : ~ $false )
              = X1 )
         => ( ! [X1: $i,X2: $i] :
                ( ! [X3: $i] :
                    ( ( in @ X3 @ X2 )
                   => ( in @ X3 @ X1 ) )
               => ( in @ X2 @ ( powerset @ X1 ) ) )
           => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
             => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
               => ( ! [X1: $i,X2: $i,X3: $i] :
                      ( ( in @ X2 @ ( powerset @ X1 ) )
                     => ( ( in @ X3 @ X2 )
                       => ( in @ X3 @ X1 ) ) )
                 => ( ! [X1: $i,X2: $i,X3: $i] :
                        ( ( in @ X2 @ X3 )
                       => ( ( in @ X3 @ X1 )
                         => ( in @ X2 @ ( setunion @ X1 ) ) ) )
                   => ( ! [X1: $i,X2: $i] :
                          ( ( in @ X2 @ ( setunion @ X1 ) )
                         => ! [X3: $o] :
                              ( ! [X4: $i] :
                                  ( ( in @ X2 @ X4 )
                                 => ( ( in @ X4 @ X1 )
                                   => X3 ) )
                             => X3 ) )
                     => ( ! [X1: $i,X2: $i] :
                            ( ( in @ X2 @ X1 )
                           => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
                       => ( ! [X1: $i > $o] :
                              ( ~ ! [X2: $i] :
                                    ( ( X1 @ X2 )
                                   => ~ ! [X3: $i] :
                                          ( ( X1 @ X3 )
                                         => ( X2 = X3 ) ) )
                             => ~ ! [X2: $i] :
                                    ~ ! [X3: $i] :
                                        ( ( X1 @ X3 )
                                        = ( X3 = X2 ) ) )
                         => ( ! [X1: $i] :
                                ( ( X1 != emptyset )
                               => ~ ! [X2: $i] :
                                      ~ ( in @ X2 @ X1 ) )
                           => ( ! [X1: $i,X2: $i] :
                                  ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                 => ( X1 = X2 ) )
                             => ( ! [X1: $i,X2: $i] :
                                    ( ( X1 != X2 )
                                   => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                               => ( ! [X1: $i,X2: $i] :
                                      ( ( X1 = X2 )
                                     => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                 => ( ! [X1: $i,X2: $i] :
                                        ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                       => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                          ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                         => ( ( X3 != X1 )
                                           => ( X3 = X2 ) ) )
                                     => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                       => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                         => ( ! [X1: $i,X2: $i > $o] :
                                                ( ~ ! [X3: $i] :
                                                      ( ( in @ X3 @ X1 )
                                                     => ~ ( X2 @ X3 ) )
                                               => ( ( dsetconstr @ X1 @ X2 )
                                                 != emptyset ) )
                                           => ( ! [X1: $i > $o,X2: $i] :
                                                  ( ( in @ X2 @ emptyset )
                                                 => ( X1 @ X2 ) )
                                             => ( ! [X1: $o] :
                                                    ( X1
                                                   => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                               => ( ! [X1: $o] :
                                                      ( X1
                                                     => ( set2prop @ ( prop2set @ X1 ) ) )
                                                 => ( ! [X1: $i > $o] :
                                                        ( ~ ! [X2: $i] :
                                                              ~ ( X1 @ X2 )
                                                       => ( ! [X2: $i,X3: $i] :
                                                              ( ( X1 @ X2 )
                                                             => ( ( X1 @ X3 )
                                                               => ( X2 = X3 ) ) )
                                                         => ~ ! [X2: $i] :
                                                                ( ( X1 @ X2 )
                                                               => ~ ! [X3: $i] :
                                                                      ( ( X1 @ X3 )
                                                                     => ( X2 = X3 ) ) ) ) )
                                                   => ( ! [X1: $i > $o] :
                                                          ( ~ ! [X2: $i] :
                                                                ~ ! [X3: $i] :
                                                                    ( ( X1 @ X3 )
                                                                    = ( X3 = X2 ) )
                                                         => ~ ! [X2: $i] :
                                                                ( ( X1 @ X2 )
                                                               => ~ ! [X3: $i] :
                                                                      ( ( X1 @ X3 )
                                                                     => ( X2 = X3 ) ) ) )
                                                     => ( ! [X1: $i,X2: $i] :
                                                            ( ( X1 = X2 )
                                                           => ! [X3: $i,X4: $i] :
                                                                ( ( X3 = X4 )
                                                               => ( ( in @ X3 @ X1 )
                                                                 => ( in @ X4 @ X2 ) ) ) )
                                                       => ( ! [X1: $i,X2: $i] :
                                                              ( ( X1 = X2 )
                                                             => ! [X3: $i,X4: $i] :
                                                                  ( ( X3 = X4 )
                                                                 => ( ( in @ X3 @ X1 )
                                                                    = ( in @ X4 @ X2 ) ) ) )
                                                         => ( ! [X1: $i > $o] :
                                                                ( ~ ! [X2: $i] :
                                                                      ( ( X1 @ X2 )
                                                                     => ~ ! [X3: $i] :
                                                                            ( ( X1 @ X3 )
                                                                           => ( X2 = X3 ) ) )
                                                               => ! [X2: $i,X3: $i] :
                                                                    ( ( X1 @ X2 )
                                                                   => ( ( X1 @ X3 )
                                                                     => ( X2 = X3 ) ) ) )
                                                           => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                  ( ! [X3: $i,X4: $i] :
                                                                      ( ( X3 = X4 )
                                                                     => ( ( X1 @ X3 )
                                                                        = ( X2 @ X4 ) ) )
                                                                 => ( ( ~ ! [X3: $i] :
                                                                            ( ( X1 @ X3 )
                                                                           => ~ ! [X4: $i] :
                                                                                  ( ( X1 @ X4 )
                                                                                 => ( X3 = X4 ) ) ) )
                                                                    = ( ~ ! [X3: $i] :
                                                                            ( ( X2 @ X3 )
                                                                           => ~ ! [X4: $i] :
                                                                                  ( ( X2 @ X4 )
                                                                                 => ( X3 = X4 ) ) ) ) ) )
                                                             => ( ! [X1: $i,X2: $i] :
                                                                    ( ( X1 = X2 )
                                                                   => ! [X3: $i,X4: $i] :
                                                                        ( ( X3 = X4 )
                                                                       => ( ( setadjoin @ X1 @ X3 )
                                                                          = ( setadjoin @ X2 @ X4 ) ) ) )
                                                               => ( ! [X1: $i,X2: $i] :
                                                                      ( ( X1 = X2 )
                                                                     => ( ( powerset @ X1 )
                                                                        = ( powerset @ X2 ) ) )
                                                                 => ( ! [X1: $i,X2: $i] :
                                                                        ( ( X1 = X2 )
                                                                       => ( ( setunion @ X1 )
                                                                          = ( setunion @ X2 ) ) )
                                                                   => ( ! [X1: $i > $o] :
                                                                          ( ~ ! [X2: $i] :
                                                                                ( ( X1 @ X2 )
                                                                               => ~ ! [X3: $i] :
                                                                                      ( ( X1 @ X3 )
                                                                                     => ( X2 = X3 ) ) )
                                                                         => ! [X2: $i,X3: $i] :
                                                                              ( ( X1 @ X2 )
                                                                             => ( ( X1 @ X3 )
                                                                               => ( X2 = X3 ) ) ) )
                                                                     => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                            ( ! [X3: $i,X4: $i] :
                                                                                ( ( X3 = X4 )
                                                                               => ( ( X1 @ X3 )
                                                                                  = ( X2 @ X4 ) ) )
                                                                           => ( ~ ! [X3: $i] :
                                                                                    ( ( X1 @ X3 )
                                                                                   => ~ ! [X4: $i] :
                                                                                          ( ( X1 @ X4 )
                                                                                         => ( X3 = X4 ) ) )
                                                                             => ( ~ ! [X3: $i] :
                                                                                      ( ( X2 @ X3 )
                                                                                     => ~ ! [X4: $i] :
                                                                                            ( ( X2 @ X4 )
                                                                                           => ( X3 = X4 ) ) )
                                                                               => ( ( descr @ X1 )
                                                                                  = ( descr @ X2 ) ) ) ) )
                                                                       => ( ! [X1: $i,X2: $i] :
                                                                              ( ( X1 = X2 )
                                                                             => ! [X3: $i > $o,X4: $i > $o] :
                                                                                  ( ! [X5: $i] :
                                                                                      ( ( in @ X5 @ X1 )
                                                                                     => ! [X6: $i] :
                                                                                          ( ( in @ X6 @ X2 )
                                                                                         => ( ( X5 = X6 )
                                                                                           => ( ( X3 @ X5 )
                                                                                              = ( X4 @ X6 ) ) ) ) )
                                                                                 => ( ( dsetconstr @ X1 @ X3 )
                                                                                    = ( dsetconstr @ X2 @ X4 ) ) ) )
                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                ( ! [X3: $i] :
                                                                                    ( ( in @ X3 @ X1 )
                                                                                   => ( in @ X3 @ X2 ) )
                                                                               => ( subset @ X1 @ X2 ) )
                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                  ( ( X1 = X2 )
                                                                                 => ( subset @ X2 @ X1 ) )
                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                    ( ( X1 = X2 )
                                                                                   => ( subset @ X1 @ X2 ) )
                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                      ( ! [X3: $i] :
                                                                                          ( ( in @ X3 @ X1 )
                                                                                         => ( in @ X3 @ X2 ) )
                                                                                     => ( subset @ X1 @ X2 ) )
                                                                                 => ( ! [X1: $i] : ( subset @ emptyset @ X1 )
                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                          ( ( subset @ X1 @ X2 )
                                                                                         => ( ( in @ X3 @ X1 )
                                                                                           => ( in @ X3 @ X2 ) ) )
                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                            ( ( subset @ X1 @ X2 )
                                                                                           => ( ~ ( in @ X3 @ X2 )
                                                                                             => ~ ( in @ X3 @ X1 ) ) )
                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                              ( ( in @ X3 @ X1 )
                                                                                             => ( ~ ( in @ X3 @ X2 )
                                                                                               => ~ ( subset @ X1 @ X2 ) ) )
                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                ( ~ ( subset @ X1 @ X2 )
                                                                                               => ( X1 != X2 ) )
                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                 => ( ~ ( in @ X3 @ X2 )
                                                                                                   => ( X1 != X2 ) ) )
                                                                                             => ( ! [X1: $i] : ( subset @ X1 @ X1 )
                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                      ( ( subset @ X1 @ X2 )
                                                                                                     => ( ( subset @ X2 @ X3 )
                                                                                                       => ( subset @ X1 @ X3 ) ) )
                                                                                                 => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) )
                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                          ( ( subset @ X1 @ X3 )
                                                                                                         => ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                            ( ( subset @ X1 @ X2 )
                                                                                                           => ( in @ X1 @ ( powerset @ X2 ) ) )
                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                              ( ( subset @ X1 @ X2 )
                                                                                                             => ( ( subset @ X2 @ X1 )
                                                                                                               => ( X1 = X2 ) ) )
                                                                                                         => ( ! [X1: $i] :
                                                                                                                ( ( subset @ X1 @ emptyset )
                                                                                                               => ( X1 = emptyset ) )
                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                  ( ( subset @ X2 @ X1 )
                                                                                                                 => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                    ( ( in @ X2 @ ( powerset @ X1 ) )
                                                                                                                   => ( subset @ X2 @ X1 ) )
                                                                                                               => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                        ( ( subset @ X1 @ X2 )
                                                                                                                       => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
                                                                                                                   => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                                                                                                                     => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                             => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                                         => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                  ( ( in @ X3 @ X2 )
                                                                                                                                 => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                                                                                                                    ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                   => ( ( ( in @ X3 @ X1 )
                                                                                                                                       => X4 )
                                                                                                                                     => ( ( ( in @ X3 @ X2 )
                                                                                                                                         => X4 )
                                                                                                                                       => X4 ) ) )
                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                      ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                     => ( ~ ( in @ X3 @ X1 )
                                                                                                                                       => ( in @ X3 @ X2 ) ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                           => ( ( in @ X3 @ X2 )
                                                                                                                                             => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                              ( ( subset @ X3 @ X1 )
                                                                                                                                             => ( ( subset @ X3 @ X2 )
                                                                                                                                               => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                               => ( in @ X3 @ X1 ) )
                                                                                                                                           => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                    ( ( subset @ X1 @ X2 )
                                                                                                                                                   => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                      = X1 ) )
                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                      ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                                        = X2 )
                                                                                                                                                     => ( subset @ X2 @ X1 ) )
                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                        ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                                       => ( in @ X3 @ X2 ) )
                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                          ( ! [X3: $i] :
                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                             => ~ ( in @ X3 @ X2 ) )
                                                                                                                                                         => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                            = emptyset ) )
                                                                                                                                                     => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                              ( ( subset @ X2 @ X1 )
                                                                                                                                                             => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                = X2 ) )
                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                  = X1 )
                                                                                                                                                               => ( subset @ X1 @ X2 ) )
                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                  ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                                                                                                                                  = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                   => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                     => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                      ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                     => ( in @ X3 @ X1 ) )
                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                        ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                       => ~ ( in @ X3 @ X2 ) )
                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                          ( ( subset @ X1 @ X2 )
                                                                                                                                                                         => ( ( setminus @ X1 @ X2 )
                                                                                                                                                                            = emptyset ) )
                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                            ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                           => ( ( in @ X3 @ X1 )
                                                                                                                                                                             => ( in @ X3 @ X2 ) ) )
                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                              ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                             => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                               => ~ ( in @ X3 @ X1 ) ) )
                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                               => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                  ( ( in @ X3 @ X2 )
                                                                                                                                                                                 => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                                             => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                      ( ( ( setminus @ X1 @ X2 )
                                                                                                                                                                                        = emptyset )
                                                                                                                                                                                     => ( subset @ X1 @ X2 ) )
                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                        ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                                                                                                                       => ! [X4: $o] :
                                                                                                                                                                                            ( ( ( in @ X3 @ X1 )
                                                                                                                                                                                             => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                               => X4 ) )
                                                                                                                                                                                           => ( ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                               => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                 => X4 ) )
                                                                                                                                                                                             => X4 ) ) )
                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                         => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                           => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                            ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                           => ( ( in @ X3 @ X2 )
                                                                                                                                                                                             => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                             => ( ( in @ X3 @ X2 )
                                                                                                                                                                                               => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                               => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                 => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                            ( ( in @ X2 @ X1 )
                                                                                                                                                                                                           => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                              ( ( in @ X2 @ X1 )
                                                                                                                                                                                                             => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                               => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                  ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                 => ( ( X3 != X1 )
                                                                                                                                                                                                                   => ( X3 = X2 ) ) )
                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                       => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                         => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                           => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                             => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                               => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                 => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                               => ~ ! [X4: $i] :
                                                                                                                                                                                                                                      ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                     => ! [X5: $i] :
                                                                                                                                                                                                                                          ( ( in @ X5 @ X2 )
                                                                                                                                                                                                                                         => ( X3
                                                                                                                                                                                                                                           != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                                                                                                                           => ( sP5
                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                    ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                                                                                                                                   => ~ ! [X3: $i] :
                                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                         => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                                                                                                                               => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                                                                                                                                 => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                                   => ( ! [X1: $i] :
                                                                                                                                                                                                                                          ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                                                                                                                          = X1 )
                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                            ( ! [X3: $i] :
                                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                                                                                    ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                   => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                     => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                       => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                                           => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                   => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                                             => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                    ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                   => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                     != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                              ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                    ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                   => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                     != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                                                                                                                             => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                   => ~ ( X2 @ X3 ) ) )
                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                               => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                 => ( ! [X4: $i] :
                                                                                                                                                                                                                                                        ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                       => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                         => ( X4 = X3 ) ) )
                                                                                                                                                                                                                                                   => ~ ! [X4: $i] :
                                                                                                                                                                                                                                                          ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                         => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                           != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                  ( ! [X3: $i] :
                                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                                                                                                          ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                         => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                           => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                             => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                                                 => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                         => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                                                   => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                          ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                         => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                           != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                    ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                                                                                                                      = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                   => ( X1 = X2 ) )
                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                      ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                     => ( X1 = X3 ) )
                                                                                                                                                                                                                                                 => ( ! [X1: $i] :
                                                                                                                                                                                                                                                        ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                       => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                              ( ( in @ X2
                                                                                                                                                                                                                                                                @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                  @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                                                                                                                             => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                  @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                                                               != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                                   => ( ! [X1: $i] :
                                                                                                                                                                                                                                                          ( ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                                               => ( X1
                                                                                                                                                                                                                                                                 != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                                         => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                            ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                            = X1 )
                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                              ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                             => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                  = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                               => ( X1 = X3 ) )
                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                  ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                                    = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                 => ( X1 = X3 ) )
                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                    ( ( X1 = X2 )
                                                                                                                                                                                                                                                                   => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                      = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                      ( ( X1 = X2 )
                                                                                                                                                                                                                                                                     => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                        = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                        ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                          = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                       => ( ( X3 = X4 )
                                                                                                                                                                                                                                                                         => ( X2 = X4 ) ) )
                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                          ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                            = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                                                                                                                         => ( X1 = X2 ) )
                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                            ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                              = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                           => ( X2 = X4 ) )
                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                              ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                                                = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                             => ( X2 = X4 ) )
                                                                                                                                                                                                                                                                         => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                                               => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                      ( ( in @ X2
                                                                                                                                                                                                                                                                                        @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                          @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                                              ( X1
                                                                                                                                                                                                                                                                                              = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                                                                                                                     => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                          @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                                              ( X1
                                                                                                                                                                                                                                                                                              = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                                                                                                                       != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                  ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                  = X2 )
                                                                                                                                                                                                                                                                             => ( sP8
                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                      ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                     => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                        ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                       => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                          ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                         => ( in @ X4 @ X2 ) )
                                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                               => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                  = X3 ) ) )
                                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                                 => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                    = X4 ) ) )
                                                                                                                                                                                                                                                                                         => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                              ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                             => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                                                                                                                                = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h58,assumption,
    ! [X1: $i,X2: $i,X3: $i] :
      ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
     => ! [X4: $o] :
          ( ( ( X3 = X1 )
           => X4 )
         => ( ( ( in @ X3 @ X2 )
             => X4 )
           => X4 ) ) ),
    introduced(assumption,[]) ).

thf(h59,assumption,
    ~ ( ! [X1: $i,X2: $i,X3: $i] :
          ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
         => ( ( X3 != X1 )
           => ( in @ X3 @ X2 ) ) )
     => ( ! [X1: $i] :
            ( ( dsetconstr @ X1
              @ ^ [X2: $i] : ~ $false )
            = X1 )
       => ( ! [X1: $i,X2: $i] :
              ( ! [X3: $i] :
                  ( ( in @ X3 @ X2 )
                 => ( in @ X3 @ X1 ) )
             => ( in @ X2 @ ( powerset @ X1 ) ) )
         => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
           => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
             => ( ! [X1: $i,X2: $i,X3: $i] :
                    ( ( in @ X2 @ ( powerset @ X1 ) )
                   => ( ( in @ X3 @ X2 )
                     => ( in @ X3 @ X1 ) ) )
               => ( ! [X1: $i,X2: $i,X3: $i] :
                      ( ( in @ X2 @ X3 )
                     => ( ( in @ X3 @ X1 )
                       => ( in @ X2 @ ( setunion @ X1 ) ) ) )
                 => ( ! [X1: $i,X2: $i] :
                        ( ( in @ X2 @ ( setunion @ X1 ) )
                       => ! [X3: $o] :
                            ( ! [X4: $i] :
                                ( ( in @ X2 @ X4 )
                               => ( ( in @ X4 @ X1 )
                                 => X3 ) )
                           => X3 ) )
                   => ( ! [X1: $i,X2: $i] :
                          ( ( in @ X2 @ X1 )
                         => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
                     => ( ! [X1: $i > $o] :
                            ( ~ ! [X2: $i] :
                                  ( ( X1 @ X2 )
                                 => ~ ! [X3: $i] :
                                        ( ( X1 @ X3 )
                                       => ( X2 = X3 ) ) )
                           => ~ ! [X2: $i] :
                                  ~ ! [X3: $i] :
                                      ( ( X1 @ X3 )
                                      = ( X3 = X2 ) ) )
                       => ( ! [X1: $i] :
                              ( ( X1 != emptyset )
                             => ~ ! [X2: $i] :
                                    ~ ( in @ X2 @ X1 ) )
                         => ( ! [X1: $i,X2: $i] :
                                ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                               => ( X1 = X2 ) )
                           => ( ! [X1: $i,X2: $i] :
                                  ( ( X1 != X2 )
                                 => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                             => ( ! [X1: $i,X2: $i] :
                                    ( ( X1 = X2 )
                                   => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                               => ( ! [X1: $i,X2: $i] :
                                      ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                     => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                        ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                       => ( ( X3 != X1 )
                                         => ( X3 = X2 ) ) )
                                   => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                     => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                       => ( ! [X1: $i,X2: $i > $o] :
                                              ( ~ ! [X3: $i] :
                                                    ( ( in @ X3 @ X1 )
                                                   => ~ ( X2 @ X3 ) )
                                             => ( ( dsetconstr @ X1 @ X2 )
                                               != emptyset ) )
                                         => ( ! [X1: $i > $o,X2: $i] :
                                                ( ( in @ X2 @ emptyset )
                                               => ( X1 @ X2 ) )
                                           => ( ! [X1: $o] :
                                                  ( X1
                                                 => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                             => ( ! [X1: $o] :
                                                    ( X1
                                                   => ( set2prop @ ( prop2set @ X1 ) ) )
                                               => ( ! [X1: $i > $o] :
                                                      ( ~ ! [X2: $i] :
                                                            ~ ( X1 @ X2 )
                                                     => ( ! [X2: $i,X3: $i] :
                                                            ( ( X1 @ X2 )
                                                           => ( ( X1 @ X3 )
                                                             => ( X2 = X3 ) ) )
                                                       => ~ ! [X2: $i] :
                                                              ( ( X1 @ X2 )
                                                             => ~ ! [X3: $i] :
                                                                    ( ( X1 @ X3 )
                                                                   => ( X2 = X3 ) ) ) ) )
                                                 => ( ! [X1: $i > $o] :
                                                        ( ~ ! [X2: $i] :
                                                              ~ ! [X3: $i] :
                                                                  ( ( X1 @ X3 )
                                                                  = ( X3 = X2 ) )
                                                       => ~ ! [X2: $i] :
                                                              ( ( X1 @ X2 )
                                                             => ~ ! [X3: $i] :
                                                                    ( ( X1 @ X3 )
                                                                   => ( X2 = X3 ) ) ) )
                                                   => ( ! [X1: $i,X2: $i] :
                                                          ( ( X1 = X2 )
                                                         => ! [X3: $i,X4: $i] :
                                                              ( ( X3 = X4 )
                                                             => ( ( in @ X3 @ X1 )
                                                               => ( in @ X4 @ X2 ) ) ) )
                                                     => ( ! [X1: $i,X2: $i] :
                                                            ( ( X1 = X2 )
                                                           => ! [X3: $i,X4: $i] :
                                                                ( ( X3 = X4 )
                                                               => ( ( in @ X3 @ X1 )
                                                                  = ( in @ X4 @ X2 ) ) ) )
                                                       => ( ! [X1: $i > $o] :
                                                              ( ~ ! [X2: $i] :
                                                                    ( ( X1 @ X2 )
                                                                   => ~ ! [X3: $i] :
                                                                          ( ( X1 @ X3 )
                                                                         => ( X2 = X3 ) ) )
                                                             => ! [X2: $i,X3: $i] :
                                                                  ( ( X1 @ X2 )
                                                                 => ( ( X1 @ X3 )
                                                                   => ( X2 = X3 ) ) ) )
                                                         => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                ( ! [X3: $i,X4: $i] :
                                                                    ( ( X3 = X4 )
                                                                   => ( ( X1 @ X3 )
                                                                      = ( X2 @ X4 ) ) )
                                                               => ( ( ~ ! [X3: $i] :
                                                                          ( ( X1 @ X3 )
                                                                         => ~ ! [X4: $i] :
                                                                                ( ( X1 @ X4 )
                                                                               => ( X3 = X4 ) ) ) )
                                                                  = ( ~ ! [X3: $i] :
                                                                          ( ( X2 @ X3 )
                                                                         => ~ ! [X4: $i] :
                                                                                ( ( X2 @ X4 )
                                                                               => ( X3 = X4 ) ) ) ) ) )
                                                           => ( ! [X1: $i,X2: $i] :
                                                                  ( ( X1 = X2 )
                                                                 => ! [X3: $i,X4: $i] :
                                                                      ( ( X3 = X4 )
                                                                     => ( ( setadjoin @ X1 @ X3 )
                                                                        = ( setadjoin @ X2 @ X4 ) ) ) )
                                                             => ( ! [X1: $i,X2: $i] :
                                                                    ( ( X1 = X2 )
                                                                   => ( ( powerset @ X1 )
                                                                      = ( powerset @ X2 ) ) )
                                                               => ( ! [X1: $i,X2: $i] :
                                                                      ( ( X1 = X2 )
                                                                     => ( ( setunion @ X1 )
                                                                        = ( setunion @ X2 ) ) )
                                                                 => ( ! [X1: $i > $o] :
                                                                        ( ~ ! [X2: $i] :
                                                                              ( ( X1 @ X2 )
                                                                             => ~ ! [X3: $i] :
                                                                                    ( ( X1 @ X3 )
                                                                                   => ( X2 = X3 ) ) )
                                                                       => ! [X2: $i,X3: $i] :
                                                                            ( ( X1 @ X2 )
                                                                           => ( ( X1 @ X3 )
                                                                             => ( X2 = X3 ) ) ) )
                                                                   => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                          ( ! [X3: $i,X4: $i] :
                                                                              ( ( X3 = X4 )
                                                                             => ( ( X1 @ X3 )
                                                                                = ( X2 @ X4 ) ) )
                                                                         => ( ~ ! [X3: $i] :
                                                                                  ( ( X1 @ X3 )
                                                                                 => ~ ! [X4: $i] :
                                                                                        ( ( X1 @ X4 )
                                                                                       => ( X3 = X4 ) ) )
                                                                           => ( ~ ! [X3: $i] :
                                                                                    ( ( X2 @ X3 )
                                                                                   => ~ ! [X4: $i] :
                                                                                          ( ( X2 @ X4 )
                                                                                         => ( X3 = X4 ) ) )
                                                                             => ( ( descr @ X1 )
                                                                                = ( descr @ X2 ) ) ) ) )
                                                                     => ( ! [X1: $i,X2: $i] :
                                                                            ( ( X1 = X2 )
                                                                           => ! [X3: $i > $o,X4: $i > $o] :
                                                                                ( ! [X5: $i] :
                                                                                    ( ( in @ X5 @ X1 )
                                                                                   => ! [X6: $i] :
                                                                                        ( ( in @ X6 @ X2 )
                                                                                       => ( ( X5 = X6 )
                                                                                         => ( ( X3 @ X5 )
                                                                                            = ( X4 @ X6 ) ) ) ) )
                                                                               => ( ( dsetconstr @ X1 @ X3 )
                                                                                  = ( dsetconstr @ X2 @ X4 ) ) ) )
                                                                       => ( ! [X1: $i,X2: $i] :
                                                                              ( ! [X3: $i] :
                                                                                  ( ( in @ X3 @ X1 )
                                                                                 => ( in @ X3 @ X2 ) )
                                                                             => ( subset @ X1 @ X2 ) )
                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                ( ( X1 = X2 )
                                                                               => ( subset @ X2 @ X1 ) )
                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                  ( ( X1 = X2 )
                                                                                 => ( subset @ X1 @ X2 ) )
                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                    ( ! [X3: $i] :
                                                                                        ( ( in @ X3 @ X1 )
                                                                                       => ( in @ X3 @ X2 ) )
                                                                                   => ( subset @ X1 @ X2 ) )
                                                                               => ( ! [X1: $i] : ( subset @ emptyset @ X1 )
                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                        ( ( subset @ X1 @ X2 )
                                                                                       => ( ( in @ X3 @ X1 )
                                                                                         => ( in @ X3 @ X2 ) ) )
                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                          ( ( subset @ X1 @ X2 )
                                                                                         => ( ~ ( in @ X3 @ X2 )
                                                                                           => ~ ( in @ X3 @ X1 ) ) )
                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                            ( ( in @ X3 @ X1 )
                                                                                           => ( ~ ( in @ X3 @ X2 )
                                                                                             => ~ ( subset @ X1 @ X2 ) ) )
                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                              ( ~ ( subset @ X1 @ X2 )
                                                                                             => ( X1 != X2 ) )
                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                ( ( in @ X3 @ X1 )
                                                                                               => ( ~ ( in @ X3 @ X2 )
                                                                                                 => ( X1 != X2 ) ) )
                                                                                           => ( ! [X1: $i] : ( subset @ X1 @ X1 )
                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                    ( ( subset @ X1 @ X2 )
                                                                                                   => ( ( subset @ X2 @ X3 )
                                                                                                     => ( subset @ X1 @ X3 ) ) )
                                                                                               => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) )
                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                        ( ( subset @ X1 @ X3 )
                                                                                                       => ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                          ( ( subset @ X1 @ X2 )
                                                                                                         => ( in @ X1 @ ( powerset @ X2 ) ) )
                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                            ( ( subset @ X1 @ X2 )
                                                                                                           => ( ( subset @ X2 @ X1 )
                                                                                                             => ( X1 = X2 ) ) )
                                                                                                       => ( ! [X1: $i] :
                                                                                                              ( ( subset @ X1 @ emptyset )
                                                                                                             => ( X1 = emptyset ) )
                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                ( ( subset @ X2 @ X1 )
                                                                                                               => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                  ( ( in @ X2 @ ( powerset @ X1 ) )
                                                                                                                 => ( subset @ X2 @ X1 ) )
                                                                                                             => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                      ( ( subset @ X1 @ X2 )
                                                                                                                     => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
                                                                                                                 => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                                                                                                                   => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                           => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                                       => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                ( ( in @ X3 @ X2 )
                                                                                                                               => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                                                                                                                  ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                 => ( ( ( in @ X3 @ X1 )
                                                                                                                                     => X4 )
                                                                                                                                   => ( ( ( in @ X3 @ X2 )
                                                                                                                                       => X4 )
                                                                                                                                     => X4 ) ) )
                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                    ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                   => ( ~ ( in @ X3 @ X1 )
                                                                                                                                     => ( in @ X3 @ X2 ) ) )
                                                                                                                               => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                         => ( ( in @ X3 @ X2 )
                                                                                                                                           => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                            ( ( subset @ X3 @ X1 )
                                                                                                                                           => ( ( subset @ X3 @ X2 )
                                                                                                                                             => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                              ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                             => ( in @ X3 @ X1 ) )
                                                                                                                                         => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                  ( ( subset @ X1 @ X2 )
                                                                                                                                                 => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                    = X1 ) )
                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                    ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                                      = X2 )
                                                                                                                                                   => ( subset @ X2 @ X1 ) )
                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                      ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                                     => ( in @ X3 @ X2 ) )
                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                        ( ! [X3: $i] :
                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                           => ~ ( in @ X3 @ X2 ) )
                                                                                                                                                       => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                          = emptyset ) )
                                                                                                                                                   => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                            ( ( subset @ X2 @ X1 )
                                                                                                                                                           => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                              = X2 ) )
                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                              ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                = X1 )
                                                                                                                                                             => ( subset @ X1 @ X2 ) )
                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                                                                                                                                = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                 => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                   => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                    ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                   => ( in @ X3 @ X1 ) )
                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                      ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                     => ~ ( in @ X3 @ X2 ) )
                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                        ( ( subset @ X1 @ X2 )
                                                                                                                                                                       => ( ( setminus @ X1 @ X2 )
                                                                                                                                                                          = emptyset ) )
                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                          ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                         => ( ( in @ X3 @ X1 )
                                                                                                                                                                           => ( in @ X3 @ X2 ) ) )
                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                            ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                           => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                             => ~ ( in @ X3 @ X1 ) ) )
                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                              ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                             => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                ( ( in @ X3 @ X2 )
                                                                                                                                                                               => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                                           => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                    ( ( ( setminus @ X1 @ X2 )
                                                                                                                                                                                      = emptyset )
                                                                                                                                                                                   => ( subset @ X1 @ X2 ) )
                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                      ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                                                                                                                     => ! [X4: $o] :
                                                                                                                                                                                          ( ( ( in @ X3 @ X1 )
                                                                                                                                                                                           => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                             => X4 ) )
                                                                                                                                                                                         => ( ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                             => ( ( in @ X3 @ X2 )
                                                                                                                                                                                               => X4 ) )
                                                                                                                                                                                           => X4 ) ) )
                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                       => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                         => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                          ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                         => ( ( in @ X3 @ X2 )
                                                                                                                                                                                           => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                           => ( ( in @ X3 @ X2 )
                                                                                                                                                                                             => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                              ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                             => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                               => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                          ( ( in @ X2 @ X1 )
                                                                                                                                                                                                         => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                            ( ( in @ X2 @ X1 )
                                                                                                                                                                                                           => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                             => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                               => ( ( X3 != X1 )
                                                                                                                                                                                                                 => ( X3 = X2 ) ) )
                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                     => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                       => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                         => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                           => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                             => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                               => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                              ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                             => ~ ! [X4: $i] :
                                                                                                                                                                                                                                    ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                   => ! [X5: $i] :
                                                                                                                                                                                                                                        ( ( in @ X5 @ X2 )
                                                                                                                                                                                                                                       => ( X3
                                                                                                                                                                                                                                         != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                                                                                                                         => ( sP5
                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                  ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                                                                                                                                 => ~ ! [X3: $i] :
                                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                       => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                                                                                                                             => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                                                                                                                               => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                                 => ( ! [X1: $i] :
                                                                                                                                                                                                                                        ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                                                                                                                        = X1 )
                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                          ( ! [X3: $i] :
                                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                                                                                  ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                 => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                   => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                     => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                                         => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                 => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                                           => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                  ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                 => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                   != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                            ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                  ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                 => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                   != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                                                                                                                           => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                 => ~ ( X2 @ X3 ) ) )
                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                             => ( ( X2 @ X3 )
                                                                                                                                                                                                                                               => ( ! [X4: $i] :
                                                                                                                                                                                                                                                      ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                     => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                       => ( X4 = X3 ) ) )
                                                                                                                                                                                                                                                 => ~ ! [X4: $i] :
                                                                                                                                                                                                                                                        ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                       => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                         != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                ( ! [X3: $i] :
                                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                                                                                                        ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                       => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                         => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                           => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                                               => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                       => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                                                 => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                        ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                       => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                         != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                  ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                                                                                                                    = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                 => ( X1 = X2 ) )
                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                    ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                   => ( X1 = X3 ) )
                                                                                                                                                                                                                                               => ( ! [X1: $i] :
                                                                                                                                                                                                                                                      ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                     => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                            ( ( in @ X2
                                                                                                                                                                                                                                                              @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                                                                                                                           => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                                                             != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                                 => ( ! [X1: $i] :
                                                                                                                                                                                                                                                        ( ~ ! [X2: $i] :
                                                                                                                                                                                                                                                              ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                                             => ( X1
                                                                                                                                                                                                                                                               != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                                       => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                          ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                          = X1 )
                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                            ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                           => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                              ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                             => ( X1 = X3 ) )
                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                                  = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                               => ( X1 = X3 ) )
                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                  ( ( X1 = X2 )
                                                                                                                                                                                                                                                                 => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                    = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                    ( ( X1 = X2 )
                                                                                                                                                                                                                                                                   => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                      = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                      ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                        = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                     => ( ( X3 = X4 )
                                                                                                                                                                                                                                                                       => ( X2 = X4 ) ) )
                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                        ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                          = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                                                                                                                       => ( X1 = X2 ) )
                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                          ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                            = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                         => ( X2 = X4 ) )
                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                            ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                                              = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                           => ( X2 = X4 ) )
                                                                                                                                                                                                                                                                       => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                              ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                                             => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                    ( ( in @ X2
                                                                                                                                                                                                                                                                                      @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                        @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                                            ( X1
                                                                                                                                                                                                                                                                                            = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                                                                                                                   => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                        @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                                            ( X1
                                                                                                                                                                                                                                                                                            = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                                                                                                                     != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                = X2 )
                                                                                                                                                                                                                                                                           => ( sP8
                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                    ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                   => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                      ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                     => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                        ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                       => ( in @ X4 @ X2 ) )
                                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                             => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                = X3 ) ) )
                                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                               => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                  = X4 ) ) )
                                                                                                                                                                                                                                                                                       => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                            ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                           => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                                                                                                                              = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h60,assumption,
    ! [X1: $i,X2: $i,X3: $i] :
      ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
     => ( ( X3 != X1 )
       => ( in @ X3 @ X2 ) ) ),
    introduced(assumption,[]) ).

thf(h61,assumption,
    ~ ( ! [X1: $i] :
          ( ( dsetconstr @ X1
            @ ^ [X2: $i] : ~ $false )
          = X1 )
     => ( ! [X1: $i,X2: $i] :
            ( ! [X3: $i] :
                ( ( in @ X3 @ X2 )
               => ( in @ X3 @ X1 ) )
           => ( in @ X2 @ ( powerset @ X1 ) ) )
       => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
         => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
           => ( ! [X1: $i,X2: $i,X3: $i] :
                  ( ( in @ X2 @ ( powerset @ X1 ) )
                 => ( ( in @ X3 @ X2 )
                   => ( in @ X3 @ X1 ) ) )
             => ( ! [X1: $i,X2: $i,X3: $i] :
                    ( ( in @ X2 @ X3 )
                   => ( ( in @ X3 @ X1 )
                     => ( in @ X2 @ ( setunion @ X1 ) ) ) )
               => ( ! [X1: $i,X2: $i] :
                      ( ( in @ X2 @ ( setunion @ X1 ) )
                     => ! [X3: $o] :
                          ( ! [X4: $i] :
                              ( ( in @ X2 @ X4 )
                             => ( ( in @ X4 @ X1 )
                               => X3 ) )
                         => X3 ) )
                 => ( ! [X1: $i,X2: $i] :
                        ( ( in @ X2 @ X1 )
                       => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
                   => ( ! [X1: $i > $o] :
                          ( ~ ! [X2: $i] :
                                ( ( X1 @ X2 )
                               => ~ ! [X3: $i] :
                                      ( ( X1 @ X3 )
                                     => ( X2 = X3 ) ) )
                         => ~ ! [X2: $i] :
                                ~ ! [X3: $i] :
                                    ( ( X1 @ X3 )
                                    = ( X3 = X2 ) ) )
                     => ( ! [X1: $i] :
                            ( ( X1 != emptyset )
                           => ~ ! [X2: $i] :
                                  ~ ( in @ X2 @ X1 ) )
                       => ( ! [X1: $i,X2: $i] :
                              ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                             => ( X1 = X2 ) )
                         => ( ! [X1: $i,X2: $i] :
                                ( ( X1 != X2 )
                               => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                           => ( ! [X1: $i,X2: $i] :
                                  ( ( X1 = X2 )
                                 => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                             => ( ! [X1: $i,X2: $i] :
                                    ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                   => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                      ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                     => ( ( X3 != X1 )
                                       => ( X3 = X2 ) ) )
                                 => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                   => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                     => ( ! [X1: $i,X2: $i > $o] :
                                            ( ~ ! [X3: $i] :
                                                  ( ( in @ X3 @ X1 )
                                                 => ~ ( X2 @ X3 ) )
                                           => ( ( dsetconstr @ X1 @ X2 )
                                             != emptyset ) )
                                       => ( ! [X1: $i > $o,X2: $i] :
                                              ( ( in @ X2 @ emptyset )
                                             => ( X1 @ X2 ) )
                                         => ( ! [X1: $o] :
                                                ( X1
                                               => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                           => ( ! [X1: $o] :
                                                  ( X1
                                                 => ( set2prop @ ( prop2set @ X1 ) ) )
                                             => ( ! [X1: $i > $o] :
                                                    ( ~ ! [X2: $i] :
                                                          ~ ( X1 @ X2 )
                                                   => ( ! [X2: $i,X3: $i] :
                                                          ( ( X1 @ X2 )
                                                         => ( ( X1 @ X3 )
                                                           => ( X2 = X3 ) ) )
                                                     => ~ ! [X2: $i] :
                                                            ( ( X1 @ X2 )
                                                           => ~ ! [X3: $i] :
                                                                  ( ( X1 @ X3 )
                                                                 => ( X2 = X3 ) ) ) ) )
                                               => ( ! [X1: $i > $o] :
                                                      ( ~ ! [X2: $i] :
                                                            ~ ! [X3: $i] :
                                                                ( ( X1 @ X3 )
                                                                = ( X3 = X2 ) )
                                                     => ~ ! [X2: $i] :
                                                            ( ( X1 @ X2 )
                                                           => ~ ! [X3: $i] :
                                                                  ( ( X1 @ X3 )
                                                                 => ( X2 = X3 ) ) ) )
                                                 => ( ! [X1: $i,X2: $i] :
                                                        ( ( X1 = X2 )
                                                       => ! [X3: $i,X4: $i] :
                                                            ( ( X3 = X4 )
                                                           => ( ( in @ X3 @ X1 )
                                                             => ( in @ X4 @ X2 ) ) ) )
                                                   => ( ! [X1: $i,X2: $i] :
                                                          ( ( X1 = X2 )
                                                         => ! [X3: $i,X4: $i] :
                                                              ( ( X3 = X4 )
                                                             => ( ( in @ X3 @ X1 )
                                                                = ( in @ X4 @ X2 ) ) ) )
                                                     => ( ! [X1: $i > $o] :
                                                            ( ~ ! [X2: $i] :
                                                                  ( ( X1 @ X2 )
                                                                 => ~ ! [X3: $i] :
                                                                        ( ( X1 @ X3 )
                                                                       => ( X2 = X3 ) ) )
                                                           => ! [X2: $i,X3: $i] :
                                                                ( ( X1 @ X2 )
                                                               => ( ( X1 @ X3 )
                                                                 => ( X2 = X3 ) ) ) )
                                                       => ( ! [X1: $i > $o,X2: $i > $o] :
                                                              ( ! [X3: $i,X4: $i] :
                                                                  ( ( X3 = X4 )
                                                                 => ( ( X1 @ X3 )
                                                                    = ( X2 @ X4 ) ) )
                                                             => ( ( ~ ! [X3: $i] :
                                                                        ( ( X1 @ X3 )
                                                                       => ~ ! [X4: $i] :
                                                                              ( ( X1 @ X4 )
                                                                             => ( X3 = X4 ) ) ) )
                                                                = ( ~ ! [X3: $i] :
                                                                        ( ( X2 @ X3 )
                                                                       => ~ ! [X4: $i] :
                                                                              ( ( X2 @ X4 )
                                                                             => ( X3 = X4 ) ) ) ) ) )
                                                         => ( ! [X1: $i,X2: $i] :
                                                                ( ( X1 = X2 )
                                                               => ! [X3: $i,X4: $i] :
                                                                    ( ( X3 = X4 )
                                                                   => ( ( setadjoin @ X1 @ X3 )
                                                                      = ( setadjoin @ X2 @ X4 ) ) ) )
                                                           => ( ! [X1: $i,X2: $i] :
                                                                  ( ( X1 = X2 )
                                                                 => ( ( powerset @ X1 )
                                                                    = ( powerset @ X2 ) ) )
                                                             => ( ! [X1: $i,X2: $i] :
                                                                    ( ( X1 = X2 )
                                                                   => ( ( setunion @ X1 )
                                                                      = ( setunion @ X2 ) ) )
                                                               => ( ! [X1: $i > $o] :
                                                                      ( ~ ! [X2: $i] :
                                                                            ( ( X1 @ X2 )
                                                                           => ~ ! [X3: $i] :
                                                                                  ( ( X1 @ X3 )
                                                                                 => ( X2 = X3 ) ) )
                                                                     => ! [X2: $i,X3: $i] :
                                                                          ( ( X1 @ X2 )
                                                                         => ( ( X1 @ X3 )
                                                                           => ( X2 = X3 ) ) ) )
                                                                 => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                        ( ! [X3: $i,X4: $i] :
                                                                            ( ( X3 = X4 )
                                                                           => ( ( X1 @ X3 )
                                                                              = ( X2 @ X4 ) ) )
                                                                       => ( ~ ! [X3: $i] :
                                                                                ( ( X1 @ X3 )
                                                                               => ~ ! [X4: $i] :
                                                                                      ( ( X1 @ X4 )
                                                                                     => ( X3 = X4 ) ) )
                                                                         => ( ~ ! [X3: $i] :
                                                                                  ( ( X2 @ X3 )
                                                                                 => ~ ! [X4: $i] :
                                                                                        ( ( X2 @ X4 )
                                                                                       => ( X3 = X4 ) ) )
                                                                           => ( ( descr @ X1 )
                                                                              = ( descr @ X2 ) ) ) ) )
                                                                   => ( ! [X1: $i,X2: $i] :
                                                                          ( ( X1 = X2 )
                                                                         => ! [X3: $i > $o,X4: $i > $o] :
                                                                              ( ! [X5: $i] :
                                                                                  ( ( in @ X5 @ X1 )
                                                                                 => ! [X6: $i] :
                                                                                      ( ( in @ X6 @ X2 )
                                                                                     => ( ( X5 = X6 )
                                                                                       => ( ( X3 @ X5 )
                                                                                          = ( X4 @ X6 ) ) ) ) )
                                                                             => ( ( dsetconstr @ X1 @ X3 )
                                                                                = ( dsetconstr @ X2 @ X4 ) ) ) )
                                                                     => ( ! [X1: $i,X2: $i] :
                                                                            ( ! [X3: $i] :
                                                                                ( ( in @ X3 @ X1 )
                                                                               => ( in @ X3 @ X2 ) )
                                                                           => ( subset @ X1 @ X2 ) )
                                                                       => ( ! [X1: $i,X2: $i] :
                                                                              ( ( X1 = X2 )
                                                                             => ( subset @ X2 @ X1 ) )
                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                ( ( X1 = X2 )
                                                                               => ( subset @ X1 @ X2 ) )
                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                  ( ! [X3: $i] :
                                                                                      ( ( in @ X3 @ X1 )
                                                                                     => ( in @ X3 @ X2 ) )
                                                                                 => ( subset @ X1 @ X2 ) )
                                                                             => ( ! [X1: $i] : ( subset @ emptyset @ X1 )
                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                      ( ( subset @ X1 @ X2 )
                                                                                     => ( ( in @ X3 @ X1 )
                                                                                       => ( in @ X3 @ X2 ) ) )
                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                        ( ( subset @ X1 @ X2 )
                                                                                       => ( ~ ( in @ X3 @ X2 )
                                                                                         => ~ ( in @ X3 @ X1 ) ) )
                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                          ( ( in @ X3 @ X1 )
                                                                                         => ( ~ ( in @ X3 @ X2 )
                                                                                           => ~ ( subset @ X1 @ X2 ) ) )
                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                            ( ~ ( subset @ X1 @ X2 )
                                                                                           => ( X1 != X2 ) )
                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                              ( ( in @ X3 @ X1 )
                                                                                             => ( ~ ( in @ X3 @ X2 )
                                                                                               => ( X1 != X2 ) ) )
                                                                                         => ( ! [X1: $i] : ( subset @ X1 @ X1 )
                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                  ( ( subset @ X1 @ X2 )
                                                                                                 => ( ( subset @ X2 @ X3 )
                                                                                                   => ( subset @ X1 @ X3 ) ) )
                                                                                             => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) )
                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                      ( ( subset @ X1 @ X3 )
                                                                                                     => ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                        ( ( subset @ X1 @ X2 )
                                                                                                       => ( in @ X1 @ ( powerset @ X2 ) ) )
                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                          ( ( subset @ X1 @ X2 )
                                                                                                         => ( ( subset @ X2 @ X1 )
                                                                                                           => ( X1 = X2 ) ) )
                                                                                                     => ( ! [X1: $i] :
                                                                                                            ( ( subset @ X1 @ emptyset )
                                                                                                           => ( X1 = emptyset ) )
                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                              ( ( subset @ X2 @ X1 )
                                                                                                             => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                ( ( in @ X2 @ ( powerset @ X1 ) )
                                                                                                               => ( subset @ X2 @ X1 ) )
                                                                                                           => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                    ( ( subset @ X1 @ X2 )
                                                                                                                   => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
                                                                                                               => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                                                                                                                 => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                         => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                                     => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                              ( ( in @ X3 @ X2 )
                                                                                                                             => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                                                                                                                ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                               => ( ( ( in @ X3 @ X1 )
                                                                                                                                   => X4 )
                                                                                                                                 => ( ( ( in @ X3 @ X2 )
                                                                                                                                     => X4 )
                                                                                                                                   => X4 ) ) )
                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                  ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                 => ( ~ ( in @ X3 @ X1 )
                                                                                                                                   => ( in @ X3 @ X2 ) ) )
                                                                                                                             => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                                                                                                                               => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                       => ( ( in @ X3 @ X2 )
                                                                                                                                         => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                          ( ( subset @ X3 @ X1 )
                                                                                                                                         => ( ( subset @ X3 @ X2 )
                                                                                                                                           => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                            ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                           => ( in @ X3 @ X1 ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                ( ( subset @ X1 @ X2 )
                                                                                                                                               => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                  = X1 ) )
                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                  ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                                    = X2 )
                                                                                                                                                 => ( subset @ X2 @ X1 ) )
                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                    ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                                   => ( in @ X3 @ X2 ) )
                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                      ( ! [X3: $i] :
                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                         => ~ ( in @ X3 @ X2 ) )
                                                                                                                                                     => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                        = emptyset ) )
                                                                                                                                                 => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                          ( ( subset @ X2 @ X1 )
                                                                                                                                                         => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                            = X2 ) )
                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                            ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                                              = X1 )
                                                                                                                                                           => ( subset @ X1 @ X2 ) )
                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                              ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                                                                                                                              = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                               => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                 => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                  ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                 => ( in @ X3 @ X1 ) )
                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                    ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                   => ~ ( in @ X3 @ X2 ) )
                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                      ( ( subset @ X1 @ X2 )
                                                                                                                                                                     => ( ( setminus @ X1 @ X2 )
                                                                                                                                                                        = emptyset ) )
                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                        ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                       => ( ( in @ X3 @ X1 )
                                                                                                                                                                         => ( in @ X3 @ X2 ) ) )
                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                          ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                         => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                           => ~ ( in @ X3 @ X1 ) ) )
                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                            ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                           => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                              ( ( in @ X3 @ X2 )
                                                                                                                                                                             => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                                         => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                  ( ( ( setminus @ X1 @ X2 )
                                                                                                                                                                                    = emptyset )
                                                                                                                                                                                 => ( subset @ X1 @ X2 ) )
                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                    ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                                                                                                                   => ! [X4: $o] :
                                                                                                                                                                                        ( ( ( in @ X3 @ X1 )
                                                                                                                                                                                         => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                           => X4 ) )
                                                                                                                                                                                       => ( ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                           => ( ( in @ X3 @ X2 )
                                                                                                                                                                                             => X4 ) )
                                                                                                                                                                                         => X4 ) ) )
                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                     => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                       => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                        ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                       => ( ( in @ X3 @ X2 )
                                                                                                                                                                                         => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                         => ( ( in @ X3 @ X2 )
                                                                                                                                                                                           => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                            ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                           => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                             => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                        ( ( in @ X2 @ X1 )
                                                                                                                                                                                                       => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                          ( ( in @ X2 @ X1 )
                                                                                                                                                                                                         => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                           => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                              ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                             => ( ( X3 != X1 )
                                                                                                                                                                                                               => ( X3 = X2 ) ) )
                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                   => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                     => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                       => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                         => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                           => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                             => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                            ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                           => ~ ! [X4: $i] :
                                                                                                                                                                                                                                  ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                 => ! [X5: $i] :
                                                                                                                                                                                                                                      ( ( in @ X5 @ X2 )
                                                                                                                                                                                                                                     => ( X3
                                                                                                                                                                                                                                       != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                                                                                                                       => ( sP5
                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                                                                                                                               => ~ ! [X3: $i] :
                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                     => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                                                                                                                           => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                                                                                                                             => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                               => ( ! [X1: $i] :
                                                                                                                                                                                                                                      ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                                                                                                                      = X1 )
                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                        ( ! [X3: $i] :
                                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                                                                                                ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                               => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                 => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                   => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                                       => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                               => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                                         => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                               => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                 != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                          ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                               => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                 != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                                                                                                                         => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                               => ~ ( X2 @ X3 ) ) )
                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                           => ( ( X2 @ X3 )
                                                                                                                                                                                                                                             => ( ! [X4: $i] :
                                                                                                                                                                                                                                                    ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                   => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                     => ( X4 = X3 ) ) )
                                                                                                                                                                                                                                               => ~ ! [X4: $i] :
                                                                                                                                                                                                                                                      ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                     => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                       != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                              ( ! [X3: $i] :
                                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                                                                                                      ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                     => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                       => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                         => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                                             => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                     => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                                               => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                      ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                     => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                       != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                                                                                                                  = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                               => ( X1 = X2 ) )
                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                  ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                 => ( X1 = X3 ) )
                                                                                                                                                                                                                                             => ( ! [X1: $i] :
                                                                                                                                                                                                                                                    ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                   => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                          ( ( in @ X2
                                                                                                                                                                                                                                                            @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                              @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                                                                                                                         => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                              @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                                                           != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                               => ( ! [X1: $i] :
                                                                                                                                                                                                                                                      ( ~ ! [X2: $i] :
                                                                                                                                                                                                                                                            ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                                           => ( X1
                                                                                                                                                                                                                                                             != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                                     => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                        ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                        = X1 )
                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                         => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                            ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                              = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                           => ( X1 = X3 ) )
                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                              ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                                = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                             => ( X1 = X3 ) )
                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                ( ( X1 = X2 )
                                                                                                                                                                                                                                                               => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                  = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                  ( ( X1 = X2 )
                                                                                                                                                                                                                                                                 => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                    = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                    ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                      = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                   => ( ( X3 = X4 )
                                                                                                                                                                                                                                                                     => ( X2 = X4 ) ) )
                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                      ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                        = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                                                                                                                     => ( X1 = X2 ) )
                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                        ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                          = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                       => ( X2 = X4 ) )
                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                          ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                                            = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                         => ( X2 = X4 ) )
                                                                                                                                                                                                                                                                     => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                            ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                                           => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                  ( ( in @ X2
                                                                                                                                                                                                                                                                                    @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                      @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                                          ( X1
                                                                                                                                                                                                                                                                                          = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                                                                                                                 => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                      @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                                          ( X1
                                                                                                                                                                                                                                                                                          = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                                                                                                                   != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                              ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                              = X2 )
                                                                                                                                                                                                                                                                         => ( sP8
                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                  ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                 => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                    ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                   => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                      ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                     => ( in @ X4 @ X2 ) )
                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                           => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                              = X3 ) ) )
                                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                             => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                = X4 ) ) )
                                                                                                                                                                                                                                                                                     => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                         => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                                                                                                                            = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h62,assumption,
    ! [X1: $i] :
      ( ( dsetconstr @ X1
        @ ^ [X2: $i] : ~ $false )
      = X1 ),
    introduced(assumption,[]) ).

thf(h63,assumption,
    ~ ( ! [X1: $i,X2: $i] :
          ( ! [X3: $i] :
              ( ( in @ X3 @ X2 )
             => ( in @ X3 @ X1 ) )
         => ( in @ X2 @ ( powerset @ X1 ) ) )
     => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
       => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
         => ( ! [X1: $i,X2: $i,X3: $i] :
                ( ( in @ X2 @ ( powerset @ X1 ) )
               => ( ( in @ X3 @ X2 )
                 => ( in @ X3 @ X1 ) ) )
           => ( ! [X1: $i,X2: $i,X3: $i] :
                  ( ( in @ X2 @ X3 )
                 => ( ( in @ X3 @ X1 )
                   => ( in @ X2 @ ( setunion @ X1 ) ) ) )
             => ( ! [X1: $i,X2: $i] :
                    ( ( in @ X2 @ ( setunion @ X1 ) )
                   => ! [X3: $o] :
                        ( ! [X4: $i] :
                            ( ( in @ X2 @ X4 )
                           => ( ( in @ X4 @ X1 )
                             => X3 ) )
                       => X3 ) )
               => ( ! [X1: $i,X2: $i] :
                      ( ( in @ X2 @ X1 )
                     => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
                 => ( ! [X1: $i > $o] :
                        ( ~ ! [X2: $i] :
                              ( ( X1 @ X2 )
                             => ~ ! [X3: $i] :
                                    ( ( X1 @ X3 )
                                   => ( X2 = X3 ) ) )
                       => ~ ! [X2: $i] :
                              ~ ! [X3: $i] :
                                  ( ( X1 @ X3 )
                                  = ( X3 = X2 ) ) )
                   => ( ! [X1: $i] :
                          ( ( X1 != emptyset )
                         => ~ ! [X2: $i] :
                                ~ ( in @ X2 @ X1 ) )
                     => ( ! [X1: $i,X2: $i] :
                            ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                           => ( X1 = X2 ) )
                       => ( ! [X1: $i,X2: $i] :
                              ( ( X1 != X2 )
                             => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                         => ( ! [X1: $i,X2: $i] :
                                ( ( X1 = X2 )
                               => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                           => ( ! [X1: $i,X2: $i] :
                                  ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                 => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                    ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                   => ( ( X3 != X1 )
                                     => ( X3 = X2 ) ) )
                               => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                 => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                   => ( ! [X1: $i,X2: $i > $o] :
                                          ( ~ ! [X3: $i] :
                                                ( ( in @ X3 @ X1 )
                                               => ~ ( X2 @ X3 ) )
                                         => ( ( dsetconstr @ X1 @ X2 )
                                           != emptyset ) )
                                     => ( ! [X1: $i > $o,X2: $i] :
                                            ( ( in @ X2 @ emptyset )
                                           => ( X1 @ X2 ) )
                                       => ( ! [X1: $o] :
                                              ( X1
                                             => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                         => ( ! [X1: $o] :
                                                ( X1
                                               => ( set2prop @ ( prop2set @ X1 ) ) )
                                           => ( ! [X1: $i > $o] :
                                                  ( ~ ! [X2: $i] :
                                                        ~ ( X1 @ X2 )
                                                 => ( ! [X2: $i,X3: $i] :
                                                        ( ( X1 @ X2 )
                                                       => ( ( X1 @ X3 )
                                                         => ( X2 = X3 ) ) )
                                                   => ~ ! [X2: $i] :
                                                          ( ( X1 @ X2 )
                                                         => ~ ! [X3: $i] :
                                                                ( ( X1 @ X3 )
                                                               => ( X2 = X3 ) ) ) ) )
                                             => ( ! [X1: $i > $o] :
                                                    ( ~ ! [X2: $i] :
                                                          ~ ! [X3: $i] :
                                                              ( ( X1 @ X3 )
                                                              = ( X3 = X2 ) )
                                                   => ~ ! [X2: $i] :
                                                          ( ( X1 @ X2 )
                                                         => ~ ! [X3: $i] :
                                                                ( ( X1 @ X3 )
                                                               => ( X2 = X3 ) ) ) )
                                               => ( ! [X1: $i,X2: $i] :
                                                      ( ( X1 = X2 )
                                                     => ! [X3: $i,X4: $i] :
                                                          ( ( X3 = X4 )
                                                         => ( ( in @ X3 @ X1 )
                                                           => ( in @ X4 @ X2 ) ) ) )
                                                 => ( ! [X1: $i,X2: $i] :
                                                        ( ( X1 = X2 )
                                                       => ! [X3: $i,X4: $i] :
                                                            ( ( X3 = X4 )
                                                           => ( ( in @ X3 @ X1 )
                                                              = ( in @ X4 @ X2 ) ) ) )
                                                   => ( ! [X1: $i > $o] :
                                                          ( ~ ! [X2: $i] :
                                                                ( ( X1 @ X2 )
                                                               => ~ ! [X3: $i] :
                                                                      ( ( X1 @ X3 )
                                                                     => ( X2 = X3 ) ) )
                                                         => ! [X2: $i,X3: $i] :
                                                              ( ( X1 @ X2 )
                                                             => ( ( X1 @ X3 )
                                                               => ( X2 = X3 ) ) ) )
                                                     => ( ! [X1: $i > $o,X2: $i > $o] :
                                                            ( ! [X3: $i,X4: $i] :
                                                                ( ( X3 = X4 )
                                                               => ( ( X1 @ X3 )
                                                                  = ( X2 @ X4 ) ) )
                                                           => ( ( ~ ! [X3: $i] :
                                                                      ( ( X1 @ X3 )
                                                                     => ~ ! [X4: $i] :
                                                                            ( ( X1 @ X4 )
                                                                           => ( X3 = X4 ) ) ) )
                                                              = ( ~ ! [X3: $i] :
                                                                      ( ( X2 @ X3 )
                                                                     => ~ ! [X4: $i] :
                                                                            ( ( X2 @ X4 )
                                                                           => ( X3 = X4 ) ) ) ) ) )
                                                       => ( ! [X1: $i,X2: $i] :
                                                              ( ( X1 = X2 )
                                                             => ! [X3: $i,X4: $i] :
                                                                  ( ( X3 = X4 )
                                                                 => ( ( setadjoin @ X1 @ X3 )
                                                                    = ( setadjoin @ X2 @ X4 ) ) ) )
                                                         => ( ! [X1: $i,X2: $i] :
                                                                ( ( X1 = X2 )
                                                               => ( ( powerset @ X1 )
                                                                  = ( powerset @ X2 ) ) )
                                                           => ( ! [X1: $i,X2: $i] :
                                                                  ( ( X1 = X2 )
                                                                 => ( ( setunion @ X1 )
                                                                    = ( setunion @ X2 ) ) )
                                                             => ( ! [X1: $i > $o] :
                                                                    ( ~ ! [X2: $i] :
                                                                          ( ( X1 @ X2 )
                                                                         => ~ ! [X3: $i] :
                                                                                ( ( X1 @ X3 )
                                                                               => ( X2 = X3 ) ) )
                                                                   => ! [X2: $i,X3: $i] :
                                                                        ( ( X1 @ X2 )
                                                                       => ( ( X1 @ X3 )
                                                                         => ( X2 = X3 ) ) ) )
                                                               => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                      ( ! [X3: $i,X4: $i] :
                                                                          ( ( X3 = X4 )
                                                                         => ( ( X1 @ X3 )
                                                                            = ( X2 @ X4 ) ) )
                                                                     => ( ~ ! [X3: $i] :
                                                                              ( ( X1 @ X3 )
                                                                             => ~ ! [X4: $i] :
                                                                                    ( ( X1 @ X4 )
                                                                                   => ( X3 = X4 ) ) )
                                                                       => ( ~ ! [X3: $i] :
                                                                                ( ( X2 @ X3 )
                                                                               => ~ ! [X4: $i] :
                                                                                      ( ( X2 @ X4 )
                                                                                     => ( X3 = X4 ) ) )
                                                                         => ( ( descr @ X1 )
                                                                            = ( descr @ X2 ) ) ) ) )
                                                                 => ( ! [X1: $i,X2: $i] :
                                                                        ( ( X1 = X2 )
                                                                       => ! [X3: $i > $o,X4: $i > $o] :
                                                                            ( ! [X5: $i] :
                                                                                ( ( in @ X5 @ X1 )
                                                                               => ! [X6: $i] :
                                                                                    ( ( in @ X6 @ X2 )
                                                                                   => ( ( X5 = X6 )
                                                                                     => ( ( X3 @ X5 )
                                                                                        = ( X4 @ X6 ) ) ) ) )
                                                                           => ( ( dsetconstr @ X1 @ X3 )
                                                                              = ( dsetconstr @ X2 @ X4 ) ) ) )
                                                                   => ( ! [X1: $i,X2: $i] :
                                                                          ( ! [X3: $i] :
                                                                              ( ( in @ X3 @ X1 )
                                                                             => ( in @ X3 @ X2 ) )
                                                                         => ( subset @ X1 @ X2 ) )
                                                                     => ( ! [X1: $i,X2: $i] :
                                                                            ( ( X1 = X2 )
                                                                           => ( subset @ X2 @ X1 ) )
                                                                       => ( ! [X1: $i,X2: $i] :
                                                                              ( ( X1 = X2 )
                                                                             => ( subset @ X1 @ X2 ) )
                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                ( ! [X3: $i] :
                                                                                    ( ( in @ X3 @ X1 )
                                                                                   => ( in @ X3 @ X2 ) )
                                                                               => ( subset @ X1 @ X2 ) )
                                                                           => ( ! [X1: $i] : ( subset @ emptyset @ X1 )
                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                    ( ( subset @ X1 @ X2 )
                                                                                   => ( ( in @ X3 @ X1 )
                                                                                     => ( in @ X3 @ X2 ) ) )
                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                      ( ( subset @ X1 @ X2 )
                                                                                     => ( ~ ( in @ X3 @ X2 )
                                                                                       => ~ ( in @ X3 @ X1 ) ) )
                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                        ( ( in @ X3 @ X1 )
                                                                                       => ( ~ ( in @ X3 @ X2 )
                                                                                         => ~ ( subset @ X1 @ X2 ) ) )
                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                          ( ~ ( subset @ X1 @ X2 )
                                                                                         => ( X1 != X2 ) )
                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                            ( ( in @ X3 @ X1 )
                                                                                           => ( ~ ( in @ X3 @ X2 )
                                                                                             => ( X1 != X2 ) ) )
                                                                                       => ( ! [X1: $i] : ( subset @ X1 @ X1 )
                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                ( ( subset @ X1 @ X2 )
                                                                                               => ( ( subset @ X2 @ X3 )
                                                                                                 => ( subset @ X1 @ X3 ) ) )
                                                                                           => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) )
                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                    ( ( subset @ X1 @ X3 )
                                                                                                   => ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                      ( ( subset @ X1 @ X2 )
                                                                                                     => ( in @ X1 @ ( powerset @ X2 ) ) )
                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                        ( ( subset @ X1 @ X2 )
                                                                                                       => ( ( subset @ X2 @ X1 )
                                                                                                         => ( X1 = X2 ) ) )
                                                                                                   => ( ! [X1: $i] :
                                                                                                          ( ( subset @ X1 @ emptyset )
                                                                                                         => ( X1 = emptyset ) )
                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                            ( ( subset @ X2 @ X1 )
                                                                                                           => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                              ( ( in @ X2 @ ( powerset @ X1 ) )
                                                                                                             => ( subset @ X2 @ X1 ) )
                                                                                                         => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                  ( ( subset @ X1 @ X2 )
                                                                                                                 => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
                                                                                                             => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                                                                                                               => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                       => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                                   => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                            ( ( in @ X3 @ X2 )
                                                                                                                           => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                                                                                                              ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                             => ( ( ( in @ X3 @ X1 )
                                                                                                                                 => X4 )
                                                                                                                               => ( ( ( in @ X3 @ X2 )
                                                                                                                                   => X4 )
                                                                                                                                 => X4 ) ) )
                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                               => ( ~ ( in @ X3 @ X1 )
                                                                                                                                 => ( in @ X3 @ X2 ) ) )
                                                                                                                           => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                                                                                                                             => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                     => ( ( in @ X3 @ X2 )
                                                                                                                                       => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                        ( ( subset @ X3 @ X1 )
                                                                                                                                       => ( ( subset @ X3 @ X2 )
                                                                                                                                         => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                          ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                         => ( in @ X3 @ X1 ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                              ( ( subset @ X1 @ X2 )
                                                                                                                                             => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                = X1 ) )
                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                                  = X2 )
                                                                                                                                               => ( subset @ X2 @ X1 ) )
                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                  ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                                 => ( in @ X3 @ X2 ) )
                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                    ( ! [X3: $i] :
                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                       => ~ ( in @ X3 @ X2 ) )
                                                                                                                                                   => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                      = emptyset ) )
                                                                                                                                               => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                        ( ( subset @ X2 @ X1 )
                                                                                                                                                       => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                          = X2 ) )
                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                          ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                                            = X1 )
                                                                                                                                                         => ( subset @ X1 @ X2 ) )
                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                            ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                                                                                                                            = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                             => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                               => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                               => ( in @ X3 @ X1 ) )
                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                  ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                 => ~ ( in @ X3 @ X2 ) )
                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                    ( ( subset @ X1 @ X2 )
                                                                                                                                                                   => ( ( setminus @ X1 @ X2 )
                                                                                                                                                                      = emptyset ) )
                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                      ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                     => ( ( in @ X3 @ X1 )
                                                                                                                                                                       => ( in @ X3 @ X2 ) ) )
                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                        ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                       => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                         => ~ ( in @ X3 @ X1 ) ) )
                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                          ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                         => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                            ( ( in @ X3 @ X2 )
                                                                                                                                                                           => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                                       => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                ( ( ( setminus @ X1 @ X2 )
                                                                                                                                                                                  = emptyset )
                                                                                                                                                                               => ( subset @ X1 @ X2 ) )
                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                  ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                                                                                                                 => ! [X4: $o] :
                                                                                                                                                                                      ( ( ( in @ X3 @ X1 )
                                                                                                                                                                                       => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                         => X4 ) )
                                                                                                                                                                                     => ( ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                         => ( ( in @ X3 @ X2 )
                                                                                                                                                                                           => X4 ) )
                                                                                                                                                                                       => X4 ) ) )
                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                   => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                     => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                      ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                     => ( ( in @ X3 @ X2 )
                                                                                                                                                                                       => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                       => ( ( in @ X3 @ X2 )
                                                                                                                                                                                         => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                          ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                         => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                           => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                      ( ( in @ X2 @ X1 )
                                                                                                                                                                                                     => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                        ( ( in @ X2 @ X1 )
                                                                                                                                                                                                       => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                         => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                            ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                           => ( ( X3 != X1 )
                                                                                                                                                                                                             => ( X3 = X2 ) ) )
                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                 => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                   => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                     => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                       => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                         => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                           => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                         => ~ ! [X4: $i] :
                                                                                                                                                                                                                                ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                               => ! [X5: $i] :
                                                                                                                                                                                                                                    ( ( in @ X5 @ X2 )
                                                                                                                                                                                                                                   => ( X3
                                                                                                                                                                                                                                     != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                                                                                                                     => ( sP5
                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                              ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                                                                                                                             => ~ ! [X3: $i] :
                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                   => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                                                                                                                         => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                                                                                                                           => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                             => ( ! [X1: $i] :
                                                                                                                                                                                                                                    ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                                                                                                                    = X1 )
                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                      ( ! [X3: $i] :
                                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                                                                                              ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                             => ( ( X2 @ X3 )
                                                                                                                                                                                                                                               => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                 => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                                     => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                             => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                                       => ~ ! [X3: $i] :
                                                                                                                                                                                                                                              ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                             => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                               != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                        ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                              ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                             => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                               != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                                                                                                                       => ~ ! [X3: $i] :
                                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                             => ~ ( X2 @ X3 ) ) )
                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                         => ( ( X2 @ X3 )
                                                                                                                                                                                                                                           => ( ! [X4: $i] :
                                                                                                                                                                                                                                                  ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                 => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                   => ( X4 = X3 ) ) )
                                                                                                                                                                                                                                             => ~ ! [X4: $i] :
                                                                                                                                                                                                                                                    ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                   => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                     != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                            ( ! [X3: $i] :
                                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                                                                                    ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                   => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                     => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                       => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                                           => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                   => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                                             => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                    ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                   => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                     != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                              ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                                                                                                                = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                             => ( X1 = X2 ) )
                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                               => ( X1 = X3 ) )
                                                                                                                                                                                                                                           => ( ! [X1: $i] :
                                                                                                                                                                                                                                                  ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                 => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                        ( ( in @ X2
                                                                                                                                                                                                                                                          @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                            @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                                                                                                                       => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                            @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                                                         != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                             => ( ! [X1: $i] :
                                                                                                                                                                                                                                                    ( ~ ! [X2: $i] :
                                                                                                                                                                                                                                                          ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                                         => ( X1
                                                                                                                                                                                                                                                           != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                                   => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                      ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                      = X1 )
                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                       => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                          ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                            = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                         => ( X1 = X3 ) )
                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                            ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                              = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                           => ( X1 = X3 ) )
                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                              ( ( X1 = X2 )
                                                                                                                                                                                                                                                             => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                ( ( X1 = X2 )
                                                                                                                                                                                                                                                               => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                  = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                  ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                    = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                 => ( ( X3 = X4 )
                                                                                                                                                                                                                                                                   => ( X2 = X4 ) ) )
                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                    ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                      = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                                                                                                                   => ( X1 = X2 ) )
                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                      ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                        = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                     => ( X2 = X4 ) )
                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                        ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                                          = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                       => ( X2 = X4 ) )
                                                                                                                                                                                                                                                                   => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                          ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                                         => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                ( ( in @ X2
                                                                                                                                                                                                                                                                                  @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                    @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                                        ( X1
                                                                                                                                                                                                                                                                                        = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                                                                                                               => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                    @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                                        ( X1
                                                                                                                                                                                                                                                                                        = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                                                                                                                 != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                            ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                            = X2 )
                                                                                                                                                                                                                                                                       => ( sP8
                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                               => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                  ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                 => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                    ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                   => ( in @ X4 @ X2 ) )
                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                         => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                            = X3 ) ) )
                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                           => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                              = X4 ) ) )
                                                                                                                                                                                                                                                                                   => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                       => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                                                                                                                          = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h64,assumption,
    ! [X1: $i,X2: $i] :
      ( ! [X3: $i] :
          ( ( in @ X3 @ X2 )
         => ( in @ X3 @ X1 ) )
     => ( in @ X2 @ ( powerset @ X1 ) ) ),
    introduced(assumption,[]) ).

thf(h65,assumption,
    ~ ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
     => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
       => ( ! [X1: $i,X2: $i,X3: $i] :
              ( ( in @ X2 @ ( powerset @ X1 ) )
             => ( ( in @ X3 @ X2 )
               => ( in @ X3 @ X1 ) ) )
         => ( ! [X1: $i,X2: $i,X3: $i] :
                ( ( in @ X2 @ X3 )
               => ( ( in @ X3 @ X1 )
                 => ( in @ X2 @ ( setunion @ X1 ) ) ) )
           => ( ! [X1: $i,X2: $i] :
                  ( ( in @ X2 @ ( setunion @ X1 ) )
                 => ! [X3: $o] :
                      ( ! [X4: $i] :
                          ( ( in @ X2 @ X4 )
                         => ( ( in @ X4 @ X1 )
                           => X3 ) )
                     => X3 ) )
             => ( ! [X1: $i,X2: $i] :
                    ( ( in @ X2 @ X1 )
                   => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
               => ( ! [X1: $i > $o] :
                      ( ~ ! [X2: $i] :
                            ( ( X1 @ X2 )
                           => ~ ! [X3: $i] :
                                  ( ( X1 @ X3 )
                                 => ( X2 = X3 ) ) )
                     => ~ ! [X2: $i] :
                            ~ ! [X3: $i] :
                                ( ( X1 @ X3 )
                                = ( X3 = X2 ) ) )
                 => ( ! [X1: $i] :
                        ( ( X1 != emptyset )
                       => ~ ! [X2: $i] :
                              ~ ( in @ X2 @ X1 ) )
                   => ( ! [X1: $i,X2: $i] :
                          ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                         => ( X1 = X2 ) )
                     => ( ! [X1: $i,X2: $i] :
                            ( ( X1 != X2 )
                           => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                       => ( ! [X1: $i,X2: $i] :
                              ( ( X1 = X2 )
                             => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                         => ( ! [X1: $i,X2: $i] :
                                ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                               => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                  ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                 => ( ( X3 != X1 )
                                   => ( X3 = X2 ) ) )
                             => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                               => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                 => ( ! [X1: $i,X2: $i > $o] :
                                        ( ~ ! [X3: $i] :
                                              ( ( in @ X3 @ X1 )
                                             => ~ ( X2 @ X3 ) )
                                       => ( ( dsetconstr @ X1 @ X2 )
                                         != emptyset ) )
                                   => ( ! [X1: $i > $o,X2: $i] :
                                          ( ( in @ X2 @ emptyset )
                                         => ( X1 @ X2 ) )
                                     => ( ! [X1: $o] :
                                            ( X1
                                           => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                       => ( ! [X1: $o] :
                                              ( X1
                                             => ( set2prop @ ( prop2set @ X1 ) ) )
                                         => ( ! [X1: $i > $o] :
                                                ( ~ ! [X2: $i] :
                                                      ~ ( X1 @ X2 )
                                               => ( ! [X2: $i,X3: $i] :
                                                      ( ( X1 @ X2 )
                                                     => ( ( X1 @ X3 )
                                                       => ( X2 = X3 ) ) )
                                                 => ~ ! [X2: $i] :
                                                        ( ( X1 @ X2 )
                                                       => ~ ! [X3: $i] :
                                                              ( ( X1 @ X3 )
                                                             => ( X2 = X3 ) ) ) ) )
                                           => ( ! [X1: $i > $o] :
                                                  ( ~ ! [X2: $i] :
                                                        ~ ! [X3: $i] :
                                                            ( ( X1 @ X3 )
                                                            = ( X3 = X2 ) )
                                                 => ~ ! [X2: $i] :
                                                        ( ( X1 @ X2 )
                                                       => ~ ! [X3: $i] :
                                                              ( ( X1 @ X3 )
                                                             => ( X2 = X3 ) ) ) )
                                             => ( ! [X1: $i,X2: $i] :
                                                    ( ( X1 = X2 )
                                                   => ! [X3: $i,X4: $i] :
                                                        ( ( X3 = X4 )
                                                       => ( ( in @ X3 @ X1 )
                                                         => ( in @ X4 @ X2 ) ) ) )
                                               => ( ! [X1: $i,X2: $i] :
                                                      ( ( X1 = X2 )
                                                     => ! [X3: $i,X4: $i] :
                                                          ( ( X3 = X4 )
                                                         => ( ( in @ X3 @ X1 )
                                                            = ( in @ X4 @ X2 ) ) ) )
                                                 => ( ! [X1: $i > $o] :
                                                        ( ~ ! [X2: $i] :
                                                              ( ( X1 @ X2 )
                                                             => ~ ! [X3: $i] :
                                                                    ( ( X1 @ X3 )
                                                                   => ( X2 = X3 ) ) )
                                                       => ! [X2: $i,X3: $i] :
                                                            ( ( X1 @ X2 )
                                                           => ( ( X1 @ X3 )
                                                             => ( X2 = X3 ) ) ) )
                                                   => ( ! [X1: $i > $o,X2: $i > $o] :
                                                          ( ! [X3: $i,X4: $i] :
                                                              ( ( X3 = X4 )
                                                             => ( ( X1 @ X3 )
                                                                = ( X2 @ X4 ) ) )
                                                         => ( ( ~ ! [X3: $i] :
                                                                    ( ( X1 @ X3 )
                                                                   => ~ ! [X4: $i] :
                                                                          ( ( X1 @ X4 )
                                                                         => ( X3 = X4 ) ) ) )
                                                            = ( ~ ! [X3: $i] :
                                                                    ( ( X2 @ X3 )
                                                                   => ~ ! [X4: $i] :
                                                                          ( ( X2 @ X4 )
                                                                         => ( X3 = X4 ) ) ) ) ) )
                                                     => ( ! [X1: $i,X2: $i] :
                                                            ( ( X1 = X2 )
                                                           => ! [X3: $i,X4: $i] :
                                                                ( ( X3 = X4 )
                                                               => ( ( setadjoin @ X1 @ X3 )
                                                                  = ( setadjoin @ X2 @ X4 ) ) ) )
                                                       => ( ! [X1: $i,X2: $i] :
                                                              ( ( X1 = X2 )
                                                             => ( ( powerset @ X1 )
                                                                = ( powerset @ X2 ) ) )
                                                         => ( ! [X1: $i,X2: $i] :
                                                                ( ( X1 = X2 )
                                                               => ( ( setunion @ X1 )
                                                                  = ( setunion @ X2 ) ) )
                                                           => ( ! [X1: $i > $o] :
                                                                  ( ~ ! [X2: $i] :
                                                                        ( ( X1 @ X2 )
                                                                       => ~ ! [X3: $i] :
                                                                              ( ( X1 @ X3 )
                                                                             => ( X2 = X3 ) ) )
                                                                 => ! [X2: $i,X3: $i] :
                                                                      ( ( X1 @ X2 )
                                                                     => ( ( X1 @ X3 )
                                                                       => ( X2 = X3 ) ) ) )
                                                             => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                    ( ! [X3: $i,X4: $i] :
                                                                        ( ( X3 = X4 )
                                                                       => ( ( X1 @ X3 )
                                                                          = ( X2 @ X4 ) ) )
                                                                   => ( ~ ! [X3: $i] :
                                                                            ( ( X1 @ X3 )
                                                                           => ~ ! [X4: $i] :
                                                                                  ( ( X1 @ X4 )
                                                                                 => ( X3 = X4 ) ) )
                                                                     => ( ~ ! [X3: $i] :
                                                                              ( ( X2 @ X3 )
                                                                             => ~ ! [X4: $i] :
                                                                                    ( ( X2 @ X4 )
                                                                                   => ( X3 = X4 ) ) )
                                                                       => ( ( descr @ X1 )
                                                                          = ( descr @ X2 ) ) ) ) )
                                                               => ( ! [X1: $i,X2: $i] :
                                                                      ( ( X1 = X2 )
                                                                     => ! [X3: $i > $o,X4: $i > $o] :
                                                                          ( ! [X5: $i] :
                                                                              ( ( in @ X5 @ X1 )
                                                                             => ! [X6: $i] :
                                                                                  ( ( in @ X6 @ X2 )
                                                                                 => ( ( X5 = X6 )
                                                                                   => ( ( X3 @ X5 )
                                                                                      = ( X4 @ X6 ) ) ) ) )
                                                                         => ( ( dsetconstr @ X1 @ X3 )
                                                                            = ( dsetconstr @ X2 @ X4 ) ) ) )
                                                                 => ( ! [X1: $i,X2: $i] :
                                                                        ( ! [X3: $i] :
                                                                            ( ( in @ X3 @ X1 )
                                                                           => ( in @ X3 @ X2 ) )
                                                                       => ( subset @ X1 @ X2 ) )
                                                                   => ( ! [X1: $i,X2: $i] :
                                                                          ( ( X1 = X2 )
                                                                         => ( subset @ X2 @ X1 ) )
                                                                     => ( ! [X1: $i,X2: $i] :
                                                                            ( ( X1 = X2 )
                                                                           => ( subset @ X1 @ X2 ) )
                                                                       => ( ! [X1: $i,X2: $i] :
                                                                              ( ! [X3: $i] :
                                                                                  ( ( in @ X3 @ X1 )
                                                                                 => ( in @ X3 @ X2 ) )
                                                                             => ( subset @ X1 @ X2 ) )
                                                                         => ( ! [X1: $i] : ( subset @ emptyset @ X1 )
                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                  ( ( subset @ X1 @ X2 )
                                                                                 => ( ( in @ X3 @ X1 )
                                                                                   => ( in @ X3 @ X2 ) ) )
                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                    ( ( subset @ X1 @ X2 )
                                                                                   => ( ~ ( in @ X3 @ X2 )
                                                                                     => ~ ( in @ X3 @ X1 ) ) )
                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                      ( ( in @ X3 @ X1 )
                                                                                     => ( ~ ( in @ X3 @ X2 )
                                                                                       => ~ ( subset @ X1 @ X2 ) ) )
                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                        ( ~ ( subset @ X1 @ X2 )
                                                                                       => ( X1 != X2 ) )
                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                          ( ( in @ X3 @ X1 )
                                                                                         => ( ~ ( in @ X3 @ X2 )
                                                                                           => ( X1 != X2 ) ) )
                                                                                     => ( ! [X1: $i] : ( subset @ X1 @ X1 )
                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                              ( ( subset @ X1 @ X2 )
                                                                                             => ( ( subset @ X2 @ X3 )
                                                                                               => ( subset @ X1 @ X3 ) ) )
                                                                                         => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) )
                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                  ( ( subset @ X1 @ X3 )
                                                                                                 => ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                    ( ( subset @ X1 @ X2 )
                                                                                                   => ( in @ X1 @ ( powerset @ X2 ) ) )
                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                      ( ( subset @ X1 @ X2 )
                                                                                                     => ( ( subset @ X2 @ X1 )
                                                                                                       => ( X1 = X2 ) ) )
                                                                                                 => ( ! [X1: $i] :
                                                                                                        ( ( subset @ X1 @ emptyset )
                                                                                                       => ( X1 = emptyset ) )
                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                          ( ( subset @ X2 @ X1 )
                                                                                                         => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                            ( ( in @ X2 @ ( powerset @ X1 ) )
                                                                                                           => ( subset @ X2 @ X1 ) )
                                                                                                       => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                ( ( subset @ X1 @ X2 )
                                                                                                               => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
                                                                                                           => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                                                                                                             => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                     => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                                 => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                          ( ( in @ X3 @ X2 )
                                                                                                                         => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                                                                                                            ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                           => ( ( ( in @ X3 @ X1 )
                                                                                                                               => X4 )
                                                                                                                             => ( ( ( in @ X3 @ X2 )
                                                                                                                                 => X4 )
                                                                                                                               => X4 ) ) )
                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                              ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                             => ( ~ ( in @ X3 @ X1 )
                                                                                                                               => ( in @ X3 @ X2 ) ) )
                                                                                                                         => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                                                                                                                           => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                   => ( ( in @ X3 @ X2 )
                                                                                                                                     => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                      ( ( subset @ X3 @ X1 )
                                                                                                                                     => ( ( subset @ X3 @ X2 )
                                                                                                                                       => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                        ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                       => ( in @ X3 @ X1 ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                            ( ( subset @ X1 @ X2 )
                                                                                                                                           => ( ( binintersect @ X1 @ X2 )
                                                                                                                                              = X1 ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                              ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                                = X2 )
                                                                                                                                             => ( subset @ X2 @ X1 ) )
                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                               => ( in @ X3 @ X2 ) )
                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                  ( ! [X3: $i] :
                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                     => ~ ( in @ X3 @ X2 ) )
                                                                                                                                                 => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                    = emptyset ) )
                                                                                                                                             => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                      ( ( subset @ X2 @ X1 )
                                                                                                                                                     => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                        = X2 ) )
                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                        ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                                          = X1 )
                                                                                                                                                       => ( subset @ X1 @ X2 ) )
                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                          ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                                                                                                                          = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                           => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                             => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                              ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                             => ( in @ X3 @ X1 ) )
                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                               => ~ ( in @ X3 @ X2 ) )
                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                  ( ( subset @ X1 @ X2 )
                                                                                                                                                                 => ( ( setminus @ X1 @ X2 )
                                                                                                                                                                    = emptyset ) )
                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                    ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                   => ( ( in @ X3 @ X1 )
                                                                                                                                                                     => ( in @ X3 @ X2 ) ) )
                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                      ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                     => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                       => ~ ( in @ X3 @ X1 ) ) )
                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                        ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                       => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                          ( ( in @ X3 @ X2 )
                                                                                                                                                                         => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                                     => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                              ( ( ( setminus @ X1 @ X2 )
                                                                                                                                                                                = emptyset )
                                                                                                                                                                             => ( subset @ X1 @ X2 ) )
                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                                                                                                               => ! [X4: $o] :
                                                                                                                                                                                    ( ( ( in @ X3 @ X1 )
                                                                                                                                                                                     => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                       => X4 ) )
                                                                                                                                                                                   => ( ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                       => ( ( in @ X3 @ X2 )
                                                                                                                                                                                         => X4 ) )
                                                                                                                                                                                     => X4 ) ) )
                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                 => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                   => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                    ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                   => ( ( in @ X3 @ X2 )
                                                                                                                                                                                     => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                     => ( ( in @ X3 @ X2 )
                                                                                                                                                                                       => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                        ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                       => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                         => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                    ( ( in @ X2 @ X1 )
                                                                                                                                                                                                   => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                      ( ( in @ X2 @ X1 )
                                                                                                                                                                                                     => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                       => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                          ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                         => ( ( X3 != X1 )
                                                                                                                                                                                                           => ( X3 = X2 ) ) )
                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                                                                                                               => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                 => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                   => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                     => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                       => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                         => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                       => ~ ! [X4: $i] :
                                                                                                                                                                                                                              ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                             => ! [X5: $i] :
                                                                                                                                                                                                                                  ( ( in @ X5 @ X2 )
                                                                                                                                                                                                                                 => ( X3
                                                                                                                                                                                                                                   != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                                                                                                                   => ( sP5
                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                            ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                                                                                                                           => ~ ! [X3: $i] :
                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                 => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                                                                                                                       => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                                                                                                                         => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                           => ( ! [X1: $i] :
                                                                                                                                                                                                                                  ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                                                                                                                  = X1 )
                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                    ( ! [X3: $i] :
                                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                                                                                            ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                           => ( ( X2 @ X3 )
                                                                                                                                                                                                                                             => ( ( X2 @ X4 )
                                                                                                                                                                                                                                               => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                                   => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                           => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                                     => ~ ! [X3: $i] :
                                                                                                                                                                                                                                            ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                           => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                             != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                      ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                            ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                           => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                             != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                                                                                                                     => ~ ! [X3: $i] :
                                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                           => ~ ( X2 @ X3 ) ) )
                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                       => ( ( X2 @ X3 )
                                                                                                                                                                                                                                         => ( ! [X4: $i] :
                                                                                                                                                                                                                                                ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                               => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                 => ( X4 = X3 ) ) )
                                                                                                                                                                                                                                           => ~ ! [X4: $i] :
                                                                                                                                                                                                                                                  ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                 => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                   != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                          ( ! [X3: $i] :
                                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                                                                                  ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                 => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                   => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                     => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                                         => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                 => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                                           => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                  ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                 => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                   != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                            ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                                                                                                              = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                           => ( X1 = X2 ) )
                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                              ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                             => ( X1 = X3 ) )
                                                                                                                                                                                                                                         => ( ! [X1: $i] :
                                                                                                                                                                                                                                                ( ( iskpair @ X1 )
                                                                                                                                                                                                                                               => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                      ( ( in @ X2
                                                                                                                                                                                                                                                        @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                          @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                                                                                                                     => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                          @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                                                       != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                           => ( ! [X1: $i] :
                                                                                                                                                                                                                                                  ( ~ ! [X2: $i] :
                                                                                                                                                                                                                                                        ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                                       => ( X1
                                                                                                                                                                                                                                                         != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                                 => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                    ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                    = X1 )
                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                      ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                     => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                        ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                          = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                       => ( X1 = X3 ) )
                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                          ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                            = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                         => ( X1 = X3 ) )
                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                            ( ( X1 = X2 )
                                                                                                                                                                                                                                                           => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                              = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                              ( ( X1 = X2 )
                                                                                                                                                                                                                                                             => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                  = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                               => ( ( X3 = X4 )
                                                                                                                                                                                                                                                                 => ( X2 = X4 ) ) )
                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                  ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                    = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                                                                                                                 => ( X1 = X2 ) )
                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                    ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                      = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                   => ( X2 = X4 ) )
                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                      ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                                        = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                     => ( X2 = X4 ) )
                                                                                                                                                                                                                                                                 => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                        ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                                       => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                              ( ( in @ X2
                                                                                                                                                                                                                                                                                @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                  @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                                      ( X1
                                                                                                                                                                                                                                                                                      = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                                                                                                             => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                  @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                                      ( X1
                                                                                                                                                                                                                                                                                      = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                                                                                                               != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                          ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                          = X2 )
                                                                                                                                                                                                                                                                     => ( sP8
                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                              ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                             => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                               => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                  ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                 => ( in @ X4 @ X2 ) )
                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                       => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                          = X3 ) ) )
                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                         => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                            = X4 ) ) )
                                                                                                                                                                                                                                                                                 => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                      ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                     => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                                                                                                                        = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h66,assumption,
    ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) ),
    introduced(assumption,[]) ).

thf(h67,assumption,
    ~ ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
     => ( ! [X1: $i,X2: $i,X3: $i] :
            ( ( in @ X2 @ ( powerset @ X1 ) )
           => ( ( in @ X3 @ X2 )
             => ( in @ X3 @ X1 ) ) )
       => ( ! [X1: $i,X2: $i,X3: $i] :
              ( ( in @ X2 @ X3 )
             => ( ( in @ X3 @ X1 )
               => ( in @ X2 @ ( setunion @ X1 ) ) ) )
         => ( ! [X1: $i,X2: $i] :
                ( ( in @ X2 @ ( setunion @ X1 ) )
               => ! [X3: $o] :
                    ( ! [X4: $i] :
                        ( ( in @ X2 @ X4 )
                       => ( ( in @ X4 @ X1 )
                         => X3 ) )
                   => X3 ) )
           => ( ! [X1: $i,X2: $i] :
                  ( ( in @ X2 @ X1 )
                 => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
             => ( ! [X1: $i > $o] :
                    ( ~ ! [X2: $i] :
                          ( ( X1 @ X2 )
                         => ~ ! [X3: $i] :
                                ( ( X1 @ X3 )
                               => ( X2 = X3 ) ) )
                   => ~ ! [X2: $i] :
                          ~ ! [X3: $i] :
                              ( ( X1 @ X3 )
                              = ( X3 = X2 ) ) )
               => ( ! [X1: $i] :
                      ( ( X1 != emptyset )
                     => ~ ! [X2: $i] :
                            ~ ( in @ X2 @ X1 ) )
                 => ( ! [X1: $i,X2: $i] :
                        ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                       => ( X1 = X2 ) )
                   => ( ! [X1: $i,X2: $i] :
                          ( ( X1 != X2 )
                         => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                     => ( ! [X1: $i,X2: $i] :
                            ( ( X1 = X2 )
                           => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                       => ( ! [X1: $i,X2: $i] :
                              ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                             => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                               => ( ( X3 != X1 )
                                 => ( X3 = X2 ) ) )
                           => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                             => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                               => ( ! [X1: $i,X2: $i > $o] :
                                      ( ~ ! [X3: $i] :
                                            ( ( in @ X3 @ X1 )
                                           => ~ ( X2 @ X3 ) )
                                     => ( ( dsetconstr @ X1 @ X2 )
                                       != emptyset ) )
                                 => ( ! [X1: $i > $o,X2: $i] :
                                        ( ( in @ X2 @ emptyset )
                                       => ( X1 @ X2 ) )
                                   => ( ! [X1: $o] :
                                          ( X1
                                         => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                     => ( ! [X1: $o] :
                                            ( X1
                                           => ( set2prop @ ( prop2set @ X1 ) ) )
                                       => ( ! [X1: $i > $o] :
                                              ( ~ ! [X2: $i] :
                                                    ~ ( X1 @ X2 )
                                             => ( ! [X2: $i,X3: $i] :
                                                    ( ( X1 @ X2 )
                                                   => ( ( X1 @ X3 )
                                                     => ( X2 = X3 ) ) )
                                               => ~ ! [X2: $i] :
                                                      ( ( X1 @ X2 )
                                                     => ~ ! [X3: $i] :
                                                            ( ( X1 @ X3 )
                                                           => ( X2 = X3 ) ) ) ) )
                                         => ( ! [X1: $i > $o] :
                                                ( ~ ! [X2: $i] :
                                                      ~ ! [X3: $i] :
                                                          ( ( X1 @ X3 )
                                                          = ( X3 = X2 ) )
                                               => ~ ! [X2: $i] :
                                                      ( ( X1 @ X2 )
                                                     => ~ ! [X3: $i] :
                                                            ( ( X1 @ X3 )
                                                           => ( X2 = X3 ) ) ) )
                                           => ( ! [X1: $i,X2: $i] :
                                                  ( ( X1 = X2 )
                                                 => ! [X3: $i,X4: $i] :
                                                      ( ( X3 = X4 )
                                                     => ( ( in @ X3 @ X1 )
                                                       => ( in @ X4 @ X2 ) ) ) )
                                             => ( ! [X1: $i,X2: $i] :
                                                    ( ( X1 = X2 )
                                                   => ! [X3: $i,X4: $i] :
                                                        ( ( X3 = X4 )
                                                       => ( ( in @ X3 @ X1 )
                                                          = ( in @ X4 @ X2 ) ) ) )
                                               => ( ! [X1: $i > $o] :
                                                      ( ~ ! [X2: $i] :
                                                            ( ( X1 @ X2 )
                                                           => ~ ! [X3: $i] :
                                                                  ( ( X1 @ X3 )
                                                                 => ( X2 = X3 ) ) )
                                                     => ! [X2: $i,X3: $i] :
                                                          ( ( X1 @ X2 )
                                                         => ( ( X1 @ X3 )
                                                           => ( X2 = X3 ) ) ) )
                                                 => ( ! [X1: $i > $o,X2: $i > $o] :
                                                        ( ! [X3: $i,X4: $i] :
                                                            ( ( X3 = X4 )
                                                           => ( ( X1 @ X3 )
                                                              = ( X2 @ X4 ) ) )
                                                       => ( ( ~ ! [X3: $i] :
                                                                  ( ( X1 @ X3 )
                                                                 => ~ ! [X4: $i] :
                                                                        ( ( X1 @ X4 )
                                                                       => ( X3 = X4 ) ) ) )
                                                          = ( ~ ! [X3: $i] :
                                                                  ( ( X2 @ X3 )
                                                                 => ~ ! [X4: $i] :
                                                                        ( ( X2 @ X4 )
                                                                       => ( X3 = X4 ) ) ) ) ) )
                                                   => ( ! [X1: $i,X2: $i] :
                                                          ( ( X1 = X2 )
                                                         => ! [X3: $i,X4: $i] :
                                                              ( ( X3 = X4 )
                                                             => ( ( setadjoin @ X1 @ X3 )
                                                                = ( setadjoin @ X2 @ X4 ) ) ) )
                                                     => ( ! [X1: $i,X2: $i] :
                                                            ( ( X1 = X2 )
                                                           => ( ( powerset @ X1 )
                                                              = ( powerset @ X2 ) ) )
                                                       => ( ! [X1: $i,X2: $i] :
                                                              ( ( X1 = X2 )
                                                             => ( ( setunion @ X1 )
                                                                = ( setunion @ X2 ) ) )
                                                         => ( ! [X1: $i > $o] :
                                                                ( ~ ! [X2: $i] :
                                                                      ( ( X1 @ X2 )
                                                                     => ~ ! [X3: $i] :
                                                                            ( ( X1 @ X3 )
                                                                           => ( X2 = X3 ) ) )
                                                               => ! [X2: $i,X3: $i] :
                                                                    ( ( X1 @ X2 )
                                                                   => ( ( X1 @ X3 )
                                                                     => ( X2 = X3 ) ) ) )
                                                           => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                  ( ! [X3: $i,X4: $i] :
                                                                      ( ( X3 = X4 )
                                                                     => ( ( X1 @ X3 )
                                                                        = ( X2 @ X4 ) ) )
                                                                 => ( ~ ! [X3: $i] :
                                                                          ( ( X1 @ X3 )
                                                                         => ~ ! [X4: $i] :
                                                                                ( ( X1 @ X4 )
                                                                               => ( X3 = X4 ) ) )
                                                                   => ( ~ ! [X3: $i] :
                                                                            ( ( X2 @ X3 )
                                                                           => ~ ! [X4: $i] :
                                                                                  ( ( X2 @ X4 )
                                                                                 => ( X3 = X4 ) ) )
                                                                     => ( ( descr @ X1 )
                                                                        = ( descr @ X2 ) ) ) ) )
                                                             => ( ! [X1: $i,X2: $i] :
                                                                    ( ( X1 = X2 )
                                                                   => ! [X3: $i > $o,X4: $i > $o] :
                                                                        ( ! [X5: $i] :
                                                                            ( ( in @ X5 @ X1 )
                                                                           => ! [X6: $i] :
                                                                                ( ( in @ X6 @ X2 )
                                                                               => ( ( X5 = X6 )
                                                                                 => ( ( X3 @ X5 )
                                                                                    = ( X4 @ X6 ) ) ) ) )
                                                                       => ( ( dsetconstr @ X1 @ X3 )
                                                                          = ( dsetconstr @ X2 @ X4 ) ) ) )
                                                               => ( ! [X1: $i,X2: $i] :
                                                                      ( ! [X3: $i] :
                                                                          ( ( in @ X3 @ X1 )
                                                                         => ( in @ X3 @ X2 ) )
                                                                     => ( subset @ X1 @ X2 ) )
                                                                 => ( ! [X1: $i,X2: $i] :
                                                                        ( ( X1 = X2 )
                                                                       => ( subset @ X2 @ X1 ) )
                                                                   => ( ! [X1: $i,X2: $i] :
                                                                          ( ( X1 = X2 )
                                                                         => ( subset @ X1 @ X2 ) )
                                                                     => ( ! [X1: $i,X2: $i] :
                                                                            ( ! [X3: $i] :
                                                                                ( ( in @ X3 @ X1 )
                                                                               => ( in @ X3 @ X2 ) )
                                                                           => ( subset @ X1 @ X2 ) )
                                                                       => ( ! [X1: $i] : ( subset @ emptyset @ X1 )
                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                ( ( subset @ X1 @ X2 )
                                                                               => ( ( in @ X3 @ X1 )
                                                                                 => ( in @ X3 @ X2 ) ) )
                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                  ( ( subset @ X1 @ X2 )
                                                                                 => ( ~ ( in @ X3 @ X2 )
                                                                                   => ~ ( in @ X3 @ X1 ) ) )
                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                    ( ( in @ X3 @ X1 )
                                                                                   => ( ~ ( in @ X3 @ X2 )
                                                                                     => ~ ( subset @ X1 @ X2 ) ) )
                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                      ( ~ ( subset @ X1 @ X2 )
                                                                                     => ( X1 != X2 ) )
                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                        ( ( in @ X3 @ X1 )
                                                                                       => ( ~ ( in @ X3 @ X2 )
                                                                                         => ( X1 != X2 ) ) )
                                                                                   => ( ! [X1: $i] : ( subset @ X1 @ X1 )
                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                            ( ( subset @ X1 @ X2 )
                                                                                           => ( ( subset @ X2 @ X3 )
                                                                                             => ( subset @ X1 @ X3 ) ) )
                                                                                       => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) )
                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                ( ( subset @ X1 @ X3 )
                                                                                               => ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                  ( ( subset @ X1 @ X2 )
                                                                                                 => ( in @ X1 @ ( powerset @ X2 ) ) )
                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                    ( ( subset @ X1 @ X2 )
                                                                                                   => ( ( subset @ X2 @ X1 )
                                                                                                     => ( X1 = X2 ) ) )
                                                                                               => ( ! [X1: $i] :
                                                                                                      ( ( subset @ X1 @ emptyset )
                                                                                                     => ( X1 = emptyset ) )
                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                        ( ( subset @ X2 @ X1 )
                                                                                                       => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                          ( ( in @ X2 @ ( powerset @ X1 ) )
                                                                                                         => ( subset @ X2 @ X1 ) )
                                                                                                     => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                              ( ( subset @ X1 @ X2 )
                                                                                                             => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
                                                                                                         => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                                                                                                           => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                   => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                               => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                        ( ( in @ X3 @ X2 )
                                                                                                                       => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                                                                                                          ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                         => ( ( ( in @ X3 @ X1 )
                                                                                                                             => X4 )
                                                                                                                           => ( ( ( in @ X3 @ X2 )
                                                                                                                               => X4 )
                                                                                                                             => X4 ) ) )
                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                            ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                           => ( ~ ( in @ X3 @ X1 )
                                                                                                                             => ( in @ X3 @ X2 ) ) )
                                                                                                                       => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                                                                                                                         => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                 => ( ( in @ X3 @ X2 )
                                                                                                                                   => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                    ( ( subset @ X3 @ X1 )
                                                                                                                                   => ( ( subset @ X3 @ X2 )
                                                                                                                                     => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                      ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                     => ( in @ X3 @ X1 ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                          ( ( subset @ X1 @ X2 )
                                                                                                                                         => ( ( binintersect @ X1 @ X2 )
                                                                                                                                            = X1 ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                            ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                              = X2 )
                                                                                                                                           => ( subset @ X2 @ X1 ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                              ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                             => ( in @ X3 @ X2 ) )
                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                ( ! [X3: $i] :
                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                   => ~ ( in @ X3 @ X2 ) )
                                                                                                                                               => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                  = emptyset ) )
                                                                                                                                           => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                    ( ( subset @ X2 @ X1 )
                                                                                                                                                   => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                      = X2 ) )
                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                      ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                                        = X1 )
                                                                                                                                                     => ( subset @ X1 @ X2 ) )
                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                        ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                                                                                                                        = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                         => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                           => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                            ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                           => ( in @ X3 @ X1 ) )
                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                              ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                             => ~ ( in @ X3 @ X2 ) )
                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                ( ( subset @ X1 @ X2 )
                                                                                                                                                               => ( ( setminus @ X1 @ X2 )
                                                                                                                                                                  = emptyset ) )
                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                  ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                 => ( ( in @ X3 @ X1 )
                                                                                                                                                                   => ( in @ X3 @ X2 ) ) )
                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                    ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                   => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                     => ~ ( in @ X3 @ X1 ) ) )
                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                      ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                     => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                        ( ( in @ X3 @ X2 )
                                                                                                                                                                       => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                                   => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                            ( ( ( setminus @ X1 @ X2 )
                                                                                                                                                                              = emptyset )
                                                                                                                                                                           => ( subset @ X1 @ X2 ) )
                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                              ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                                                                                                             => ! [X4: $o] :
                                                                                                                                                                                  ( ( ( in @ X3 @ X1 )
                                                                                                                                                                                   => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                     => X4 ) )
                                                                                                                                                                                 => ( ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                     => ( ( in @ X3 @ X2 )
                                                                                                                                                                                       => X4 ) )
                                                                                                                                                                                   => X4 ) ) )
                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                               => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                 => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                  ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                 => ( ( in @ X3 @ X2 )
                                                                                                                                                                                   => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                   => ( ( in @ X3 @ X2 )
                                                                                                                                                                                     => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                      ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                     => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                       => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                  ( ( in @ X2 @ X1 )
                                                                                                                                                                                                 => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                    ( ( in @ X2 @ X1 )
                                                                                                                                                                                                   => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                     => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                        ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                       => ( ( X3 != X1 )
                                                                                                                                                                                                         => ( X3 = X2 ) ) )
                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                                                                                                             => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                                                                                                               => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                 => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                   => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                     => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                       => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                      ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                     => ~ ! [X4: $i] :
                                                                                                                                                                                                                            ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                           => ! [X5: $i] :
                                                                                                                                                                                                                                ( ( in @ X5 @ X2 )
                                                                                                                                                                                                                               => ( X3
                                                                                                                                                                                                                                 != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                                                                                                                 => ( sP5
                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                          ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                                                                                                                         => ~ ! [X3: $i] :
                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                               => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                                                                                                                     => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                                                                                                                       => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                         => ( ! [X1: $i] :
                                                                                                                                                                                                                                ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                                                                                                                = X1 )
                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                  ( ! [X3: $i] :
                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                                                                                          ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                         => ( ( X2 @ X3 )
                                                                                                                                                                                                                                           => ( ( X2 @ X4 )
                                                                                                                                                                                                                                             => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                                 => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                         => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                                   => ~ ! [X3: $i] :
                                                                                                                                                                                                                                          ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                         => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                           != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                    ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                          ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                         => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                           != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                                                                                                                   => ~ ! [X3: $i] :
                                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                         => ~ ( X2 @ X3 ) ) )
                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                     => ( ( X2 @ X3 )
                                                                                                                                                                                                                                       => ( ! [X4: $i] :
                                                                                                                                                                                                                                              ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                             => ( ( X2 @ X4 )
                                                                                                                                                                                                                                               => ( X4 = X3 ) ) )
                                                                                                                                                                                                                                         => ~ ! [X4: $i] :
                                                                                                                                                                                                                                                ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                               => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                 != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                        ( ! [X3: $i] :
                                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                                                                                                ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                               => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                 => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                   => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                                       => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                               => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                                         => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                               => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                 != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                          ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                                                                                                            = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                         => ( X1 = X2 ) )
                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                            ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                           => ( X1 = X3 ) )
                                                                                                                                                                                                                                       => ( ! [X1: $i] :
                                                                                                                                                                                                                                              ( ( iskpair @ X1 )
                                                                                                                                                                                                                                             => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                    ( ( in @ X2
                                                                                                                                                                                                                                                      @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                        @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                                                                                                                   => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                        @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                                                     != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                         => ( ! [X1: $i] :
                                                                                                                                                                                                                                                ( ~ ! [X2: $i] :
                                                                                                                                                                                                                                                      ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                                     => ( X1
                                                                                                                                                                                                                                                       != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                               => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                  ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                  = X1 )
                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                    ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                   => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                      ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                        = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                     => ( X1 = X3 ) )
                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                        ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                          = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                       => ( X1 = X3 ) )
                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                          ( ( X1 = X2 )
                                                                                                                                                                                                                                                         => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                            = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                            ( ( X1 = X2 )
                                                                                                                                                                                                                                                           => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                              = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                              ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                             => ( ( X3 = X4 )
                                                                                                                                                                                                                                                               => ( X2 = X4 ) ) )
                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                  = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                                                                                                               => ( X1 = X2 ) )
                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                  ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                    = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                 => ( X2 = X4 ) )
                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                    ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                                      = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                   => ( X2 = X4 ) )
                                                                                                                                                                                                                                                               => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                      ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                                     => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                            ( ( in @ X2
                                                                                                                                                                                                                                                                              @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                                    ( X1
                                                                                                                                                                                                                                                                                    = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                                                                                                           => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                                    ( X1
                                                                                                                                                                                                                                                                                    = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                                                                                                             != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                        ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                        = X2 )
                                                                                                                                                                                                                                                                   => ( sP8
                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                            ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                           => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                              ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                             => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                               => ( in @ X4 @ X2 ) )
                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                     => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                        = X3 ) ) )
                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                       => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                          = X4 ) ) )
                                                                                                                                                                                                                                                                               => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                    ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                   => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                                                                                                                      = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h68,assumption,
    ~ ( ! [X1: $i,X2: $i,X3: $i] :
          ( ( in @ X2 @ ( powerset @ X1 ) )
         => ( ( in @ X3 @ X2 )
           => ( in @ X3 @ X1 ) ) )
     => ( ! [X1: $i,X2: $i,X3: $i] :
            ( ( in @ X2 @ X3 )
           => ( ( in @ X3 @ X1 )
             => ( in @ X2 @ ( setunion @ X1 ) ) ) )
       => ( ! [X1: $i,X2: $i] :
              ( ( in @ X2 @ ( setunion @ X1 ) )
             => ! [X3: $o] :
                  ( ! [X4: $i] :
                      ( ( in @ X2 @ X4 )
                     => ( ( in @ X4 @ X1 )
                       => X3 ) )
                 => X3 ) )
         => ( ! [X1: $i,X2: $i] :
                ( ( in @ X2 @ X1 )
               => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
           => ( ! [X1: $i > $o] :
                  ( ~ ! [X2: $i] :
                        ( ( X1 @ X2 )
                       => ~ ! [X3: $i] :
                              ( ( X1 @ X3 )
                             => ( X2 = X3 ) ) )
                 => ~ ! [X2: $i] :
                        ~ ! [X3: $i] :
                            ( ( X1 @ X3 )
                            = ( X3 = X2 ) ) )
             => ( ! [X1: $i] :
                    ( ( X1 != emptyset )
                   => ~ ! [X2: $i] :
                          ~ ( in @ X2 @ X1 ) )
               => ( ! [X1: $i,X2: $i] :
                      ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                     => ( X1 = X2 ) )
                 => ( ! [X1: $i,X2: $i] :
                        ( ( X1 != X2 )
                       => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                   => ( ! [X1: $i,X2: $i] :
                          ( ( X1 = X2 )
                         => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                     => ( ! [X1: $i,X2: $i] :
                            ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                           => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                       => ( ! [X1: $i,X2: $i,X3: $i] :
                              ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                             => ( ( X3 != X1 )
                               => ( X3 = X2 ) ) )
                         => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                           => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                             => ( ! [X1: $i,X2: $i > $o] :
                                    ( ~ ! [X3: $i] :
                                          ( ( in @ X3 @ X1 )
                                         => ~ ( X2 @ X3 ) )
                                   => ( ( dsetconstr @ X1 @ X2 )
                                     != emptyset ) )
                               => ( ! [X1: $i > $o,X2: $i] :
                                      ( ( in @ X2 @ emptyset )
                                     => ( X1 @ X2 ) )
                                 => ( ! [X1: $o] :
                                        ( X1
                                       => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                   => ( ! [X1: $o] :
                                          ( X1
                                         => ( set2prop @ ( prop2set @ X1 ) ) )
                                     => ( ! [X1: $i > $o] :
                                            ( ~ ! [X2: $i] :
                                                  ~ ( X1 @ X2 )
                                           => ( ! [X2: $i,X3: $i] :
                                                  ( ( X1 @ X2 )
                                                 => ( ( X1 @ X3 )
                                                   => ( X2 = X3 ) ) )
                                             => ~ ! [X2: $i] :
                                                    ( ( X1 @ X2 )
                                                   => ~ ! [X3: $i] :
                                                          ( ( X1 @ X3 )
                                                         => ( X2 = X3 ) ) ) ) )
                                       => ( ! [X1: $i > $o] :
                                              ( ~ ! [X2: $i] :
                                                    ~ ! [X3: $i] :
                                                        ( ( X1 @ X3 )
                                                        = ( X3 = X2 ) )
                                             => ~ ! [X2: $i] :
                                                    ( ( X1 @ X2 )
                                                   => ~ ! [X3: $i] :
                                                          ( ( X1 @ X3 )
                                                         => ( X2 = X3 ) ) ) )
                                         => ( ! [X1: $i,X2: $i] :
                                                ( ( X1 = X2 )
                                               => ! [X3: $i,X4: $i] :
                                                    ( ( X3 = X4 )
                                                   => ( ( in @ X3 @ X1 )
                                                     => ( in @ X4 @ X2 ) ) ) )
                                           => ( ! [X1: $i,X2: $i] :
                                                  ( ( X1 = X2 )
                                                 => ! [X3: $i,X4: $i] :
                                                      ( ( X3 = X4 )
                                                     => ( ( in @ X3 @ X1 )
                                                        = ( in @ X4 @ X2 ) ) ) )
                                             => ( ! [X1: $i > $o] :
                                                    ( ~ ! [X2: $i] :
                                                          ( ( X1 @ X2 )
                                                         => ~ ! [X3: $i] :
                                                                ( ( X1 @ X3 )
                                                               => ( X2 = X3 ) ) )
                                                   => ! [X2: $i,X3: $i] :
                                                        ( ( X1 @ X2 )
                                                       => ( ( X1 @ X3 )
                                                         => ( X2 = X3 ) ) ) )
                                               => ( ! [X1: $i > $o,X2: $i > $o] :
                                                      ( ! [X3: $i,X4: $i] :
                                                          ( ( X3 = X4 )
                                                         => ( ( X1 @ X3 )
                                                            = ( X2 @ X4 ) ) )
                                                     => ( ( ~ ! [X3: $i] :
                                                                ( ( X1 @ X3 )
                                                               => ~ ! [X4: $i] :
                                                                      ( ( X1 @ X4 )
                                                                     => ( X3 = X4 ) ) ) )
                                                        = ( ~ ! [X3: $i] :
                                                                ( ( X2 @ X3 )
                                                               => ~ ! [X4: $i] :
                                                                      ( ( X2 @ X4 )
                                                                     => ( X3 = X4 ) ) ) ) ) )
                                                 => ( ! [X1: $i,X2: $i] :
                                                        ( ( X1 = X2 )
                                                       => ! [X3: $i,X4: $i] :
                                                            ( ( X3 = X4 )
                                                           => ( ( setadjoin @ X1 @ X3 )
                                                              = ( setadjoin @ X2 @ X4 ) ) ) )
                                                   => ( ! [X1: $i,X2: $i] :
                                                          ( ( X1 = X2 )
                                                         => ( ( powerset @ X1 )
                                                            = ( powerset @ X2 ) ) )
                                                     => ( ! [X1: $i,X2: $i] :
                                                            ( ( X1 = X2 )
                                                           => ( ( setunion @ X1 )
                                                              = ( setunion @ X2 ) ) )
                                                       => ( ! [X1: $i > $o] :
                                                              ( ~ ! [X2: $i] :
                                                                    ( ( X1 @ X2 )
                                                                   => ~ ! [X3: $i] :
                                                                          ( ( X1 @ X3 )
                                                                         => ( X2 = X3 ) ) )
                                                             => ! [X2: $i,X3: $i] :
                                                                  ( ( X1 @ X2 )
                                                                 => ( ( X1 @ X3 )
                                                                   => ( X2 = X3 ) ) ) )
                                                         => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                ( ! [X3: $i,X4: $i] :
                                                                    ( ( X3 = X4 )
                                                                   => ( ( X1 @ X3 )
                                                                      = ( X2 @ X4 ) ) )
                                                               => ( ~ ! [X3: $i] :
                                                                        ( ( X1 @ X3 )
                                                                       => ~ ! [X4: $i] :
                                                                              ( ( X1 @ X4 )
                                                                             => ( X3 = X4 ) ) )
                                                                 => ( ~ ! [X3: $i] :
                                                                          ( ( X2 @ X3 )
                                                                         => ~ ! [X4: $i] :
                                                                                ( ( X2 @ X4 )
                                                                               => ( X3 = X4 ) ) )
                                                                   => ( ( descr @ X1 )
                                                                      = ( descr @ X2 ) ) ) ) )
                                                           => ( ! [X1: $i,X2: $i] :
                                                                  ( ( X1 = X2 )
                                                                 => ! [X3: $i > $o,X4: $i > $o] :
                                                                      ( ! [X5: $i] :
                                                                          ( ( in @ X5 @ X1 )
                                                                         => ! [X6: $i] :
                                                                              ( ( in @ X6 @ X2 )
                                                                             => ( ( X5 = X6 )
                                                                               => ( ( X3 @ X5 )
                                                                                  = ( X4 @ X6 ) ) ) ) )
                                                                     => ( ( dsetconstr @ X1 @ X3 )
                                                                        = ( dsetconstr @ X2 @ X4 ) ) ) )
                                                             => ( ! [X1: $i,X2: $i] :
                                                                    ( ! [X3: $i] :
                                                                        ( ( in @ X3 @ X1 )
                                                                       => ( in @ X3 @ X2 ) )
                                                                   => ( subset @ X1 @ X2 ) )
                                                               => ( ! [X1: $i,X2: $i] :
                                                                      ( ( X1 = X2 )
                                                                     => ( subset @ X2 @ X1 ) )
                                                                 => ( ! [X1: $i,X2: $i] :
                                                                        ( ( X1 = X2 )
                                                                       => ( subset @ X1 @ X2 ) )
                                                                   => ( ! [X1: $i,X2: $i] :
                                                                          ( ! [X3: $i] :
                                                                              ( ( in @ X3 @ X1 )
                                                                             => ( in @ X3 @ X2 ) )
                                                                         => ( subset @ X1 @ X2 ) )
                                                                     => ( ! [X1: $i] : ( subset @ emptyset @ X1 )
                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                              ( ( subset @ X1 @ X2 )
                                                                             => ( ( in @ X3 @ X1 )
                                                                               => ( in @ X3 @ X2 ) ) )
                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                ( ( subset @ X1 @ X2 )
                                                                               => ( ~ ( in @ X3 @ X2 )
                                                                                 => ~ ( in @ X3 @ X1 ) ) )
                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                  ( ( in @ X3 @ X1 )
                                                                                 => ( ~ ( in @ X3 @ X2 )
                                                                                   => ~ ( subset @ X1 @ X2 ) ) )
                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                    ( ~ ( subset @ X1 @ X2 )
                                                                                   => ( X1 != X2 ) )
                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                      ( ( in @ X3 @ X1 )
                                                                                     => ( ~ ( in @ X3 @ X2 )
                                                                                       => ( X1 != X2 ) ) )
                                                                                 => ( ! [X1: $i] : ( subset @ X1 @ X1 )
                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                          ( ( subset @ X1 @ X2 )
                                                                                         => ( ( subset @ X2 @ X3 )
                                                                                           => ( subset @ X1 @ X3 ) ) )
                                                                                     => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) )
                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                              ( ( subset @ X1 @ X3 )
                                                                                             => ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                ( ( subset @ X1 @ X2 )
                                                                                               => ( in @ X1 @ ( powerset @ X2 ) ) )
                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                  ( ( subset @ X1 @ X2 )
                                                                                                 => ( ( subset @ X2 @ X1 )
                                                                                                   => ( X1 = X2 ) ) )
                                                                                             => ( ! [X1: $i] :
                                                                                                    ( ( subset @ X1 @ emptyset )
                                                                                                   => ( X1 = emptyset ) )
                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                      ( ( subset @ X2 @ X1 )
                                                                                                     => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                        ( ( in @ X2 @ ( powerset @ X1 ) )
                                                                                                       => ( subset @ X2 @ X1 ) )
                                                                                                   => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                            ( ( subset @ X1 @ X2 )
                                                                                                           => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
                                                                                                       => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                                                                                                         => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                 => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                             => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                      ( ( in @ X3 @ X2 )
                                                                                                                     => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                                                                                                        ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                       => ( ( ( in @ X3 @ X1 )
                                                                                                                           => X4 )
                                                                                                                         => ( ( ( in @ X3 @ X2 )
                                                                                                                             => X4 )
                                                                                                                           => X4 ) ) )
                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                          ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                         => ( ~ ( in @ X3 @ X1 )
                                                                                                                           => ( in @ X3 @ X2 ) ) )
                                                                                                                     => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                                                                                                                       => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                               => ( ( in @ X3 @ X2 )
                                                                                                                                 => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                  ( ( subset @ X3 @ X1 )
                                                                                                                                 => ( ( subset @ X3 @ X2 )
                                                                                                                                   => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                    ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                   => ( in @ X3 @ X1 ) )
                                                                                                                               => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                        ( ( subset @ X1 @ X2 )
                                                                                                                                       => ( ( binintersect @ X1 @ X2 )
                                                                                                                                          = X1 ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                          ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                            = X2 )
                                                                                                                                         => ( subset @ X2 @ X1 ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                            ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                           => ( in @ X3 @ X2 ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                              ( ! [X3: $i] :
                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                 => ~ ( in @ X3 @ X2 ) )
                                                                                                                                             => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                = emptyset ) )
                                                                                                                                         => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                  ( ( subset @ X2 @ X1 )
                                                                                                                                                 => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                    = X2 ) )
                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                    ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                                      = X1 )
                                                                                                                                                   => ( subset @ X1 @ X2 ) )
                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                      ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                                                                                                                      = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                       => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                         => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                          ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                         => ( in @ X3 @ X1 ) )
                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                            ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                           => ~ ( in @ X3 @ X2 ) )
                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                              ( ( subset @ X1 @ X2 )
                                                                                                                                                             => ( ( setminus @ X1 @ X2 )
                                                                                                                                                                = emptyset ) )
                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                               => ( ( in @ X3 @ X1 )
                                                                                                                                                                 => ( in @ X3 @ X2 ) ) )
                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                  ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                 => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                   => ~ ( in @ X3 @ X1 ) ) )
                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                    ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                   => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                      ( ( in @ X3 @ X2 )
                                                                                                                                                                     => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                                 => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                          ( ( ( setminus @ X1 @ X2 )
                                                                                                                                                                            = emptyset )
                                                                                                                                                                         => ( subset @ X1 @ X2 ) )
                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                            ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                                                                                                           => ! [X4: $o] :
                                                                                                                                                                                ( ( ( in @ X3 @ X1 )
                                                                                                                                                                                 => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                   => X4 ) )
                                                                                                                                                                               => ( ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                   => ( ( in @ X3 @ X2 )
                                                                                                                                                                                     => X4 ) )
                                                                                                                                                                                 => X4 ) ) )
                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                             => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                               => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                               => ( ( in @ X3 @ X2 )
                                                                                                                                                                                 => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                 => ( ( in @ X3 @ X2 )
                                                                                                                                                                                   => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                    ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                   => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                     => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                               => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                ( ( in @ X2 @ X1 )
                                                                                                                                                                                               => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                  ( ( in @ X2 @ X1 )
                                                                                                                                                                                                 => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                   => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                      ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                     => ( ( X3 != X1 )
                                                                                                                                                                                                       => ( X3 = X2 ) ) )
                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                                                                                           => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                                                                                                             => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                                                                                                               => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                 => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                   => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                     => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                    ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                   => ~ ! [X4: $i] :
                                                                                                                                                                                                                          ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                         => ! [X5: $i] :
                                                                                                                                                                                                                              ( ( in @ X5 @ X2 )
                                                                                                                                                                                                                             => ( X3
                                                                                                                                                                                                                               != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                                                                                                               => ( sP5
                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                        ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                                                                                                                       => ~ ! [X3: $i] :
                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                             => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                                                                                                                   => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                                                                                                                     => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                       => ( ! [X1: $i] :
                                                                                                                                                                                                                              ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                                                                                                              = X1 )
                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                ( ! [X3: $i] :
                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                                                                                        ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                       => ( ( X2 @ X3 )
                                                                                                                                                                                                                                         => ( ( X2 @ X4 )
                                                                                                                                                                                                                                           => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                               => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                       => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                                 => ~ ! [X3: $i] :
                                                                                                                                                                                                                                        ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                       => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                         != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                  ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                        ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                       => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                         != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                                                                                                                 => ~ ! [X3: $i] :
                                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                       => ~ ( X2 @ X3 ) ) )
                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                   => ( ( X2 @ X3 )
                                                                                                                                                                                                                                     => ( ! [X4: $i] :
                                                                                                                                                                                                                                            ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                           => ( ( X2 @ X4 )
                                                                                                                                                                                                                                             => ( X4 = X3 ) ) )
                                                                                                                                                                                                                                       => ~ ! [X4: $i] :
                                                                                                                                                                                                                                              ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                             => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                               != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                      ( ! [X3: $i] :
                                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                                                                                              ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                             => ( ( X2 @ X3 )
                                                                                                                                                                                                                                               => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                 => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                                     => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                             => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                                       => ~ ! [X3: $i] :
                                                                                                                                                                                                                                              ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                             => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                               != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                        ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                                                                                                          = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                       => ( X1 = X2 ) )
                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                          ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                         => ( X1 = X3 ) )
                                                                                                                                                                                                                                     => ( ! [X1: $i] :
                                                                                                                                                                                                                                            ( ( iskpair @ X1 )
                                                                                                                                                                                                                                           => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                  ( ( in @ X2
                                                                                                                                                                                                                                                    @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                      @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                                                                                                                 => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                      @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                                                   != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                       => ( ! [X1: $i] :
                                                                                                                                                                                                                                              ( ~ ! [X2: $i] :
                                                                                                                                                                                                                                                    ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                                   => ( X1
                                                                                                                                                                                                                                                     != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                             => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                = X1 )
                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                  ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                 => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                    ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                      = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                   => ( X1 = X3 ) )
                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                      ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                        = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                     => ( X1 = X3 ) )
                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                        ( ( X1 = X2 )
                                                                                                                                                                                                                                                       => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                          = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                          ( ( X1 = X2 )
                                                                                                                                                                                                                                                         => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                            = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                            ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                              = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                           => ( ( X3 = X4 )
                                                                                                                                                                                                                                                             => ( X2 = X4 ) ) )
                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                              ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                                                                                                             => ( X1 = X2 ) )
                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                  = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                               => ( X2 = X4 ) )
                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                  ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                                    = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                 => ( X2 = X4 ) )
                                                                                                                                                                                                                                                             => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                    ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                                   => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                          ( ( in @ X2
                                                                                                                                                                                                                                                                            @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                              @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                                  ( X1
                                                                                                                                                                                                                                                                                  = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                                                                                                         => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                              @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                                  ( X1
                                                                                                                                                                                                                                                                                  = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                                                                                                           != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                      ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                      = X2 )
                                                                                                                                                                                                                                                                 => ( sP8
                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                         => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                            ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                           => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                              ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                             => ( in @ X4 @ X2 ) )
                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                   => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                      = X3 ) ) )
                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                     => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                        = X4 ) ) )
                                                                                                                                                                                                                                                                             => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                  ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                 => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                                                                                                                    = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h69,assumption,
    ! [X1: $i,X2: $i,X3: $i] :
      ( ( in @ X2 @ ( powerset @ X1 ) )
     => ( ( in @ X3 @ X2 )
       => ( in @ X3 @ X1 ) ) ),
    introduced(assumption,[]) ).

thf(h70,assumption,
    ~ ( ! [X1: $i,X2: $i,X3: $i] :
          ( ( in @ X2 @ X3 )
         => ( ( in @ X3 @ X1 )
           => ( in @ X2 @ ( setunion @ X1 ) ) ) )
     => ( ! [X1: $i,X2: $i] :
            ( ( in @ X2 @ ( setunion @ X1 ) )
           => ! [X3: $o] :
                ( ! [X4: $i] :
                    ( ( in @ X2 @ X4 )
                   => ( ( in @ X4 @ X1 )
                     => X3 ) )
               => X3 ) )
       => ( ! [X1: $i,X2: $i] :
              ( ( in @ X2 @ X1 )
             => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
         => ( ! [X1: $i > $o] :
                ( ~ ! [X2: $i] :
                      ( ( X1 @ X2 )
                     => ~ ! [X3: $i] :
                            ( ( X1 @ X3 )
                           => ( X2 = X3 ) ) )
               => ~ ! [X2: $i] :
                      ~ ! [X3: $i] :
                          ( ( X1 @ X3 )
                          = ( X3 = X2 ) ) )
           => ( ! [X1: $i] :
                  ( ( X1 != emptyset )
                 => ~ ! [X2: $i] :
                        ~ ( in @ X2 @ X1 ) )
             => ( ! [X1: $i,X2: $i] :
                    ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                   => ( X1 = X2 ) )
               => ( ! [X1: $i,X2: $i] :
                      ( ( X1 != X2 )
                     => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                 => ( ! [X1: $i,X2: $i] :
                        ( ( X1 = X2 )
                       => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                   => ( ! [X1: $i,X2: $i] :
                          ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                         => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                     => ( ! [X1: $i,X2: $i,X3: $i] :
                            ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                           => ( ( X3 != X1 )
                             => ( X3 = X2 ) ) )
                       => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                         => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                           => ( ! [X1: $i,X2: $i > $o] :
                                  ( ~ ! [X3: $i] :
                                        ( ( in @ X3 @ X1 )
                                       => ~ ( X2 @ X3 ) )
                                 => ( ( dsetconstr @ X1 @ X2 )
                                   != emptyset ) )
                             => ( ! [X1: $i > $o,X2: $i] :
                                    ( ( in @ X2 @ emptyset )
                                   => ( X1 @ X2 ) )
                               => ( ! [X1: $o] :
                                      ( X1
                                     => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                 => ( ! [X1: $o] :
                                        ( X1
                                       => ( set2prop @ ( prop2set @ X1 ) ) )
                                   => ( ! [X1: $i > $o] :
                                          ( ~ ! [X2: $i] :
                                                ~ ( X1 @ X2 )
                                         => ( ! [X2: $i,X3: $i] :
                                                ( ( X1 @ X2 )
                                               => ( ( X1 @ X3 )
                                                 => ( X2 = X3 ) ) )
                                           => ~ ! [X2: $i] :
                                                  ( ( X1 @ X2 )
                                                 => ~ ! [X3: $i] :
                                                        ( ( X1 @ X3 )
                                                       => ( X2 = X3 ) ) ) ) )
                                     => ( ! [X1: $i > $o] :
                                            ( ~ ! [X2: $i] :
                                                  ~ ! [X3: $i] :
                                                      ( ( X1 @ X3 )
                                                      = ( X3 = X2 ) )
                                           => ~ ! [X2: $i] :
                                                  ( ( X1 @ X2 )
                                                 => ~ ! [X3: $i] :
                                                        ( ( X1 @ X3 )
                                                       => ( X2 = X3 ) ) ) )
                                       => ( ! [X1: $i,X2: $i] :
                                              ( ( X1 = X2 )
                                             => ! [X3: $i,X4: $i] :
                                                  ( ( X3 = X4 )
                                                 => ( ( in @ X3 @ X1 )
                                                   => ( in @ X4 @ X2 ) ) ) )
                                         => ( ! [X1: $i,X2: $i] :
                                                ( ( X1 = X2 )
                                               => ! [X3: $i,X4: $i] :
                                                    ( ( X3 = X4 )
                                                   => ( ( in @ X3 @ X1 )
                                                      = ( in @ X4 @ X2 ) ) ) )
                                           => ( ! [X1: $i > $o] :
                                                  ( ~ ! [X2: $i] :
                                                        ( ( X1 @ X2 )
                                                       => ~ ! [X3: $i] :
                                                              ( ( X1 @ X3 )
                                                             => ( X2 = X3 ) ) )
                                                 => ! [X2: $i,X3: $i] :
                                                      ( ( X1 @ X2 )
                                                     => ( ( X1 @ X3 )
                                                       => ( X2 = X3 ) ) ) )
                                             => ( ! [X1: $i > $o,X2: $i > $o] :
                                                    ( ! [X3: $i,X4: $i] :
                                                        ( ( X3 = X4 )
                                                       => ( ( X1 @ X3 )
                                                          = ( X2 @ X4 ) ) )
                                                   => ( ( ~ ! [X3: $i] :
                                                              ( ( X1 @ X3 )
                                                             => ~ ! [X4: $i] :
                                                                    ( ( X1 @ X4 )
                                                                   => ( X3 = X4 ) ) ) )
                                                      = ( ~ ! [X3: $i] :
                                                              ( ( X2 @ X3 )
                                                             => ~ ! [X4: $i] :
                                                                    ( ( X2 @ X4 )
                                                                   => ( X3 = X4 ) ) ) ) ) )
                                               => ( ! [X1: $i,X2: $i] :
                                                      ( ( X1 = X2 )
                                                     => ! [X3: $i,X4: $i] :
                                                          ( ( X3 = X4 )
                                                         => ( ( setadjoin @ X1 @ X3 )
                                                            = ( setadjoin @ X2 @ X4 ) ) ) )
                                                 => ( ! [X1: $i,X2: $i] :
                                                        ( ( X1 = X2 )
                                                       => ( ( powerset @ X1 )
                                                          = ( powerset @ X2 ) ) )
                                                   => ( ! [X1: $i,X2: $i] :
                                                          ( ( X1 = X2 )
                                                         => ( ( setunion @ X1 )
                                                            = ( setunion @ X2 ) ) )
                                                     => ( ! [X1: $i > $o] :
                                                            ( ~ ! [X2: $i] :
                                                                  ( ( X1 @ X2 )
                                                                 => ~ ! [X3: $i] :
                                                                        ( ( X1 @ X3 )
                                                                       => ( X2 = X3 ) ) )
                                                           => ! [X2: $i,X3: $i] :
                                                                ( ( X1 @ X2 )
                                                               => ( ( X1 @ X3 )
                                                                 => ( X2 = X3 ) ) ) )
                                                       => ( ! [X1: $i > $o,X2: $i > $o] :
                                                              ( ! [X3: $i,X4: $i] :
                                                                  ( ( X3 = X4 )
                                                                 => ( ( X1 @ X3 )
                                                                    = ( X2 @ X4 ) ) )
                                                             => ( ~ ! [X3: $i] :
                                                                      ( ( X1 @ X3 )
                                                                     => ~ ! [X4: $i] :
                                                                            ( ( X1 @ X4 )
                                                                           => ( X3 = X4 ) ) )
                                                               => ( ~ ! [X3: $i] :
                                                                        ( ( X2 @ X3 )
                                                                       => ~ ! [X4: $i] :
                                                                              ( ( X2 @ X4 )
                                                                             => ( X3 = X4 ) ) )
                                                                 => ( ( descr @ X1 )
                                                                    = ( descr @ X2 ) ) ) ) )
                                                         => ( ! [X1: $i,X2: $i] :
                                                                ( ( X1 = X2 )
                                                               => ! [X3: $i > $o,X4: $i > $o] :
                                                                    ( ! [X5: $i] :
                                                                        ( ( in @ X5 @ X1 )
                                                                       => ! [X6: $i] :
                                                                            ( ( in @ X6 @ X2 )
                                                                           => ( ( X5 = X6 )
                                                                             => ( ( X3 @ X5 )
                                                                                = ( X4 @ X6 ) ) ) ) )
                                                                   => ( ( dsetconstr @ X1 @ X3 )
                                                                      = ( dsetconstr @ X2 @ X4 ) ) ) )
                                                           => ( ! [X1: $i,X2: $i] :
                                                                  ( ! [X3: $i] :
                                                                      ( ( in @ X3 @ X1 )
                                                                     => ( in @ X3 @ X2 ) )
                                                                 => ( subset @ X1 @ X2 ) )
                                                             => ( ! [X1: $i,X2: $i] :
                                                                    ( ( X1 = X2 )
                                                                   => ( subset @ X2 @ X1 ) )
                                                               => ( ! [X1: $i,X2: $i] :
                                                                      ( ( X1 = X2 )
                                                                     => ( subset @ X1 @ X2 ) )
                                                                 => ( ! [X1: $i,X2: $i] :
                                                                        ( ! [X3: $i] :
                                                                            ( ( in @ X3 @ X1 )
                                                                           => ( in @ X3 @ X2 ) )
                                                                       => ( subset @ X1 @ X2 ) )
                                                                   => ( ! [X1: $i] : ( subset @ emptyset @ X1 )
                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                            ( ( subset @ X1 @ X2 )
                                                                           => ( ( in @ X3 @ X1 )
                                                                             => ( in @ X3 @ X2 ) ) )
                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                              ( ( subset @ X1 @ X2 )
                                                                             => ( ~ ( in @ X3 @ X2 )
                                                                               => ~ ( in @ X3 @ X1 ) ) )
                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                ( ( in @ X3 @ X1 )
                                                                               => ( ~ ( in @ X3 @ X2 )
                                                                                 => ~ ( subset @ X1 @ X2 ) ) )
                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                  ( ~ ( subset @ X1 @ X2 )
                                                                                 => ( X1 != X2 ) )
                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                    ( ( in @ X3 @ X1 )
                                                                                   => ( ~ ( in @ X3 @ X2 )
                                                                                     => ( X1 != X2 ) ) )
                                                                               => ( ! [X1: $i] : ( subset @ X1 @ X1 )
                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                        ( ( subset @ X1 @ X2 )
                                                                                       => ( ( subset @ X2 @ X3 )
                                                                                         => ( subset @ X1 @ X3 ) ) )
                                                                                   => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) )
                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                            ( ( subset @ X1 @ X3 )
                                                                                           => ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                              ( ( subset @ X1 @ X2 )
                                                                                             => ( in @ X1 @ ( powerset @ X2 ) ) )
                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                ( ( subset @ X1 @ X2 )
                                                                                               => ( ( subset @ X2 @ X1 )
                                                                                                 => ( X1 = X2 ) ) )
                                                                                           => ( ! [X1: $i] :
                                                                                                  ( ( subset @ X1 @ emptyset )
                                                                                                 => ( X1 = emptyset ) )
                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                    ( ( subset @ X2 @ X1 )
                                                                                                   => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                      ( ( in @ X2 @ ( powerset @ X1 ) )
                                                                                                     => ( subset @ X2 @ X1 ) )
                                                                                                 => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                          ( ( subset @ X1 @ X2 )
                                                                                                         => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
                                                                                                     => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                                                                                                       => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                               => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                           => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                    ( ( in @ X3 @ X2 )
                                                                                                                   => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                                                                                                      ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                     => ( ( ( in @ X3 @ X1 )
                                                                                                                         => X4 )
                                                                                                                       => ( ( ( in @ X3 @ X2 )
                                                                                                                           => X4 )
                                                                                                                         => X4 ) ) )
                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                        ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                       => ( ~ ( in @ X3 @ X1 )
                                                                                                                         => ( in @ X3 @ X2 ) ) )
                                                                                                                   => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                                                                                                                     => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                             => ( ( in @ X3 @ X2 )
                                                                                                                               => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                ( ( subset @ X3 @ X1 )
                                                                                                                               => ( ( subset @ X3 @ X2 )
                                                                                                                                 => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                  ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                 => ( in @ X3 @ X1 ) )
                                                                                                                             => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                      ( ( subset @ X1 @ X2 )
                                                                                                                                     => ( ( binintersect @ X1 @ X2 )
                                                                                                                                        = X1 ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                        ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                          = X2 )
                                                                                                                                       => ( subset @ X2 @ X1 ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                          ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                         => ( in @ X3 @ X2 ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                            ( ! [X3: $i] :
                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                               => ~ ( in @ X3 @ X2 ) )
                                                                                                                                           => ( ( binintersect @ X1 @ X2 )
                                                                                                                                              = emptyset ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                ( ( subset @ X2 @ X1 )
                                                                                                                                               => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                  = X2 ) )
                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                  ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                                    = X1 )
                                                                                                                                                 => ( subset @ X1 @ X2 ) )
                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                    ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                                                                                                                    = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                     => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                       => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                        ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                       => ( in @ X3 @ X1 ) )
                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                          ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                         => ~ ( in @ X3 @ X2 ) )
                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                            ( ( subset @ X1 @ X2 )
                                                                                                                                                           => ( ( setminus @ X1 @ X2 )
                                                                                                                                                              = emptyset ) )
                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                              ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                             => ( ( in @ X3 @ X1 )
                                                                                                                                                               => ( in @ X3 @ X2 ) ) )
                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                               => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                 => ~ ( in @ X3 @ X1 ) ) )
                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                  ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                 => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                    ( ( in @ X3 @ X2 )
                                                                                                                                                                   => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                               => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                        ( ( ( setminus @ X1 @ X2 )
                                                                                                                                                                          = emptyset )
                                                                                                                                                                       => ( subset @ X1 @ X2 ) )
                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                          ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                                                                                                         => ! [X4: $o] :
                                                                                                                                                                              ( ( ( in @ X3 @ X1 )
                                                                                                                                                                               => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                 => X4 ) )
                                                                                                                                                                             => ( ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                 => ( ( in @ X3 @ X2 )
                                                                                                                                                                                   => X4 ) )
                                                                                                                                                                               => X4 ) ) )
                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                           => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                             => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                              ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                             => ( ( in @ X3 @ X2 )
                                                                                                                                                                               => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                               => ( ( in @ X3 @ X2 )
                                                                                                                                                                                 => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                  ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                 => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                   => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                             => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                               => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                              ( ( in @ X2 @ X1 )
                                                                                                                                                                                             => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                ( ( in @ X2 @ X1 )
                                                                                                                                                                                               => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                 => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                    ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                   => ( ( X3 != X1 )
                                                                                                                                                                                                     => ( X3 = X2 ) ) )
                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                                                                                         => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                                                                                           => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                                                                                                             => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                                                                                                               => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                 => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                   => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                  ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                 => ~ ! [X4: $i] :
                                                                                                                                                                                                                        ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                       => ! [X5: $i] :
                                                                                                                                                                                                                            ( ( in @ X5 @ X2 )
                                                                                                                                                                                                                           => ( X3
                                                                                                                                                                                                                             != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                                                                                                             => ( sP5
                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                      ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                                                                                                                     => ~ ! [X3: $i] :
                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                           => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                                                                                                                 => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                                                                                                                   => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                     => ( ! [X1: $i] :
                                                                                                                                                                                                                            ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                                                                                                            = X1 )
                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                              ( ! [X3: $i] :
                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                                                                                      ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                     => ( ( X2 @ X3 )
                                                                                                                                                                                                                                       => ( ( X2 @ X4 )
                                                                                                                                                                                                                                         => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                             => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                     => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                               => ~ ! [X3: $i] :
                                                                                                                                                                                                                                      ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                     => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                       != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                      ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                     => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                       != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                                                                                                               => ~ ! [X3: $i] :
                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                     => ~ ( X2 @ X3 ) ) )
                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                 => ( ( X2 @ X3 )
                                                                                                                                                                                                                                   => ( ! [X4: $i] :
                                                                                                                                                                                                                                          ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                         => ( ( X2 @ X4 )
                                                                                                                                                                                                                                           => ( X4 = X3 ) ) )
                                                                                                                                                                                                                                     => ~ ! [X4: $i] :
                                                                                                                                                                                                                                            ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                           => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                             != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                    ( ! [X3: $i] :
                                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                                                                                            ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                           => ( ( X2 @ X3 )
                                                                                                                                                                                                                                             => ( ( X2 @ X4 )
                                                                                                                                                                                                                                               => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                                   => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                           => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                                     => ~ ! [X3: $i] :
                                                                                                                                                                                                                                            ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                           => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                             != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                      ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                                                                                                        = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                     => ( X1 = X2 ) )
                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                        ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                       => ( X1 = X3 ) )
                                                                                                                                                                                                                                   => ( ! [X1: $i] :
                                                                                                                                                                                                                                          ( ( iskpair @ X1 )
                                                                                                                                                                                                                                         => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                ( ( in @ X2
                                                                                                                                                                                                                                                  @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                    @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                                                                                                               => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                    @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                                                 != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                     => ( ! [X1: $i] :
                                                                                                                                                                                                                                            ( ~ ! [X2: $i] :
                                                                                                                                                                                                                                                  ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                                 => ( X1
                                                                                                                                                                                                                                                   != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                           => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                              ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                              = X1 )
                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                               => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                  ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                    = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                 => ( X1 = X3 ) )
                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                    ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                      = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                   => ( X1 = X3 ) )
                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                      ( ( X1 = X2 )
                                                                                                                                                                                                                                                     => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                        = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                        ( ( X1 = X2 )
                                                                                                                                                                                                                                                       => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                          = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                          ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                            = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                         => ( ( X3 = X4 )
                                                                                                                                                                                                                                                           => ( X2 = X4 ) ) )
                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                            ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                              = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                                                                                                           => ( X1 = X2 ) )
                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                              ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                             => ( X2 = X4 ) )
                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                                  = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                               => ( X2 = X4 ) )
                                                                                                                                                                                                                                                           => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                  ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                                 => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                        ( ( in @ X2
                                                                                                                                                                                                                                                                          @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                            @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                                ( X1
                                                                                                                                                                                                                                                                                = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                                                                                                       => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                            @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                                ( X1
                                                                                                                                                                                                                                                                                = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                                                                                                         != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                    ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                    = X2 )
                                                                                                                                                                                                                                                               => ( sP8
                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                       => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                          ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                         => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                            ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                           => ( in @ X4 @ X2 ) )
                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                 => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                    = X3 ) ) )
                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                   => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                      = X4 ) ) )
                                                                                                                                                                                                                                                                           => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                               => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                                                                                                                  = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h71,assumption,
    ! [X1: $i,X2: $i,X3: $i] :
      ( ( in @ X2 @ X3 )
     => ( ( in @ X3 @ X1 )
       => ( in @ X2 @ ( setunion @ X1 ) ) ) ),
    introduced(assumption,[]) ).

thf(h72,assumption,
    ~ ( ! [X1: $i,X2: $i] :
          ( ( in @ X2 @ ( setunion @ X1 ) )
         => ! [X3: $o] :
              ( ! [X4: $i] :
                  ( ( in @ X2 @ X4 )
                 => ( ( in @ X4 @ X1 )
                   => X3 ) )
             => X3 ) )
     => ( ! [X1: $i,X2: $i] :
            ( ( in @ X2 @ X1 )
           => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
       => ( ! [X1: $i > $o] :
              ( ~ ! [X2: $i] :
                    ( ( X1 @ X2 )
                   => ~ ! [X3: $i] :
                          ( ( X1 @ X3 )
                         => ( X2 = X3 ) ) )
             => ~ ! [X2: $i] :
                    ~ ! [X3: $i] :
                        ( ( X1 @ X3 )
                        = ( X3 = X2 ) ) )
         => ( ! [X1: $i] :
                ( ( X1 != emptyset )
               => ~ ! [X2: $i] :
                      ~ ( in @ X2 @ X1 ) )
           => ( ! [X1: $i,X2: $i] :
                  ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                 => ( X1 = X2 ) )
             => ( ! [X1: $i,X2: $i] :
                    ( ( X1 != X2 )
                   => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
               => ( ! [X1: $i,X2: $i] :
                      ( ( X1 = X2 )
                     => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                 => ( ! [X1: $i,X2: $i] :
                        ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                       => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                   => ( ! [X1: $i,X2: $i,X3: $i] :
                          ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                         => ( ( X3 != X1 )
                           => ( X3 = X2 ) ) )
                     => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                       => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                         => ( ! [X1: $i,X2: $i > $o] :
                                ( ~ ! [X3: $i] :
                                      ( ( in @ X3 @ X1 )
                                     => ~ ( X2 @ X3 ) )
                               => ( ( dsetconstr @ X1 @ X2 )
                                 != emptyset ) )
                           => ( ! [X1: $i > $o,X2: $i] :
                                  ( ( in @ X2 @ emptyset )
                                 => ( X1 @ X2 ) )
                             => ( ! [X1: $o] :
                                    ( X1
                                   => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                               => ( ! [X1: $o] :
                                      ( X1
                                     => ( set2prop @ ( prop2set @ X1 ) ) )
                                 => ( ! [X1: $i > $o] :
                                        ( ~ ! [X2: $i] :
                                              ~ ( X1 @ X2 )
                                       => ( ! [X2: $i,X3: $i] :
                                              ( ( X1 @ X2 )
                                             => ( ( X1 @ X3 )
                                               => ( X2 = X3 ) ) )
                                         => ~ ! [X2: $i] :
                                                ( ( X1 @ X2 )
                                               => ~ ! [X3: $i] :
                                                      ( ( X1 @ X3 )
                                                     => ( X2 = X3 ) ) ) ) )
                                   => ( ! [X1: $i > $o] :
                                          ( ~ ! [X2: $i] :
                                                ~ ! [X3: $i] :
                                                    ( ( X1 @ X3 )
                                                    = ( X3 = X2 ) )
                                         => ~ ! [X2: $i] :
                                                ( ( X1 @ X2 )
                                               => ~ ! [X3: $i] :
                                                      ( ( X1 @ X3 )
                                                     => ( X2 = X3 ) ) ) )
                                     => ( ! [X1: $i,X2: $i] :
                                            ( ( X1 = X2 )
                                           => ! [X3: $i,X4: $i] :
                                                ( ( X3 = X4 )
                                               => ( ( in @ X3 @ X1 )
                                                 => ( in @ X4 @ X2 ) ) ) )
                                       => ( ! [X1: $i,X2: $i] :
                                              ( ( X1 = X2 )
                                             => ! [X3: $i,X4: $i] :
                                                  ( ( X3 = X4 )
                                                 => ( ( in @ X3 @ X1 )
                                                    = ( in @ X4 @ X2 ) ) ) )
                                         => ( ! [X1: $i > $o] :
                                                ( ~ ! [X2: $i] :
                                                      ( ( X1 @ X2 )
                                                     => ~ ! [X3: $i] :
                                                            ( ( X1 @ X3 )
                                                           => ( X2 = X3 ) ) )
                                               => ! [X2: $i,X3: $i] :
                                                    ( ( X1 @ X2 )
                                                   => ( ( X1 @ X3 )
                                                     => ( X2 = X3 ) ) ) )
                                           => ( ! [X1: $i > $o,X2: $i > $o] :
                                                  ( ! [X3: $i,X4: $i] :
                                                      ( ( X3 = X4 )
                                                     => ( ( X1 @ X3 )
                                                        = ( X2 @ X4 ) ) )
                                                 => ( ( ~ ! [X3: $i] :
                                                            ( ( X1 @ X3 )
                                                           => ~ ! [X4: $i] :
                                                                  ( ( X1 @ X4 )
                                                                 => ( X3 = X4 ) ) ) )
                                                    = ( ~ ! [X3: $i] :
                                                            ( ( X2 @ X3 )
                                                           => ~ ! [X4: $i] :
                                                                  ( ( X2 @ X4 )
                                                                 => ( X3 = X4 ) ) ) ) ) )
                                             => ( ! [X1: $i,X2: $i] :
                                                    ( ( X1 = X2 )
                                                   => ! [X3: $i,X4: $i] :
                                                        ( ( X3 = X4 )
                                                       => ( ( setadjoin @ X1 @ X3 )
                                                          = ( setadjoin @ X2 @ X4 ) ) ) )
                                               => ( ! [X1: $i,X2: $i] :
                                                      ( ( X1 = X2 )
                                                     => ( ( powerset @ X1 )
                                                        = ( powerset @ X2 ) ) )
                                                 => ( ! [X1: $i,X2: $i] :
                                                        ( ( X1 = X2 )
                                                       => ( ( setunion @ X1 )
                                                          = ( setunion @ X2 ) ) )
                                                   => ( ! [X1: $i > $o] :
                                                          ( ~ ! [X2: $i] :
                                                                ( ( X1 @ X2 )
                                                               => ~ ! [X3: $i] :
                                                                      ( ( X1 @ X3 )
                                                                     => ( X2 = X3 ) ) )
                                                         => ! [X2: $i,X3: $i] :
                                                              ( ( X1 @ X2 )
                                                             => ( ( X1 @ X3 )
                                                               => ( X2 = X3 ) ) ) )
                                                     => ( ! [X1: $i > $o,X2: $i > $o] :
                                                            ( ! [X3: $i,X4: $i] :
                                                                ( ( X3 = X4 )
                                                               => ( ( X1 @ X3 )
                                                                  = ( X2 @ X4 ) ) )
                                                           => ( ~ ! [X3: $i] :
                                                                    ( ( X1 @ X3 )
                                                                   => ~ ! [X4: $i] :
                                                                          ( ( X1 @ X4 )
                                                                         => ( X3 = X4 ) ) )
                                                             => ( ~ ! [X3: $i] :
                                                                      ( ( X2 @ X3 )
                                                                     => ~ ! [X4: $i] :
                                                                            ( ( X2 @ X4 )
                                                                           => ( X3 = X4 ) ) )
                                                               => ( ( descr @ X1 )
                                                                  = ( descr @ X2 ) ) ) ) )
                                                       => ( ! [X1: $i,X2: $i] :
                                                              ( ( X1 = X2 )
                                                             => ! [X3: $i > $o,X4: $i > $o] :
                                                                  ( ! [X5: $i] :
                                                                      ( ( in @ X5 @ X1 )
                                                                     => ! [X6: $i] :
                                                                          ( ( in @ X6 @ X2 )
                                                                         => ( ( X5 = X6 )
                                                                           => ( ( X3 @ X5 )
                                                                              = ( X4 @ X6 ) ) ) ) )
                                                                 => ( ( dsetconstr @ X1 @ X3 )
                                                                    = ( dsetconstr @ X2 @ X4 ) ) ) )
                                                         => ( ! [X1: $i,X2: $i] :
                                                                ( ! [X3: $i] :
                                                                    ( ( in @ X3 @ X1 )
                                                                   => ( in @ X3 @ X2 ) )
                                                               => ( subset @ X1 @ X2 ) )
                                                           => ( ! [X1: $i,X2: $i] :
                                                                  ( ( X1 = X2 )
                                                                 => ( subset @ X2 @ X1 ) )
                                                             => ( ! [X1: $i,X2: $i] :
                                                                    ( ( X1 = X2 )
                                                                   => ( subset @ X1 @ X2 ) )
                                                               => ( ! [X1: $i,X2: $i] :
                                                                      ( ! [X3: $i] :
                                                                          ( ( in @ X3 @ X1 )
                                                                         => ( in @ X3 @ X2 ) )
                                                                     => ( subset @ X1 @ X2 ) )
                                                                 => ( ! [X1: $i] : ( subset @ emptyset @ X1 )
                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                          ( ( subset @ X1 @ X2 )
                                                                         => ( ( in @ X3 @ X1 )
                                                                           => ( in @ X3 @ X2 ) ) )
                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                            ( ( subset @ X1 @ X2 )
                                                                           => ( ~ ( in @ X3 @ X2 )
                                                                             => ~ ( in @ X3 @ X1 ) ) )
                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                              ( ( in @ X3 @ X1 )
                                                                             => ( ~ ( in @ X3 @ X2 )
                                                                               => ~ ( subset @ X1 @ X2 ) ) )
                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                ( ~ ( subset @ X1 @ X2 )
                                                                               => ( X1 != X2 ) )
                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                  ( ( in @ X3 @ X1 )
                                                                                 => ( ~ ( in @ X3 @ X2 )
                                                                                   => ( X1 != X2 ) ) )
                                                                             => ( ! [X1: $i] : ( subset @ X1 @ X1 )
                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                      ( ( subset @ X1 @ X2 )
                                                                                     => ( ( subset @ X2 @ X3 )
                                                                                       => ( subset @ X1 @ X3 ) ) )
                                                                                 => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) )
                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                          ( ( subset @ X1 @ X3 )
                                                                                         => ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                            ( ( subset @ X1 @ X2 )
                                                                                           => ( in @ X1 @ ( powerset @ X2 ) ) )
                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                              ( ( subset @ X1 @ X2 )
                                                                                             => ( ( subset @ X2 @ X1 )
                                                                                               => ( X1 = X2 ) ) )
                                                                                         => ( ! [X1: $i] :
                                                                                                ( ( subset @ X1 @ emptyset )
                                                                                               => ( X1 = emptyset ) )
                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                  ( ( subset @ X2 @ X1 )
                                                                                                 => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                    ( ( in @ X2 @ ( powerset @ X1 ) )
                                                                                                   => ( subset @ X2 @ X1 ) )
                                                                                               => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                        ( ( subset @ X1 @ X2 )
                                                                                                       => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
                                                                                                   => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                                                                                                     => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                             => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                         => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                  ( ( in @ X3 @ X2 )
                                                                                                                 => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                                                                                                    ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                   => ( ( ( in @ X3 @ X1 )
                                                                                                                       => X4 )
                                                                                                                     => ( ( ( in @ X3 @ X2 )
                                                                                                                         => X4 )
                                                                                                                       => X4 ) ) )
                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                      ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                     => ( ~ ( in @ X3 @ X1 )
                                                                                                                       => ( in @ X3 @ X2 ) ) )
                                                                                                                 => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                                                                                                                   => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                           => ( ( in @ X3 @ X2 )
                                                                                                                             => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                              ( ( subset @ X3 @ X1 )
                                                                                                                             => ( ( subset @ X3 @ X2 )
                                                                                                                               => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                               => ( in @ X3 @ X1 ) )
                                                                                                                           => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                    ( ( subset @ X1 @ X2 )
                                                                                                                                   => ( ( binintersect @ X1 @ X2 )
                                                                                                                                      = X1 ) )
                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                      ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                        = X2 )
                                                                                                                                     => ( subset @ X2 @ X1 ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                        ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                       => ( in @ X3 @ X2 ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                          ( ! [X3: $i] :
                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                             => ~ ( in @ X3 @ X2 ) )
                                                                                                                                         => ( ( binintersect @ X1 @ X2 )
                                                                                                                                            = emptyset ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                              ( ( subset @ X2 @ X1 )
                                                                                                                                             => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                = X2 ) )
                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                                  = X1 )
                                                                                                                                               => ( subset @ X1 @ X2 ) )
                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                  ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                                                                                                                  = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                   => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                     => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                      ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                     => ( in @ X3 @ X1 ) )
                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                        ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                       => ~ ( in @ X3 @ X2 ) )
                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                          ( ( subset @ X1 @ X2 )
                                                                                                                                                         => ( ( setminus @ X1 @ X2 )
                                                                                                                                                            = emptyset ) )
                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                            ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                           => ( ( in @ X3 @ X1 )
                                                                                                                                                             => ( in @ X3 @ X2 ) ) )
                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                              ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                             => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                               => ~ ( in @ X3 @ X1 ) ) )
                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                ( ~ ( in @ X3 @ X1 )
                                                                                                                                                               => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                  ( ( in @ X3 @ X2 )
                                                                                                                                                                 => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                             => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                      ( ( ( setminus @ X1 @ X2 )
                                                                                                                                                                        = emptyset )
                                                                                                                                                                     => ( subset @ X1 @ X2 ) )
                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                        ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                                                                                                       => ! [X4: $o] :
                                                                                                                                                                            ( ( ( in @ X3 @ X1 )
                                                                                                                                                                             => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                               => X4 ) )
                                                                                                                                                                           => ( ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                               => ( ( in @ X3 @ X2 )
                                                                                                                                                                                 => X4 ) )
                                                                                                                                                                             => X4 ) ) )
                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                         => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                           => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                            ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                           => ( ( in @ X3 @ X2 )
                                                                                                                                                                             => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                             => ( ( in @ X3 @ X2 )
                                                                                                                                                                               => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                               => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                 => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                           => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                             => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                               => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                            ( ( in @ X2 @ X1 )
                                                                                                                                                                                           => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                              ( ( in @ X2 @ X1 )
                                                                                                                                                                                             => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                               => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                  ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                 => ( ( X3 != X1 )
                                                                                                                                                                                                   => ( X3 = X2 ) ) )
                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                                                                                       => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                                                                                         => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                                                                                           => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                                                                                                             => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                                                                                                               => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                 => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                               => ~ ! [X4: $i] :
                                                                                                                                                                                                                      ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                     => ! [X5: $i] :
                                                                                                                                                                                                                          ( ( in @ X5 @ X2 )
                                                                                                                                                                                                                         => ( X3
                                                                                                                                                                                                                           != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                                                                                                           => ( sP5
                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                    ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                                                                                                                   => ~ ! [X3: $i] :
                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                         => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                                                                                                               => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                                                                                                                 => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                   => ( ! [X1: $i] :
                                                                                                                                                                                                                          ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                                                                                                          = X1 )
                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                            ( ! [X3: $i] :
                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                                                                    ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                   => ( ( X2 @ X3 )
                                                                                                                                                                                                                                     => ( ( X2 @ X4 )
                                                                                                                                                                                                                                       => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                           => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                   => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                             => ~ ! [X3: $i] :
                                                                                                                                                                                                                                    ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                   => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                     != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                              ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                    ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                   => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                     != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                                                                                                             => ~ ! [X3: $i] :
                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                   => ~ ( X2 @ X3 ) ) )
                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                               => ( ( X2 @ X3 )
                                                                                                                                                                                                                                 => ( ! [X4: $i] :
                                                                                                                                                                                                                                        ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                       => ( ( X2 @ X4 )
                                                                                                                                                                                                                                         => ( X4 = X3 ) ) )
                                                                                                                                                                                                                                   => ~ ! [X4: $i] :
                                                                                                                                                                                                                                          ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                         => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                           != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                  ( ! [X3: $i] :
                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                                                                                          ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                         => ( ( X2 @ X3 )
                                                                                                                                                                                                                                           => ( ( X2 @ X4 )
                                                                                                                                                                                                                                             => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                                 => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                         => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                                   => ~ ! [X3: $i] :
                                                                                                                                                                                                                                          ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                         => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                           != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                    ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                                                                                                      = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                   => ( X1 = X2 ) )
                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                      ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                     => ( X1 = X3 ) )
                                                                                                                                                                                                                                 => ( ! [X1: $i] :
                                                                                                                                                                                                                                        ( ( iskpair @ X1 )
                                                                                                                                                                                                                                       => ~ ! [X2: $i] :
                                                                                                                                                                                                                                              ( ( in @ X2
                                                                                                                                                                                                                                                @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                  @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                                                                                                             => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                  @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                                               != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                   => ( ! [X1: $i] :
                                                                                                                                                                                                                                          ( ~ ! [X2: $i] :
                                                                                                                                                                                                                                                ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                               => ( X1
                                                                                                                                                                                                                                                 != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                         => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                            ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                            = X1 )
                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                              ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                             => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                  = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                               => ( X1 = X3 ) )
                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                  ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                    = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                 => ( X1 = X3 ) )
                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                    ( ( X1 = X2 )
                                                                                                                                                                                                                                                   => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                      = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                      ( ( X1 = X2 )
                                                                                                                                                                                                                                                     => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                        = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                        ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                          = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                       => ( ( X3 = X4 )
                                                                                                                                                                                                                                                         => ( X2 = X4 ) ) )
                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                          ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                            = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                                                                                                         => ( X1 = X2 ) )
                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                            ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                              = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                           => ( X2 = X4 ) )
                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                              ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                                = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                             => ( X2 = X4 ) )
                                                                                                                                                                                                                                                         => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                               => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                      ( ( in @ X2
                                                                                                                                                                                                                                                                        @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                          @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                              ( X1
                                                                                                                                                                                                                                                                              = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                                                                                                     => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                          @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                              ( X1
                                                                                                                                                                                                                                                                              = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                                                                                                       != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                  ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                  = X2 )
                                                                                                                                                                                                                                                             => ( sP8
                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                      ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                     => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                        ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                       => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                          ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                         => ( in @ X4 @ X2 ) )
                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                               => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                  = X3 ) ) )
                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                 => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                    = X4 ) ) )
                                                                                                                                                                                                                                                                         => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                              ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                             => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                                                                                                                = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h73,assumption,
    ! [X1: $i,X2: $i] :
      ( ( in @ X2 @ ( setunion @ X1 ) )
     => ! [X3: $o] :
          ( ! [X4: $i] :
              ( ( in @ X2 @ X4 )
             => ( ( in @ X4 @ X1 )
               => X3 ) )
         => X3 ) ),
    introduced(assumption,[]) ).

thf(h74,assumption,
    ~ ( ! [X1: $i,X2: $i] :
          ( ( in @ X2 @ X1 )
         => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
     => ( ! [X1: $i > $o] :
            ( ~ ! [X2: $i] :
                  ( ( X1 @ X2 )
                 => ~ ! [X3: $i] :
                        ( ( X1 @ X3 )
                       => ( X2 = X3 ) ) )
           => ~ ! [X2: $i] :
                  ~ ! [X3: $i] :
                      ( ( X1 @ X3 )
                      = ( X3 = X2 ) ) )
       => ( ! [X1: $i] :
              ( ( X1 != emptyset )
             => ~ ! [X2: $i] :
                    ~ ( in @ X2 @ X1 ) )
         => ( ! [X1: $i,X2: $i] :
                ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
               => ( X1 = X2 ) )
           => ( ! [X1: $i,X2: $i] :
                  ( ( X1 != X2 )
                 => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
             => ( ! [X1: $i,X2: $i] :
                    ( ( X1 = X2 )
                   => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
               => ( ! [X1: $i,X2: $i] :
                      ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                     => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                 => ( ! [X1: $i,X2: $i,X3: $i] :
                        ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                       => ( ( X3 != X1 )
                         => ( X3 = X2 ) ) )
                   => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                     => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                       => ( ! [X1: $i,X2: $i > $o] :
                              ( ~ ! [X3: $i] :
                                    ( ( in @ X3 @ X1 )
                                   => ~ ( X2 @ X3 ) )
                             => ( ( dsetconstr @ X1 @ X2 )
                               != emptyset ) )
                         => ( ! [X1: $i > $o,X2: $i] :
                                ( ( in @ X2 @ emptyset )
                               => ( X1 @ X2 ) )
                           => ( ! [X1: $o] :
                                  ( X1
                                 => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                             => ( ! [X1: $o] :
                                    ( X1
                                   => ( set2prop @ ( prop2set @ X1 ) ) )
                               => ( ! [X1: $i > $o] :
                                      ( ~ ! [X2: $i] :
                                            ~ ( X1 @ X2 )
                                     => ( ! [X2: $i,X3: $i] :
                                            ( ( X1 @ X2 )
                                           => ( ( X1 @ X3 )
                                             => ( X2 = X3 ) ) )
                                       => ~ ! [X2: $i] :
                                              ( ( X1 @ X2 )
                                             => ~ ! [X3: $i] :
                                                    ( ( X1 @ X3 )
                                                   => ( X2 = X3 ) ) ) ) )
                                 => ( ! [X1: $i > $o] :
                                        ( ~ ! [X2: $i] :
                                              ~ ! [X3: $i] :
                                                  ( ( X1 @ X3 )
                                                  = ( X3 = X2 ) )
                                       => ~ ! [X2: $i] :
                                              ( ( X1 @ X2 )
                                             => ~ ! [X3: $i] :
                                                    ( ( X1 @ X3 )
                                                   => ( X2 = X3 ) ) ) )
                                   => ( ! [X1: $i,X2: $i] :
                                          ( ( X1 = X2 )
                                         => ! [X3: $i,X4: $i] :
                                              ( ( X3 = X4 )
                                             => ( ( in @ X3 @ X1 )
                                               => ( in @ X4 @ X2 ) ) ) )
                                     => ( ! [X1: $i,X2: $i] :
                                            ( ( X1 = X2 )
                                           => ! [X3: $i,X4: $i] :
                                                ( ( X3 = X4 )
                                               => ( ( in @ X3 @ X1 )
                                                  = ( in @ X4 @ X2 ) ) ) )
                                       => ( ! [X1: $i > $o] :
                                              ( ~ ! [X2: $i] :
                                                    ( ( X1 @ X2 )
                                                   => ~ ! [X3: $i] :
                                                          ( ( X1 @ X3 )
                                                         => ( X2 = X3 ) ) )
                                             => ! [X2: $i,X3: $i] :
                                                  ( ( X1 @ X2 )
                                                 => ( ( X1 @ X3 )
                                                   => ( X2 = X3 ) ) ) )
                                         => ( ! [X1: $i > $o,X2: $i > $o] :
                                                ( ! [X3: $i,X4: $i] :
                                                    ( ( X3 = X4 )
                                                   => ( ( X1 @ X3 )
                                                      = ( X2 @ X4 ) ) )
                                               => ( ( ~ ! [X3: $i] :
                                                          ( ( X1 @ X3 )
                                                         => ~ ! [X4: $i] :
                                                                ( ( X1 @ X4 )
                                                               => ( X3 = X4 ) ) ) )
                                                  = ( ~ ! [X3: $i] :
                                                          ( ( X2 @ X3 )
                                                         => ~ ! [X4: $i] :
                                                                ( ( X2 @ X4 )
                                                               => ( X3 = X4 ) ) ) ) ) )
                                           => ( ! [X1: $i,X2: $i] :
                                                  ( ( X1 = X2 )
                                                 => ! [X3: $i,X4: $i] :
                                                      ( ( X3 = X4 )
                                                     => ( ( setadjoin @ X1 @ X3 )
                                                        = ( setadjoin @ X2 @ X4 ) ) ) )
                                             => ( ! [X1: $i,X2: $i] :
                                                    ( ( X1 = X2 )
                                                   => ( ( powerset @ X1 )
                                                      = ( powerset @ X2 ) ) )
                                               => ( ! [X1: $i,X2: $i] :
                                                      ( ( X1 = X2 )
                                                     => ( ( setunion @ X1 )
                                                        = ( setunion @ X2 ) ) )
                                                 => ( ! [X1: $i > $o] :
                                                        ( ~ ! [X2: $i] :
                                                              ( ( X1 @ X2 )
                                                             => ~ ! [X3: $i] :
                                                                    ( ( X1 @ X3 )
                                                                   => ( X2 = X3 ) ) )
                                                       => ! [X2: $i,X3: $i] :
                                                            ( ( X1 @ X2 )
                                                           => ( ( X1 @ X3 )
                                                             => ( X2 = X3 ) ) ) )
                                                   => ( ! [X1: $i > $o,X2: $i > $o] :
                                                          ( ! [X3: $i,X4: $i] :
                                                              ( ( X3 = X4 )
                                                             => ( ( X1 @ X3 )
                                                                = ( X2 @ X4 ) ) )
                                                         => ( ~ ! [X3: $i] :
                                                                  ( ( X1 @ X3 )
                                                                 => ~ ! [X4: $i] :
                                                                        ( ( X1 @ X4 )
                                                                       => ( X3 = X4 ) ) )
                                                           => ( ~ ! [X3: $i] :
                                                                    ( ( X2 @ X3 )
                                                                   => ~ ! [X4: $i] :
                                                                          ( ( X2 @ X4 )
                                                                         => ( X3 = X4 ) ) )
                                                             => ( ( descr @ X1 )
                                                                = ( descr @ X2 ) ) ) ) )
                                                     => ( ! [X1: $i,X2: $i] :
                                                            ( ( X1 = X2 )
                                                           => ! [X3: $i > $o,X4: $i > $o] :
                                                                ( ! [X5: $i] :
                                                                    ( ( in @ X5 @ X1 )
                                                                   => ! [X6: $i] :
                                                                        ( ( in @ X6 @ X2 )
                                                                       => ( ( X5 = X6 )
                                                                         => ( ( X3 @ X5 )
                                                                            = ( X4 @ X6 ) ) ) ) )
                                                               => ( ( dsetconstr @ X1 @ X3 )
                                                                  = ( dsetconstr @ X2 @ X4 ) ) ) )
                                                       => ( ! [X1: $i,X2: $i] :
                                                              ( ! [X3: $i] :
                                                                  ( ( in @ X3 @ X1 )
                                                                 => ( in @ X3 @ X2 ) )
                                                             => ( subset @ X1 @ X2 ) )
                                                         => ( ! [X1: $i,X2: $i] :
                                                                ( ( X1 = X2 )
                                                               => ( subset @ X2 @ X1 ) )
                                                           => ( ! [X1: $i,X2: $i] :
                                                                  ( ( X1 = X2 )
                                                                 => ( subset @ X1 @ X2 ) )
                                                             => ( ! [X1: $i,X2: $i] :
                                                                    ( ! [X3: $i] :
                                                                        ( ( in @ X3 @ X1 )
                                                                       => ( in @ X3 @ X2 ) )
                                                                   => ( subset @ X1 @ X2 ) )
                                                               => ( ! [X1: $i] : ( subset @ emptyset @ X1 )
                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                        ( ( subset @ X1 @ X2 )
                                                                       => ( ( in @ X3 @ X1 )
                                                                         => ( in @ X3 @ X2 ) ) )
                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                          ( ( subset @ X1 @ X2 )
                                                                         => ( ~ ( in @ X3 @ X2 )
                                                                           => ~ ( in @ X3 @ X1 ) ) )
                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                            ( ( in @ X3 @ X1 )
                                                                           => ( ~ ( in @ X3 @ X2 )
                                                                             => ~ ( subset @ X1 @ X2 ) ) )
                                                                       => ( ! [X1: $i,X2: $i] :
                                                                              ( ~ ( subset @ X1 @ X2 )
                                                                             => ( X1 != X2 ) )
                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                ( ( in @ X3 @ X1 )
                                                                               => ( ~ ( in @ X3 @ X2 )
                                                                                 => ( X1 != X2 ) ) )
                                                                           => ( ! [X1: $i] : ( subset @ X1 @ X1 )
                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                    ( ( subset @ X1 @ X2 )
                                                                                   => ( ( subset @ X2 @ X3 )
                                                                                     => ( subset @ X1 @ X3 ) ) )
                                                                               => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) )
                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                        ( ( subset @ X1 @ X3 )
                                                                                       => ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                          ( ( subset @ X1 @ X2 )
                                                                                         => ( in @ X1 @ ( powerset @ X2 ) ) )
                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                            ( ( subset @ X1 @ X2 )
                                                                                           => ( ( subset @ X2 @ X1 )
                                                                                             => ( X1 = X2 ) ) )
                                                                                       => ( ! [X1: $i] :
                                                                                              ( ( subset @ X1 @ emptyset )
                                                                                             => ( X1 = emptyset ) )
                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                ( ( subset @ X2 @ X1 )
                                                                                               => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                  ( ( in @ X2 @ ( powerset @ X1 ) )
                                                                                                 => ( subset @ X2 @ X1 ) )
                                                                                             => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                      ( ( subset @ X1 @ X2 )
                                                                                                     => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
                                                                                                 => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                                                                                                   => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                           => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                       => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                ( ( in @ X3 @ X2 )
                                                                                                               => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                                                                                                  ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                 => ( ( ( in @ X3 @ X1 )
                                                                                                                     => X4 )
                                                                                                                   => ( ( ( in @ X3 @ X2 )
                                                                                                                       => X4 )
                                                                                                                     => X4 ) ) )
                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                    ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                   => ( ~ ( in @ X3 @ X1 )
                                                                                                                     => ( in @ X3 @ X2 ) ) )
                                                                                                               => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                                                                                                                 => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                         => ( ( in @ X3 @ X2 )
                                                                                                                           => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                            ( ( subset @ X3 @ X1 )
                                                                                                                           => ( ( subset @ X3 @ X2 )
                                                                                                                             => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                              ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                             => ( in @ X3 @ X1 ) )
                                                                                                                         => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                  ( ( subset @ X1 @ X2 )
                                                                                                                                 => ( ( binintersect @ X1 @ X2 )
                                                                                                                                    = X1 ) )
                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                    ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                      = X2 )
                                                                                                                                   => ( subset @ X2 @ X1 ) )
                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                      ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                     => ( in @ X3 @ X2 ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                        ( ! [X3: $i] :
                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                           => ~ ( in @ X3 @ X2 ) )
                                                                                                                                       => ( ( binintersect @ X1 @ X2 )
                                                                                                                                          = emptyset ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                            ( ( subset @ X2 @ X1 )
                                                                                                                                           => ( ( binintersect @ X1 @ X2 )
                                                                                                                                              = X2 ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                              ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                                = X1 )
                                                                                                                                             => ( subset @ X1 @ X2 ) )
                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                                                                                                                = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                 => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                   => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                    ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                   => ( in @ X3 @ X1 ) )
                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                      ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                     => ~ ( in @ X3 @ X2 ) )
                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                        ( ( subset @ X1 @ X2 )
                                                                                                                                                       => ( ( setminus @ X1 @ X2 )
                                                                                                                                                          = emptyset ) )
                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                          ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                         => ( ( in @ X3 @ X1 )
                                                                                                                                                           => ( in @ X3 @ X2 ) ) )
                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                            ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                           => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                             => ~ ( in @ X3 @ X1 ) ) )
                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                              ( ~ ( in @ X3 @ X1 )
                                                                                                                                                             => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                ( ( in @ X3 @ X2 )
                                                                                                                                                               => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                           => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                    ( ( ( setminus @ X1 @ X2 )
                                                                                                                                                                      = emptyset )
                                                                                                                                                                   => ( subset @ X1 @ X2 ) )
                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                      ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                                                                                                     => ! [X4: $o] :
                                                                                                                                                                          ( ( ( in @ X3 @ X1 )
                                                                                                                                                                           => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                             => X4 ) )
                                                                                                                                                                         => ( ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                             => ( ( in @ X3 @ X2 )
                                                                                                                                                                               => X4 ) )
                                                                                                                                                                           => X4 ) ) )
                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                       => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                         => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                          ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                         => ( ( in @ X3 @ X2 )
                                                                                                                                                                           => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                           => ( ( in @ X3 @ X2 )
                                                                                                                                                                             => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                              ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                             => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                               => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                         => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                           => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                             => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                               => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                          ( ( in @ X2 @ X1 )
                                                                                                                                                                                         => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                            ( ( in @ X2 @ X1 )
                                                                                                                                                                                           => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                             => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                               => ( ( X3 != X1 )
                                                                                                                                                                                                 => ( X3 = X2 ) ) )
                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                                                                                     => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                                                                                       => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                                                                                         => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                                                                                           => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                                                                                                             => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                                                                                                               => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                              ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                             => ~ ! [X4: $i] :
                                                                                                                                                                                                                    ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                   => ! [X5: $i] :
                                                                                                                                                                                                                        ( ( in @ X5 @ X2 )
                                                                                                                                                                                                                       => ( X3
                                                                                                                                                                                                                         != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                                                                                                         => ( sP5
                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                  ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                                                                                                                 => ~ ! [X3: $i] :
                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                       => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                                                                                                             => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                                                                                                               => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                 => ( ! [X1: $i] :
                                                                                                                                                                                                                        ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                                                                                                        = X1 )
                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                          ( ! [X3: $i] :
                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                                                                  ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                 => ( ( X2 @ X3 )
                                                                                                                                                                                                                                   => ( ( X2 @ X4 )
                                                                                                                                                                                                                                     => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                         => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                 => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                           => ~ ! [X3: $i] :
                                                                                                                                                                                                                                  ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                 => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                   != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                            ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                  ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                 => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                   != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                                                                                                           => ~ ! [X3: $i] :
                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                 => ~ ( X2 @ X3 ) ) )
                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                             => ( ( X2 @ X3 )
                                                                                                                                                                                                                               => ( ! [X4: $i] :
                                                                                                                                                                                                                                      ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                     => ( ( X2 @ X4 )
                                                                                                                                                                                                                                       => ( X4 = X3 ) ) )
                                                                                                                                                                                                                                 => ~ ! [X4: $i] :
                                                                                                                                                                                                                                        ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                       => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                         != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                ( ! [X3: $i] :
                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                                                                                        ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                       => ( ( X2 @ X3 )
                                                                                                                                                                                                                                         => ( ( X2 @ X4 )
                                                                                                                                                                                                                                           => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                               => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                       => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                                 => ~ ! [X3: $i] :
                                                                                                                                                                                                                                        ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                       => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                         != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                  ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                                                                                                    = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                 => ( X1 = X2 ) )
                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                    ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                   => ( X1 = X3 ) )
                                                                                                                                                                                                                               => ( ! [X1: $i] :
                                                                                                                                                                                                                                      ( ( iskpair @ X1 )
                                                                                                                                                                                                                                     => ~ ! [X2: $i] :
                                                                                                                                                                                                                                            ( ( in @ X2
                                                                                                                                                                                                                                              @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                                                                                                           => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                                             != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                 => ( ! [X1: $i] :
                                                                                                                                                                                                                                        ( ~ ! [X2: $i] :
                                                                                                                                                                                                                                              ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                             => ( X1
                                                                                                                                                                                                                                               != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                       => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                          ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                          = X1 )
                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                            ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                           => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                              ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                             => ( X1 = X3 ) )
                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                  = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                               => ( X1 = X3 ) )
                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                  ( ( X1 = X2 )
                                                                                                                                                                                                                                                 => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                    = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                    ( ( X1 = X2 )
                                                                                                                                                                                                                                                   => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                      = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                      ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                        = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                     => ( ( X3 = X4 )
                                                                                                                                                                                                                                                       => ( X2 = X4 ) ) )
                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                        ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                          = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                                                                                                       => ( X1 = X2 ) )
                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                          ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                            = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                         => ( X2 = X4 ) )
                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                            ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                              = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                           => ( X2 = X4 ) )
                                                                                                                                                                                                                                                       => ( ! [X1: $i] :
                                                                                                                                                                                                                                                              ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                             => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                    ( ( in @ X2
                                                                                                                                                                                                                                                                      @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                        @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                            ( X1
                                                                                                                                                                                                                                                                            = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                                                                                                   => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                        @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                            ( X1
                                                                                                                                                                                                                                                                            = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                                                                                                     != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                = X2 )
                                                                                                                                                                                                                                                           => ( sP8
                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                    ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                   => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                      ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                     => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                        ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                       => ( in @ X4 @ X2 ) )
                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                             => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                = X3 ) ) )
                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                               => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                  = X4 ) ) )
                                                                                                                                                                                                                                                                       => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                            ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                           => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                                                                                                              = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h75,assumption,
    ! [X1: $i,X2: $i] :
      ( ( in @ X2 @ X1 )
     => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) ),
    introduced(assumption,[]) ).

thf(h76,assumption,
    ~ ( ! [X1: $i > $o] :
          ( ~ ! [X2: $i] :
                ( ( X1 @ X2 )
               => ~ ! [X3: $i] :
                      ( ( X1 @ X3 )
                     => ( X2 = X3 ) ) )
         => ~ ! [X2: $i] :
                ~ ! [X3: $i] :
                    ( ( X1 @ X3 )
                    = ( X3 = X2 ) ) )
     => ( ! [X1: $i] :
            ( ( X1 != emptyset )
           => ~ ! [X2: $i] :
                  ~ ( in @ X2 @ X1 ) )
       => ( ! [X1: $i,X2: $i] :
              ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
             => ( X1 = X2 ) )
         => ( ! [X1: $i,X2: $i] :
                ( ( X1 != X2 )
               => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
           => ( ! [X1: $i,X2: $i] :
                  ( ( X1 = X2 )
                 => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
             => ( ! [X1: $i,X2: $i] :
                    ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                   => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
               => ( ! [X1: $i,X2: $i,X3: $i] :
                      ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                     => ( ( X3 != X1 )
                       => ( X3 = X2 ) ) )
                 => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                   => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                     => ( ! [X1: $i,X2: $i > $o] :
                            ( ~ ! [X3: $i] :
                                  ( ( in @ X3 @ X1 )
                                 => ~ ( X2 @ X3 ) )
                           => ( ( dsetconstr @ X1 @ X2 )
                             != emptyset ) )
                       => ( ! [X1: $i > $o,X2: $i] :
                              ( ( in @ X2 @ emptyset )
                             => ( X1 @ X2 ) )
                         => ( ! [X1: $o] :
                                ( X1
                               => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                           => ( ! [X1: $o] :
                                  ( X1
                                 => ( set2prop @ ( prop2set @ X1 ) ) )
                             => ( ! [X1: $i > $o] :
                                    ( ~ ! [X2: $i] :
                                          ~ ( X1 @ X2 )
                                   => ( ! [X2: $i,X3: $i] :
                                          ( ( X1 @ X2 )
                                         => ( ( X1 @ X3 )
                                           => ( X2 = X3 ) ) )
                                     => ~ ! [X2: $i] :
                                            ( ( X1 @ X2 )
                                           => ~ ! [X3: $i] :
                                                  ( ( X1 @ X3 )
                                                 => ( X2 = X3 ) ) ) ) )
                               => ( ! [X1: $i > $o] :
                                      ( ~ ! [X2: $i] :
                                            ~ ! [X3: $i] :
                                                ( ( X1 @ X3 )
                                                = ( X3 = X2 ) )
                                     => ~ ! [X2: $i] :
                                            ( ( X1 @ X2 )
                                           => ~ ! [X3: $i] :
                                                  ( ( X1 @ X3 )
                                                 => ( X2 = X3 ) ) ) )
                                 => ( ! [X1: $i,X2: $i] :
                                        ( ( X1 = X2 )
                                       => ! [X3: $i,X4: $i] :
                                            ( ( X3 = X4 )
                                           => ( ( in @ X3 @ X1 )
                                             => ( in @ X4 @ X2 ) ) ) )
                                   => ( ! [X1: $i,X2: $i] :
                                          ( ( X1 = X2 )
                                         => ! [X3: $i,X4: $i] :
                                              ( ( X3 = X4 )
                                             => ( ( in @ X3 @ X1 )
                                                = ( in @ X4 @ X2 ) ) ) )
                                     => ( ! [X1: $i > $o] :
                                            ( ~ ! [X2: $i] :
                                                  ( ( X1 @ X2 )
                                                 => ~ ! [X3: $i] :
                                                        ( ( X1 @ X3 )
                                                       => ( X2 = X3 ) ) )
                                           => ! [X2: $i,X3: $i] :
                                                ( ( X1 @ X2 )
                                               => ( ( X1 @ X3 )
                                                 => ( X2 = X3 ) ) ) )
                                       => ( ! [X1: $i > $o,X2: $i > $o] :
                                              ( ! [X3: $i,X4: $i] :
                                                  ( ( X3 = X4 )
                                                 => ( ( X1 @ X3 )
                                                    = ( X2 @ X4 ) ) )
                                             => ( ( ~ ! [X3: $i] :
                                                        ( ( X1 @ X3 )
                                                       => ~ ! [X4: $i] :
                                                              ( ( X1 @ X4 )
                                                             => ( X3 = X4 ) ) ) )
                                                = ( ~ ! [X3: $i] :
                                                        ( ( X2 @ X3 )
                                                       => ~ ! [X4: $i] :
                                                              ( ( X2 @ X4 )
                                                             => ( X3 = X4 ) ) ) ) ) )
                                         => ( ! [X1: $i,X2: $i] :
                                                ( ( X1 = X2 )
                                               => ! [X3: $i,X4: $i] :
                                                    ( ( X3 = X4 )
                                                   => ( ( setadjoin @ X1 @ X3 )
                                                      = ( setadjoin @ X2 @ X4 ) ) ) )
                                           => ( ! [X1: $i,X2: $i] :
                                                  ( ( X1 = X2 )
                                                 => ( ( powerset @ X1 )
                                                    = ( powerset @ X2 ) ) )
                                             => ( ! [X1: $i,X2: $i] :
                                                    ( ( X1 = X2 )
                                                   => ( ( setunion @ X1 )
                                                      = ( setunion @ X2 ) ) )
                                               => ( ! [X1: $i > $o] :
                                                      ( ~ ! [X2: $i] :
                                                            ( ( X1 @ X2 )
                                                           => ~ ! [X3: $i] :
                                                                  ( ( X1 @ X3 )
                                                                 => ( X2 = X3 ) ) )
                                                     => ! [X2: $i,X3: $i] :
                                                          ( ( X1 @ X2 )
                                                         => ( ( X1 @ X3 )
                                                           => ( X2 = X3 ) ) ) )
                                                 => ( ! [X1: $i > $o,X2: $i > $o] :
                                                        ( ! [X3: $i,X4: $i] :
                                                            ( ( X3 = X4 )
                                                           => ( ( X1 @ X3 )
                                                              = ( X2 @ X4 ) ) )
                                                       => ( ~ ! [X3: $i] :
                                                                ( ( X1 @ X3 )
                                                               => ~ ! [X4: $i] :
                                                                      ( ( X1 @ X4 )
                                                                     => ( X3 = X4 ) ) )
                                                         => ( ~ ! [X3: $i] :
                                                                  ( ( X2 @ X3 )
                                                                 => ~ ! [X4: $i] :
                                                                        ( ( X2 @ X4 )
                                                                       => ( X3 = X4 ) ) )
                                                           => ( ( descr @ X1 )
                                                              = ( descr @ X2 ) ) ) ) )
                                                   => ( ! [X1: $i,X2: $i] :
                                                          ( ( X1 = X2 )
                                                         => ! [X3: $i > $o,X4: $i > $o] :
                                                              ( ! [X5: $i] :
                                                                  ( ( in @ X5 @ X1 )
                                                                 => ! [X6: $i] :
                                                                      ( ( in @ X6 @ X2 )
                                                                     => ( ( X5 = X6 )
                                                                       => ( ( X3 @ X5 )
                                                                          = ( X4 @ X6 ) ) ) ) )
                                                             => ( ( dsetconstr @ X1 @ X3 )
                                                                = ( dsetconstr @ X2 @ X4 ) ) ) )
                                                     => ( ! [X1: $i,X2: $i] :
                                                            ( ! [X3: $i] :
                                                                ( ( in @ X3 @ X1 )
                                                               => ( in @ X3 @ X2 ) )
                                                           => ( subset @ X1 @ X2 ) )
                                                       => ( ! [X1: $i,X2: $i] :
                                                              ( ( X1 = X2 )
                                                             => ( subset @ X2 @ X1 ) )
                                                         => ( ! [X1: $i,X2: $i] :
                                                                ( ( X1 = X2 )
                                                               => ( subset @ X1 @ X2 ) )
                                                           => ( ! [X1: $i,X2: $i] :
                                                                  ( ! [X3: $i] :
                                                                      ( ( in @ X3 @ X1 )
                                                                     => ( in @ X3 @ X2 ) )
                                                                 => ( subset @ X1 @ X2 ) )
                                                             => ( ! [X1: $i] : ( subset @ emptyset @ X1 )
                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                      ( ( subset @ X1 @ X2 )
                                                                     => ( ( in @ X3 @ X1 )
                                                                       => ( in @ X3 @ X2 ) ) )
                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                        ( ( subset @ X1 @ X2 )
                                                                       => ( ~ ( in @ X3 @ X2 )
                                                                         => ~ ( in @ X3 @ X1 ) ) )
                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                          ( ( in @ X3 @ X1 )
                                                                         => ( ~ ( in @ X3 @ X2 )
                                                                           => ~ ( subset @ X1 @ X2 ) ) )
                                                                     => ( ! [X1: $i,X2: $i] :
                                                                            ( ~ ( subset @ X1 @ X2 )
                                                                           => ( X1 != X2 ) )
                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                              ( ( in @ X3 @ X1 )
                                                                             => ( ~ ( in @ X3 @ X2 )
                                                                               => ( X1 != X2 ) ) )
                                                                         => ( ! [X1: $i] : ( subset @ X1 @ X1 )
                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                  ( ( subset @ X1 @ X2 )
                                                                                 => ( ( subset @ X2 @ X3 )
                                                                                   => ( subset @ X1 @ X3 ) ) )
                                                                             => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) )
                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                      ( ( subset @ X1 @ X3 )
                                                                                     => ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                        ( ( subset @ X1 @ X2 )
                                                                                       => ( in @ X1 @ ( powerset @ X2 ) ) )
                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                          ( ( subset @ X1 @ X2 )
                                                                                         => ( ( subset @ X2 @ X1 )
                                                                                           => ( X1 = X2 ) ) )
                                                                                     => ( ! [X1: $i] :
                                                                                            ( ( subset @ X1 @ emptyset )
                                                                                           => ( X1 = emptyset ) )
                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                              ( ( subset @ X2 @ X1 )
                                                                                             => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                ( ( in @ X2 @ ( powerset @ X1 ) )
                                                                                               => ( subset @ X2 @ X1 ) )
                                                                                           => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                    ( ( subset @ X1 @ X2 )
                                                                                                   => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
                                                                                               => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                                                                                                 => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                         => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                     => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                              ( ( in @ X3 @ X2 )
                                                                                                             => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                                                                                                ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                               => ( ( ( in @ X3 @ X1 )
                                                                                                                   => X4 )
                                                                                                                 => ( ( ( in @ X3 @ X2 )
                                                                                                                     => X4 )
                                                                                                                   => X4 ) ) )
                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                  ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                 => ( ~ ( in @ X3 @ X1 )
                                                                                                                   => ( in @ X3 @ X2 ) ) )
                                                                                                             => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                                                                                                               => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                       => ( ( in @ X3 @ X2 )
                                                                                                                         => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                          ( ( subset @ X3 @ X1 )
                                                                                                                         => ( ( subset @ X3 @ X2 )
                                                                                                                           => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                            ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                           => ( in @ X3 @ X1 ) )
                                                                                                                       => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                ( ( subset @ X1 @ X2 )
                                                                                                                               => ( ( binintersect @ X1 @ X2 )
                                                                                                                                  = X1 ) )
                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                  ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                    = X2 )
                                                                                                                                 => ( subset @ X2 @ X1 ) )
                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                    ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                   => ( in @ X3 @ X2 ) )
                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                      ( ! [X3: $i] :
                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                         => ~ ( in @ X3 @ X2 ) )
                                                                                                                                     => ( ( binintersect @ X1 @ X2 )
                                                                                                                                        = emptyset ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                          ( ( subset @ X2 @ X1 )
                                                                                                                                         => ( ( binintersect @ X1 @ X2 )
                                                                                                                                            = X2 ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                            ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                              = X1 )
                                                                                                                                           => ( subset @ X1 @ X2 ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                              ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                                                                                                              = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                               => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                 => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                  ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                 => ( in @ X3 @ X1 ) )
                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                    ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                   => ~ ( in @ X3 @ X2 ) )
                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                      ( ( subset @ X1 @ X2 )
                                                                                                                                                     => ( ( setminus @ X1 @ X2 )
                                                                                                                                                        = emptyset ) )
                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                        ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                       => ( ( in @ X3 @ X1 )
                                                                                                                                                         => ( in @ X3 @ X2 ) ) )
                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                          ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                         => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                           => ~ ( in @ X3 @ X1 ) ) )
                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                            ( ~ ( in @ X3 @ X1 )
                                                                                                                                                           => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                              ( ( in @ X3 @ X2 )
                                                                                                                                                             => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                         => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                  ( ( ( setminus @ X1 @ X2 )
                                                                                                                                                                    = emptyset )
                                                                                                                                                                 => ( subset @ X1 @ X2 ) )
                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                    ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                                                                                                   => ! [X4: $o] :
                                                                                                                                                                        ( ( ( in @ X3 @ X1 )
                                                                                                                                                                         => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                           => X4 ) )
                                                                                                                                                                       => ( ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                           => ( ( in @ X3 @ X2 )
                                                                                                                                                                             => X4 ) )
                                                                                                                                                                         => X4 ) ) )
                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                     => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                       => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                        ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                       => ( ( in @ X3 @ X2 )
                                                                                                                                                                         => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                         => ( ( in @ X3 @ X2 )
                                                                                                                                                                           => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                            ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                           => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                             => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                       => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                         => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                           => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                             => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                               => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                        ( ( in @ X2 @ X1 )
                                                                                                                                                                                       => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                          ( ( in @ X2 @ X1 )
                                                                                                                                                                                         => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                           => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                              ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                             => ( ( X3 != X1 )
                                                                                                                                                                                               => ( X3 = X2 ) ) )
                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                                                                                   => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                                                                                     => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                                                                                       => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                                                                                         => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                                                                                           => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                                                                                                             => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                            ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                           => ~ ! [X4: $i] :
                                                                                                                                                                                                                  ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                 => ! [X5: $i] :
                                                                                                                                                                                                                      ( ( in @ X5 @ X2 )
                                                                                                                                                                                                                     => ( X3
                                                                                                                                                                                                                       != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                                                                                                       => ( sP5
                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                                                                                                               => ~ ! [X3: $i] :
                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                     => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                                                                                                           => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                                                                                                             => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                               => ( ! [X1: $i] :
                                                                                                                                                                                                                      ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                                                                                                      = X1 )
                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                        ( ! [X3: $i] :
                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                                                                                ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                               => ( ( X2 @ X3 )
                                                                                                                                                                                                                                 => ( ( X2 @ X4 )
                                                                                                                                                                                                                                   => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                       => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                               => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                         => ~ ! [X3: $i] :
                                                                                                                                                                                                                                ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                               => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                 != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                          ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                               => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                 != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                                                                                                         => ~ ! [X3: $i] :
                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                               => ~ ( X2 @ X3 ) ) )
                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                           => ( ( X2 @ X3 )
                                                                                                                                                                                                                             => ( ! [X4: $i] :
                                                                                                                                                                                                                                    ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                   => ( ( X2 @ X4 )
                                                                                                                                                                                                                                     => ( X4 = X3 ) ) )
                                                                                                                                                                                                                               => ~ ! [X4: $i] :
                                                                                                                                                                                                                                      ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                     => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                       != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                              ( ! [X3: $i] :
                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                                                                                      ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                     => ( ( X2 @ X3 )
                                                                                                                                                                                                                                       => ( ( X2 @ X4 )
                                                                                                                                                                                                                                         => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                             => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                     => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                               => ~ ! [X3: $i] :
                                                                                                                                                                                                                                      ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                     => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                       != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                                                                                                  = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                               => ( X1 = X2 ) )
                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                  ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                 => ( X1 = X3 ) )
                                                                                                                                                                                                                             => ( ! [X1: $i] :
                                                                                                                                                                                                                                    ( ( iskpair @ X1 )
                                                                                                                                                                                                                                   => ~ ! [X2: $i] :
                                                                                                                                                                                                                                          ( ( in @ X2
                                                                                                                                                                                                                                            @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                              @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                                                                                                         => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                              @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                                           != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                               => ( ! [X1: $i] :
                                                                                                                                                                                                                                      ( ~ ! [X2: $i] :
                                                                                                                                                                                                                                            ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                           => ( X1
                                                                                                                                                                                                                                             != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                     => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                        ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                        = X1 )
                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                         => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                            ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                              = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                           => ( X1 = X3 ) )
                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                              ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                             => ( X1 = X3 ) )
                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                ( ( X1 = X2 )
                                                                                                                                                                                                                                               => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                  = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                  ( ( X1 = X2 )
                                                                                                                                                                                                                                                 => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                    = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                    ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                      = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                   => ( ( X3 = X4 )
                                                                                                                                                                                                                                                     => ( X2 = X4 ) ) )
                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                      ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                        = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                                                                                                     => ( X1 = X2 ) )
                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                        ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                          = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                       => ( X2 = X4 ) )
                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                          ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                            = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                         => ( X2 = X4 ) )
                                                                                                                                                                                                                                                     => ( ! [X1: $i] :
                                                                                                                                                                                                                                                            ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                           => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                  ( ( in @ X2
                                                                                                                                                                                                                                                                    @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                      @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                          ( X1
                                                                                                                                                                                                                                                                          = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                                                                                                 => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                      @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                          ( X1
                                                                                                                                                                                                                                                                          = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                                                                                                   != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                              ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                              = X2 )
                                                                                                                                                                                                                                                         => ( sP8
                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                  ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                 => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                    ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                   => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                      ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                     => ( in @ X4 @ X2 ) )
                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                           => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                              = X3 ) ) )
                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                             => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                = X4 ) ) )
                                                                                                                                                                                                                                                                     => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                         => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                                                                                                            = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h77,assumption,
    ! [X1: $i > $o] :
      ( ~ ! [X2: $i] :
            ( ( X1 @ X2 )
           => ~ ! [X3: $i] :
                  ( ( X1 @ X3 )
                 => ( X2 = X3 ) ) )
     => ~ ! [X2: $i] :
            ~ ! [X3: $i] :
                ( ( X1 @ X3 )
                = ( X3 = X2 ) ) ),
    introduced(assumption,[]) ).

thf(h78,assumption,
    ~ ( ! [X1: $i] :
          ( ( X1 != emptyset )
         => ~ ! [X2: $i] :
                ~ ( in @ X2 @ X1 ) )
     => ( ! [X1: $i,X2: $i] :
            ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
           => ( X1 = X2 ) )
       => ( ! [X1: $i,X2: $i] :
              ( ( X1 != X2 )
             => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
         => ( ! [X1: $i,X2: $i] :
                ( ( X1 = X2 )
               => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
           => ( ! [X1: $i,X2: $i] :
                  ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                 => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
             => ( ! [X1: $i,X2: $i,X3: $i] :
                    ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                   => ( ( X3 != X1 )
                     => ( X3 = X2 ) ) )
               => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                 => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                   => ( ! [X1: $i,X2: $i > $o] :
                          ( ~ ! [X3: $i] :
                                ( ( in @ X3 @ X1 )
                               => ~ ( X2 @ X3 ) )
                         => ( ( dsetconstr @ X1 @ X2 )
                           != emptyset ) )
                     => ( ! [X1: $i > $o,X2: $i] :
                            ( ( in @ X2 @ emptyset )
                           => ( X1 @ X2 ) )
                       => ( ! [X1: $o] :
                              ( X1
                             => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                         => ( ! [X1: $o] :
                                ( X1
                               => ( set2prop @ ( prop2set @ X1 ) ) )
                           => ( ! [X1: $i > $o] :
                                  ( ~ ! [X2: $i] :
                                        ~ ( X1 @ X2 )
                                 => ( ! [X2: $i,X3: $i] :
                                        ( ( X1 @ X2 )
                                       => ( ( X1 @ X3 )
                                         => ( X2 = X3 ) ) )
                                   => ~ ! [X2: $i] :
                                          ( ( X1 @ X2 )
                                         => ~ ! [X3: $i] :
                                                ( ( X1 @ X3 )
                                               => ( X2 = X3 ) ) ) ) )
                             => ( ! [X1: $i > $o] :
                                    ( ~ ! [X2: $i] :
                                          ~ ! [X3: $i] :
                                              ( ( X1 @ X3 )
                                              = ( X3 = X2 ) )
                                   => ~ ! [X2: $i] :
                                          ( ( X1 @ X2 )
                                         => ~ ! [X3: $i] :
                                                ( ( X1 @ X3 )
                                               => ( X2 = X3 ) ) ) )
                               => ( ! [X1: $i,X2: $i] :
                                      ( ( X1 = X2 )
                                     => ! [X3: $i,X4: $i] :
                                          ( ( X3 = X4 )
                                         => ( ( in @ X3 @ X1 )
                                           => ( in @ X4 @ X2 ) ) ) )
                                 => ( ! [X1: $i,X2: $i] :
                                        ( ( X1 = X2 )
                                       => ! [X3: $i,X4: $i] :
                                            ( ( X3 = X4 )
                                           => ( ( in @ X3 @ X1 )
                                              = ( in @ X4 @ X2 ) ) ) )
                                   => ( ! [X1: $i > $o] :
                                          ( ~ ! [X2: $i] :
                                                ( ( X1 @ X2 )
                                               => ~ ! [X3: $i] :
                                                      ( ( X1 @ X3 )
                                                     => ( X2 = X3 ) ) )
                                         => ! [X2: $i,X3: $i] :
                                              ( ( X1 @ X2 )
                                             => ( ( X1 @ X3 )
                                               => ( X2 = X3 ) ) ) )
                                     => ( ! [X1: $i > $o,X2: $i > $o] :
                                            ( ! [X3: $i,X4: $i] :
                                                ( ( X3 = X4 )
                                               => ( ( X1 @ X3 )
                                                  = ( X2 @ X4 ) ) )
                                           => ( ( ~ ! [X3: $i] :
                                                      ( ( X1 @ X3 )
                                                     => ~ ! [X4: $i] :
                                                            ( ( X1 @ X4 )
                                                           => ( X3 = X4 ) ) ) )
                                              = ( ~ ! [X3: $i] :
                                                      ( ( X2 @ X3 )
                                                     => ~ ! [X4: $i] :
                                                            ( ( X2 @ X4 )
                                                           => ( X3 = X4 ) ) ) ) ) )
                                       => ( ! [X1: $i,X2: $i] :
                                              ( ( X1 = X2 )
                                             => ! [X3: $i,X4: $i] :
                                                  ( ( X3 = X4 )
                                                 => ( ( setadjoin @ X1 @ X3 )
                                                    = ( setadjoin @ X2 @ X4 ) ) ) )
                                         => ( ! [X1: $i,X2: $i] :
                                                ( ( X1 = X2 )
                                               => ( ( powerset @ X1 )
                                                  = ( powerset @ X2 ) ) )
                                           => ( ! [X1: $i,X2: $i] :
                                                  ( ( X1 = X2 )
                                                 => ( ( setunion @ X1 )
                                                    = ( setunion @ X2 ) ) )
                                             => ( ! [X1: $i > $o] :
                                                    ( ~ ! [X2: $i] :
                                                          ( ( X1 @ X2 )
                                                         => ~ ! [X3: $i] :
                                                                ( ( X1 @ X3 )
                                                               => ( X2 = X3 ) ) )
                                                   => ! [X2: $i,X3: $i] :
                                                        ( ( X1 @ X2 )
                                                       => ( ( X1 @ X3 )
                                                         => ( X2 = X3 ) ) ) )
                                               => ( ! [X1: $i > $o,X2: $i > $o] :
                                                      ( ! [X3: $i,X4: $i] :
                                                          ( ( X3 = X4 )
                                                         => ( ( X1 @ X3 )
                                                            = ( X2 @ X4 ) ) )
                                                     => ( ~ ! [X3: $i] :
                                                              ( ( X1 @ X3 )
                                                             => ~ ! [X4: $i] :
                                                                    ( ( X1 @ X4 )
                                                                   => ( X3 = X4 ) ) )
                                                       => ( ~ ! [X3: $i] :
                                                                ( ( X2 @ X3 )
                                                               => ~ ! [X4: $i] :
                                                                      ( ( X2 @ X4 )
                                                                     => ( X3 = X4 ) ) )
                                                         => ( ( descr @ X1 )
                                                            = ( descr @ X2 ) ) ) ) )
                                                 => ( ! [X1: $i,X2: $i] :
                                                        ( ( X1 = X2 )
                                                       => ! [X3: $i > $o,X4: $i > $o] :
                                                            ( ! [X5: $i] :
                                                                ( ( in @ X5 @ X1 )
                                                               => ! [X6: $i] :
                                                                    ( ( in @ X6 @ X2 )
                                                                   => ( ( X5 = X6 )
                                                                     => ( ( X3 @ X5 )
                                                                        = ( X4 @ X6 ) ) ) ) )
                                                           => ( ( dsetconstr @ X1 @ X3 )
                                                              = ( dsetconstr @ X2 @ X4 ) ) ) )
                                                   => ( ! [X1: $i,X2: $i] :
                                                          ( ! [X3: $i] :
                                                              ( ( in @ X3 @ X1 )
                                                             => ( in @ X3 @ X2 ) )
                                                         => ( subset @ X1 @ X2 ) )
                                                     => ( ! [X1: $i,X2: $i] :
                                                            ( ( X1 = X2 )
                                                           => ( subset @ X2 @ X1 ) )
                                                       => ( ! [X1: $i,X2: $i] :
                                                              ( ( X1 = X2 )
                                                             => ( subset @ X1 @ X2 ) )
                                                         => ( ! [X1: $i,X2: $i] :
                                                                ( ! [X3: $i] :
                                                                    ( ( in @ X3 @ X1 )
                                                                   => ( in @ X3 @ X2 ) )
                                                               => ( subset @ X1 @ X2 ) )
                                                           => ( ! [X1: $i] : ( subset @ emptyset @ X1 )
                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                    ( ( subset @ X1 @ X2 )
                                                                   => ( ( in @ X3 @ X1 )
                                                                     => ( in @ X3 @ X2 ) ) )
                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                      ( ( subset @ X1 @ X2 )
                                                                     => ( ~ ( in @ X3 @ X2 )
                                                                       => ~ ( in @ X3 @ X1 ) ) )
                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                        ( ( in @ X3 @ X1 )
                                                                       => ( ~ ( in @ X3 @ X2 )
                                                                         => ~ ( subset @ X1 @ X2 ) ) )
                                                                   => ( ! [X1: $i,X2: $i] :
                                                                          ( ~ ( subset @ X1 @ X2 )
                                                                         => ( X1 != X2 ) )
                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                            ( ( in @ X3 @ X1 )
                                                                           => ( ~ ( in @ X3 @ X2 )
                                                                             => ( X1 != X2 ) ) )
                                                                       => ( ! [X1: $i] : ( subset @ X1 @ X1 )
                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                ( ( subset @ X1 @ X2 )
                                                                               => ( ( subset @ X2 @ X3 )
                                                                                 => ( subset @ X1 @ X3 ) ) )
                                                                           => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) )
                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                    ( ( subset @ X1 @ X3 )
                                                                                   => ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                      ( ( subset @ X1 @ X2 )
                                                                                     => ( in @ X1 @ ( powerset @ X2 ) ) )
                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                        ( ( subset @ X1 @ X2 )
                                                                                       => ( ( subset @ X2 @ X1 )
                                                                                         => ( X1 = X2 ) ) )
                                                                                   => ( ! [X1: $i] :
                                                                                          ( ( subset @ X1 @ emptyset )
                                                                                         => ( X1 = emptyset ) )
                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                            ( ( subset @ X2 @ X1 )
                                                                                           => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                              ( ( in @ X2 @ ( powerset @ X1 ) )
                                                                                             => ( subset @ X2 @ X1 ) )
                                                                                         => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                  ( ( subset @ X1 @ X2 )
                                                                                                 => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
                                                                                             => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                                                                                               => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                       => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                   => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                            ( ( in @ X3 @ X2 )
                                                                                                           => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                                                                                              ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                             => ( ( ( in @ X3 @ X1 )
                                                                                                                 => X4 )
                                                                                                               => ( ( ( in @ X3 @ X2 )
                                                                                                                   => X4 )
                                                                                                                 => X4 ) ) )
                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                               => ( ~ ( in @ X3 @ X1 )
                                                                                                                 => ( in @ X3 @ X2 ) ) )
                                                                                                           => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                                                                                                             => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                     => ( ( in @ X3 @ X2 )
                                                                                                                       => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                        ( ( subset @ X3 @ X1 )
                                                                                                                       => ( ( subset @ X3 @ X2 )
                                                                                                                         => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                          ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                         => ( in @ X3 @ X1 ) )
                                                                                                                     => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                              ( ( subset @ X1 @ X2 )
                                                                                                                             => ( ( binintersect @ X1 @ X2 )
                                                                                                                                = X1 ) )
                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                  = X2 )
                                                                                                                               => ( subset @ X2 @ X1 ) )
                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                  ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                 => ( in @ X3 @ X2 ) )
                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                    ( ! [X3: $i] :
                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                       => ~ ( in @ X3 @ X2 ) )
                                                                                                                                   => ( ( binintersect @ X1 @ X2 )
                                                                                                                                      = emptyset ) )
                                                                                                                               => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                        ( ( subset @ X2 @ X1 )
                                                                                                                                       => ( ( binintersect @ X1 @ X2 )
                                                                                                                                          = X2 ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                          ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                            = X1 )
                                                                                                                                         => ( subset @ X1 @ X2 ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                            ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                                                                                                            = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                             => ( ~ ( in @ X3 @ X2 )
                                                                                                                                               => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                               => ( in @ X3 @ X1 ) )
                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                  ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                 => ~ ( in @ X3 @ X2 ) )
                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                    ( ( subset @ X1 @ X2 )
                                                                                                                                                   => ( ( setminus @ X1 @ X2 )
                                                                                                                                                      = emptyset ) )
                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                      ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                     => ( ( in @ X3 @ X1 )
                                                                                                                                                       => ( in @ X3 @ X2 ) ) )
                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                        ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                       => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                         => ~ ( in @ X3 @ X1 ) ) )
                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                          ( ~ ( in @ X3 @ X1 )
                                                                                                                                                         => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                            ( ( in @ X3 @ X2 )
                                                                                                                                                           => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                       => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                ( ( ( setminus @ X1 @ X2 )
                                                                                                                                                                  = emptyset )
                                                                                                                                                               => ( subset @ X1 @ X2 ) )
                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                  ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                                                                                                 => ! [X4: $o] :
                                                                                                                                                                      ( ( ( in @ X3 @ X1 )
                                                                                                                                                                       => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                         => X4 ) )
                                                                                                                                                                     => ( ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                         => ( ( in @ X3 @ X2 )
                                                                                                                                                                           => X4 ) )
                                                                                                                                                                       => X4 ) ) )
                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                   => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                     => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                      ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                     => ( ( in @ X3 @ X2 )
                                                                                                                                                                       => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                       => ( ( in @ X3 @ X2 )
                                                                                                                                                                         => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                          ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                         => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                           => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                     => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                       => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                         => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                           => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                             => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                      ( ( in @ X2 @ X1 )
                                                                                                                                                                                     => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                        ( ( in @ X2 @ X1 )
                                                                                                                                                                                       => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                         => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                            ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                           => ( ( X3 != X1 )
                                                                                                                                                                                             => ( X3 = X2 ) ) )
                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                                                                                 => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                                                                                   => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                                                                                     => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                                                                                       => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                                                                                         => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                                                                                           => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                         => ~ ! [X4: $i] :
                                                                                                                                                                                                                ( ( in @ X4 @ X1 )
                                                                                                                                                                                                               => ! [X5: $i] :
                                                                                                                                                                                                                    ( ( in @ X5 @ X2 )
                                                                                                                                                                                                                   => ( X3
                                                                                                                                                                                                                     != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                                                                                                     => ( sP5
                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                              ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                                                                                                             => ~ ! [X3: $i] :
                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                   => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                                                                                                         => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                                                                                                           => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                             => ( ! [X1: $i] :
                                                                                                                                                                                                                    ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                                                                                                    = X1 )
                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                      ( ! [X3: $i] :
                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                                                                              ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                             => ( ( X2 @ X3 )
                                                                                                                                                                                                                               => ( ( X2 @ X4 )
                                                                                                                                                                                                                                 => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                     => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                             => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                       => ~ ! [X3: $i] :
                                                                                                                                                                                                                              ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                             => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                               != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                        ( ~ ! [X3: $i] :
                                                                                                                                                                                                                              ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                             => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                               != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                                                                                                       => ~ ! [X3: $i] :
                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                             => ~ ( X2 @ X3 ) ) )
                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                         => ( ( X2 @ X3 )
                                                                                                                                                                                                                           => ( ! [X4: $i] :
                                                                                                                                                                                                                                  ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                 => ( ( X2 @ X4 )
                                                                                                                                                                                                                                   => ( X4 = X3 ) ) )
                                                                                                                                                                                                                             => ~ ! [X4: $i] :
                                                                                                                                                                                                                                    ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                   => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                     != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                            ( ! [X3: $i] :
                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                                                                    ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                   => ( ( X2 @ X3 )
                                                                                                                                                                                                                                     => ( ( X2 @ X4 )
                                                                                                                                                                                                                                       => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                           => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                   => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                             => ~ ! [X3: $i] :
                                                                                                                                                                                                                                    ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                   => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                     != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                              ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                                                                                                = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                             => ( X1 = X2 ) )
                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                               => ( X1 = X3 ) )
                                                                                                                                                                                                                           => ( ! [X1: $i] :
                                                                                                                                                                                                                                  ( ( iskpair @ X1 )
                                                                                                                                                                                                                                 => ~ ! [X2: $i] :
                                                                                                                                                                                                                                        ( ( in @ X2
                                                                                                                                                                                                                                          @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                            @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                                                                                                       => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                            @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                                         != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                             => ( ! [X1: $i] :
                                                                                                                                                                                                                                    ( ~ ! [X2: $i] :
                                                                                                                                                                                                                                          ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                         => ( X1
                                                                                                                                                                                                                                           != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                   => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                      ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                      = X1 )
                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                       => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                          ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                            = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                         => ( X1 = X3 ) )
                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                            ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                              = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                           => ( X1 = X3 ) )
                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                              ( ( X1 = X2 )
                                                                                                                                                                                                                                             => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                ( ( X1 = X2 )
                                                                                                                                                                                                                                               => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                  = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                  ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                    = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                 => ( ( X3 = X4 )
                                                                                                                                                                                                                                                   => ( X2 = X4 ) ) )
                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                    ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                      = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                                                                                                   => ( X1 = X2 ) )
                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                      ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                        = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                     => ( X2 = X4 ) )
                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                        ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                          = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                       => ( X2 = X4 ) )
                                                                                                                                                                                                                                                   => ( ! [X1: $i] :
                                                                                                                                                                                                                                                          ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                         => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                ( ( in @ X2
                                                                                                                                                                                                                                                                  @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                    @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                        ( X1
                                                                                                                                                                                                                                                                        = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                                                                                               => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                    @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                        ( X1
                                                                                                                                                                                                                                                                        = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                                                                                                 != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                            ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                            = X2 )
                                                                                                                                                                                                                                                       => ( sP8
                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                               => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                  ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                 => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                    ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                   => ( in @ X4 @ X2 ) )
                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                         => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                            = X3 ) ) )
                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                           => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                              = X4 ) ) )
                                                                                                                                                                                                                                                                   => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                       => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                                                                                                          = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h79,assumption,
    ~ ( ! [X1: $i,X2: $i] :
          ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
         => ( X1 = X2 ) )
     => ( ! [X1: $i,X2: $i] :
            ( ( X1 != X2 )
           => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
       => ( ! [X1: $i,X2: $i] :
              ( ( X1 = X2 )
             => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
         => ( ! [X1: $i,X2: $i] :
                ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
               => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
           => ( ! [X1: $i,X2: $i,X3: $i] :
                  ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                 => ( ( X3 != X1 )
                   => ( X3 = X2 ) ) )
             => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
               => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                 => ( ! [X1: $i,X2: $i > $o] :
                        ( ~ ! [X3: $i] :
                              ( ( in @ X3 @ X1 )
                             => ~ ( X2 @ X3 ) )
                       => ( ( dsetconstr @ X1 @ X2 )
                         != emptyset ) )
                   => ( ! [X1: $i > $o,X2: $i] :
                          ( ( in @ X2 @ emptyset )
                         => ( X1 @ X2 ) )
                     => ( ! [X1: $o] :
                            ( X1
                           => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                       => ( ! [X1: $o] :
                              ( X1
                             => ( set2prop @ ( prop2set @ X1 ) ) )
                         => ( ! [X1: $i > $o] :
                                ( ~ ! [X2: $i] :
                                      ~ ( X1 @ X2 )
                               => ( ! [X2: $i,X3: $i] :
                                      ( ( X1 @ X2 )
                                     => ( ( X1 @ X3 )
                                       => ( X2 = X3 ) ) )
                                 => ~ ! [X2: $i] :
                                        ( ( X1 @ X2 )
                                       => ~ ! [X3: $i] :
                                              ( ( X1 @ X3 )
                                             => ( X2 = X3 ) ) ) ) )
                           => ( ! [X1: $i > $o] :
                                  ( ~ ! [X2: $i] :
                                        ~ ! [X3: $i] :
                                            ( ( X1 @ X3 )
                                            = ( X3 = X2 ) )
                                 => ~ ! [X2: $i] :
                                        ( ( X1 @ X2 )
                                       => ~ ! [X3: $i] :
                                              ( ( X1 @ X3 )
                                             => ( X2 = X3 ) ) ) )
                             => ( ! [X1: $i,X2: $i] :
                                    ( ( X1 = X2 )
                                   => ! [X3: $i,X4: $i] :
                                        ( ( X3 = X4 )
                                       => ( ( in @ X3 @ X1 )
                                         => ( in @ X4 @ X2 ) ) ) )
                               => ( ! [X1: $i,X2: $i] :
                                      ( ( X1 = X2 )
                                     => ! [X3: $i,X4: $i] :
                                          ( ( X3 = X4 )
                                         => ( ( in @ X3 @ X1 )
                                            = ( in @ X4 @ X2 ) ) ) )
                                 => ( ! [X1: $i > $o] :
                                        ( ~ ! [X2: $i] :
                                              ( ( X1 @ X2 )
                                             => ~ ! [X3: $i] :
                                                    ( ( X1 @ X3 )
                                                   => ( X2 = X3 ) ) )
                                       => ! [X2: $i,X3: $i] :
                                            ( ( X1 @ X2 )
                                           => ( ( X1 @ X3 )
                                             => ( X2 = X3 ) ) ) )
                                   => ( ! [X1: $i > $o,X2: $i > $o] :
                                          ( ! [X3: $i,X4: $i] :
                                              ( ( X3 = X4 )
                                             => ( ( X1 @ X3 )
                                                = ( X2 @ X4 ) ) )
                                         => ( ( ~ ! [X3: $i] :
                                                    ( ( X1 @ X3 )
                                                   => ~ ! [X4: $i] :
                                                          ( ( X1 @ X4 )
                                                         => ( X3 = X4 ) ) ) )
                                            = ( ~ ! [X3: $i] :
                                                    ( ( X2 @ X3 )
                                                   => ~ ! [X4: $i] :
                                                          ( ( X2 @ X4 )
                                                         => ( X3 = X4 ) ) ) ) ) )
                                     => ( ! [X1: $i,X2: $i] :
                                            ( ( X1 = X2 )
                                           => ! [X3: $i,X4: $i] :
                                                ( ( X3 = X4 )
                                               => ( ( setadjoin @ X1 @ X3 )
                                                  = ( setadjoin @ X2 @ X4 ) ) ) )
                                       => ( ! [X1: $i,X2: $i] :
                                              ( ( X1 = X2 )
                                             => ( ( powerset @ X1 )
                                                = ( powerset @ X2 ) ) )
                                         => ( ! [X1: $i,X2: $i] :
                                                ( ( X1 = X2 )
                                               => ( ( setunion @ X1 )
                                                  = ( setunion @ X2 ) ) )
                                           => ( ! [X1: $i > $o] :
                                                  ( ~ ! [X2: $i] :
                                                        ( ( X1 @ X2 )
                                                       => ~ ! [X3: $i] :
                                                              ( ( X1 @ X3 )
                                                             => ( X2 = X3 ) ) )
                                                 => ! [X2: $i,X3: $i] :
                                                      ( ( X1 @ X2 )
                                                     => ( ( X1 @ X3 )
                                                       => ( X2 = X3 ) ) ) )
                                             => ( ! [X1: $i > $o,X2: $i > $o] :
                                                    ( ! [X3: $i,X4: $i] :
                                                        ( ( X3 = X4 )
                                                       => ( ( X1 @ X3 )
                                                          = ( X2 @ X4 ) ) )
                                                   => ( ~ ! [X3: $i] :
                                                            ( ( X1 @ X3 )
                                                           => ~ ! [X4: $i] :
                                                                  ( ( X1 @ X4 )
                                                                 => ( X3 = X4 ) ) )
                                                     => ( ~ ! [X3: $i] :
                                                              ( ( X2 @ X3 )
                                                             => ~ ! [X4: $i] :
                                                                    ( ( X2 @ X4 )
                                                                   => ( X3 = X4 ) ) )
                                                       => ( ( descr @ X1 )
                                                          = ( descr @ X2 ) ) ) ) )
                                               => ( ! [X1: $i,X2: $i] :
                                                      ( ( X1 = X2 )
                                                     => ! [X3: $i > $o,X4: $i > $o] :
                                                          ( ! [X5: $i] :
                                                              ( ( in @ X5 @ X1 )
                                                             => ! [X6: $i] :
                                                                  ( ( in @ X6 @ X2 )
                                                                 => ( ( X5 = X6 )
                                                                   => ( ( X3 @ X5 )
                                                                      = ( X4 @ X6 ) ) ) ) )
                                                         => ( ( dsetconstr @ X1 @ X3 )
                                                            = ( dsetconstr @ X2 @ X4 ) ) ) )
                                                 => ( ! [X1: $i,X2: $i] :
                                                        ( ! [X3: $i] :
                                                            ( ( in @ X3 @ X1 )
                                                           => ( in @ X3 @ X2 ) )
                                                       => ( subset @ X1 @ X2 ) )
                                                   => ( ! [X1: $i,X2: $i] :
                                                          ( ( X1 = X2 )
                                                         => ( subset @ X2 @ X1 ) )
                                                     => ( ! [X1: $i,X2: $i] :
                                                            ( ( X1 = X2 )
                                                           => ( subset @ X1 @ X2 ) )
                                                       => ( ! [X1: $i,X2: $i] :
                                                              ( ! [X3: $i] :
                                                                  ( ( in @ X3 @ X1 )
                                                                 => ( in @ X3 @ X2 ) )
                                                             => ( subset @ X1 @ X2 ) )
                                                         => ( ! [X1: $i] : ( subset @ emptyset @ X1 )
                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                  ( ( subset @ X1 @ X2 )
                                                                 => ( ( in @ X3 @ X1 )
                                                                   => ( in @ X3 @ X2 ) ) )
                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                    ( ( subset @ X1 @ X2 )
                                                                   => ( ~ ( in @ X3 @ X2 )
                                                                     => ~ ( in @ X3 @ X1 ) ) )
                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                      ( ( in @ X3 @ X1 )
                                                                     => ( ~ ( in @ X3 @ X2 )
                                                                       => ~ ( subset @ X1 @ X2 ) ) )
                                                                 => ( ! [X1: $i,X2: $i] :
                                                                        ( ~ ( subset @ X1 @ X2 )
                                                                       => ( X1 != X2 ) )
                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                          ( ( in @ X3 @ X1 )
                                                                         => ( ~ ( in @ X3 @ X2 )
                                                                           => ( X1 != X2 ) ) )
                                                                     => ( ! [X1: $i] : ( subset @ X1 @ X1 )
                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                              ( ( subset @ X1 @ X2 )
                                                                             => ( ( subset @ X2 @ X3 )
                                                                               => ( subset @ X1 @ X3 ) ) )
                                                                         => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) )
                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                  ( ( subset @ X1 @ X3 )
                                                                                 => ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                    ( ( subset @ X1 @ X2 )
                                                                                   => ( in @ X1 @ ( powerset @ X2 ) ) )
                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                      ( ( subset @ X1 @ X2 )
                                                                                     => ( ( subset @ X2 @ X1 )
                                                                                       => ( X1 = X2 ) ) )
                                                                                 => ( ! [X1: $i] :
                                                                                        ( ( subset @ X1 @ emptyset )
                                                                                       => ( X1 = emptyset ) )
                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                          ( ( subset @ X2 @ X1 )
                                                                                         => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                            ( ( in @ X2 @ ( powerset @ X1 ) )
                                                                                           => ( subset @ X2 @ X1 ) )
                                                                                       => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                ( ( subset @ X1 @ X2 )
                                                                                               => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
                                                                                           => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                                                                                             => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                     => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                 => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                          ( ( in @ X3 @ X2 )
                                                                                                         => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                                                                                            ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                           => ( ( ( in @ X3 @ X1 )
                                                                                                               => X4 )
                                                                                                             => ( ( ( in @ X3 @ X2 )
                                                                                                                 => X4 )
                                                                                                               => X4 ) ) )
                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                              ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                             => ( ~ ( in @ X3 @ X1 )
                                                                                                               => ( in @ X3 @ X2 ) ) )
                                                                                                         => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                                                                                                           => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                   => ( ( in @ X3 @ X2 )
                                                                                                                     => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                      ( ( subset @ X3 @ X1 )
                                                                                                                     => ( ( subset @ X3 @ X2 )
                                                                                                                       => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                        ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                       => ( in @ X3 @ X1 ) )
                                                                                                                   => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                            ( ( subset @ X1 @ X2 )
                                                                                                                           => ( ( binintersect @ X1 @ X2 )
                                                                                                                              = X1 ) )
                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                              ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                = X2 )
                                                                                                                             => ( subset @ X2 @ X1 ) )
                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                               => ( in @ X3 @ X2 ) )
                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                  ( ! [X3: $i] :
                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                     => ~ ( in @ X3 @ X2 ) )
                                                                                                                                 => ( ( binintersect @ X1 @ X2 )
                                                                                                                                    = emptyset ) )
                                                                                                                             => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                      ( ( subset @ X2 @ X1 )
                                                                                                                                     => ( ( binintersect @ X1 @ X2 )
                                                                                                                                        = X2 ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                        ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                          = X1 )
                                                                                                                                       => ( subset @ X1 @ X2 ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                          ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                                                                                                          = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                           => ( ~ ( in @ X3 @ X2 )
                                                                                                                                             => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                              ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                             => ( in @ X3 @ X1 ) )
                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                               => ~ ( in @ X3 @ X2 ) )
                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                  ( ( subset @ X1 @ X2 )
                                                                                                                                                 => ( ( setminus @ X1 @ X2 )
                                                                                                                                                    = emptyset ) )
                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                    ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                   => ( ( in @ X3 @ X1 )
                                                                                                                                                     => ( in @ X3 @ X2 ) ) )
                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                      ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                     => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                       => ~ ( in @ X3 @ X1 ) ) )
                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                        ( ~ ( in @ X3 @ X1 )
                                                                                                                                                       => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                          ( ( in @ X3 @ X2 )
                                                                                                                                                         => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                     => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                              ( ( ( setminus @ X1 @ X2 )
                                                                                                                                                                = emptyset )
                                                                                                                                                             => ( subset @ X1 @ X2 ) )
                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                                                                                               => ! [X4: $o] :
                                                                                                                                                                    ( ( ( in @ X3 @ X1 )
                                                                                                                                                                     => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                       => X4 ) )
                                                                                                                                                                   => ( ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                       => ( ( in @ X3 @ X2 )
                                                                                                                                                                         => X4 ) )
                                                                                                                                                                     => X4 ) ) )
                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                 => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                   => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                    ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                   => ( ( in @ X3 @ X2 )
                                                                                                                                                                     => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                     => ( ( in @ X3 @ X2 )
                                                                                                                                                                       => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                        ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                       => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                         => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                   => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                     => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                       => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                         => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                           => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                    ( ( in @ X2 @ X1 )
                                                                                                                                                                                   => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                      ( ( in @ X2 @ X1 )
                                                                                                                                                                                     => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                       => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                          ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                         => ( ( X3 != X1 )
                                                                                                                                                                                           => ( X3 = X2 ) ) )
                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                                                                                               => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                                                                                 => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                                                                                   => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                                                                                     => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                                                                                       => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                                                                                         => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                       => ~ ! [X4: $i] :
                                                                                                                                                                                                              ( ( in @ X4 @ X1 )
                                                                                                                                                                                                             => ! [X5: $i] :
                                                                                                                                                                                                                  ( ( in @ X5 @ X2 )
                                                                                                                                                                                                                 => ( X3
                                                                                                                                                                                                                   != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                                                                                                   => ( sP5
                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                            ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                                                                                                           => ~ ! [X3: $i] :
                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                 => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                                                                                                       => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                                                                                                         => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                           => ( ! [X1: $i] :
                                                                                                                                                                                                                  ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                                                                                                  = X1 )
                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                    ( ! [X3: $i] :
                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                                                                            ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                           => ( ( X2 @ X3 )
                                                                                                                                                                                                                             => ( ( X2 @ X4 )
                                                                                                                                                                                                                               => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                   => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                           => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                     => ~ ! [X3: $i] :
                                                                                                                                                                                                                            ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                           => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                             != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                      ( ~ ! [X3: $i] :
                                                                                                                                                                                                                            ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                           => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                             != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                                                                                                     => ~ ! [X3: $i] :
                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                           => ~ ( X2 @ X3 ) ) )
                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                       => ( ( X2 @ X3 )
                                                                                                                                                                                                                         => ( ! [X4: $i] :
                                                                                                                                                                                                                                ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                               => ( ( X2 @ X4 )
                                                                                                                                                                                                                                 => ( X4 = X3 ) ) )
                                                                                                                                                                                                                           => ~ ! [X4: $i] :
                                                                                                                                                                                                                                  ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                 => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                   != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                          ( ! [X3: $i] :
                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                                                                  ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                 => ( ( X2 @ X3 )
                                                                                                                                                                                                                                   => ( ( X2 @ X4 )
                                                                                                                                                                                                                                     => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                         => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                 => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                           => ~ ! [X3: $i] :
                                                                                                                                                                                                                                  ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                 => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                   != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                            ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                                                                                              = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                           => ( X1 = X2 ) )
                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                              ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                             => ( X1 = X3 ) )
                                                                                                                                                                                                                         => ( ! [X1: $i] :
                                                                                                                                                                                                                                ( ( iskpair @ X1 )
                                                                                                                                                                                                                               => ~ ! [X2: $i] :
                                                                                                                                                                                                                                      ( ( in @ X2
                                                                                                                                                                                                                                        @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                          @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                                                                                                     => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                          @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                                       != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                           => ( ! [X1: $i] :
                                                                                                                                                                                                                                  ( ~ ! [X2: $i] :
                                                                                                                                                                                                                                        ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                       => ( X1
                                                                                                                                                                                                                                         != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                 => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                    ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                    = X1 )
                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                      ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                     => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                        ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                          = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                       => ( X1 = X3 ) )
                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                          ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                            = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                         => ( X1 = X3 ) )
                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                            ( ( X1 = X2 )
                                                                                                                                                                                                                                           => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                              = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                              ( ( X1 = X2 )
                                                                                                                                                                                                                                             => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                  = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                               => ( ( X3 = X4 )
                                                                                                                                                                                                                                                 => ( X2 = X4 ) ) )
                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                  ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                    = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                                                                                                 => ( X1 = X2 ) )
                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                    ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                      = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                   => ( X2 = X4 ) )
                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                      ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                        = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                     => ( X2 = X4 ) )
                                                                                                                                                                                                                                                 => ( ! [X1: $i] :
                                                                                                                                                                                                                                                        ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                       => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                              ( ( in @ X2
                                                                                                                                                                                                                                                                @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                  @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                      ( X1
                                                                                                                                                                                                                                                                      = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                                                                                             => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                  @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                      ( X1
                                                                                                                                                                                                                                                                      = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                                                                                               != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                          ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                          = X2 )
                                                                                                                                                                                                                                                     => ( sP8
                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                              ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                             => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                               => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                  ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                 => ( in @ X4 @ X2 ) )
                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                       => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                          = X3 ) ) )
                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                         => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                            = X4 ) ) )
                                                                                                                                                                                                                                                                 => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                      ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                     => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                                                                                                        = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h80,assumption,
    ! [X1: $i,X2: $i] :
      ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
     => ( X1 = X2 ) ),
    introduced(assumption,[]) ).

thf(h81,assumption,
    ~ ( ! [X1: $i,X2: $i] :
          ( ( X1 != X2 )
         => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
     => ( ! [X1: $i,X2: $i] :
            ( ( X1 = X2 )
           => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
       => ( ! [X1: $i,X2: $i] :
              ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
             => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
         => ( ! [X1: $i,X2: $i,X3: $i] :
                ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
               => ( ( X3 != X1 )
                 => ( X3 = X2 ) ) )
           => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
             => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
               => ( ! [X1: $i,X2: $i > $o] :
                      ( ~ ! [X3: $i] :
                            ( ( in @ X3 @ X1 )
                           => ~ ( X2 @ X3 ) )
                     => ( ( dsetconstr @ X1 @ X2 )
                       != emptyset ) )
                 => ( ! [X1: $i > $o,X2: $i] :
                        ( ( in @ X2 @ emptyset )
                       => ( X1 @ X2 ) )
                   => ( ! [X1: $o] :
                          ( X1
                         => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                     => ( ! [X1: $o] :
                            ( X1
                           => ( set2prop @ ( prop2set @ X1 ) ) )
                       => ( ! [X1: $i > $o] :
                              ( ~ ! [X2: $i] :
                                    ~ ( X1 @ X2 )
                             => ( ! [X2: $i,X3: $i] :
                                    ( ( X1 @ X2 )
                                   => ( ( X1 @ X3 )
                                     => ( X2 = X3 ) ) )
                               => ~ ! [X2: $i] :
                                      ( ( X1 @ X2 )
                                     => ~ ! [X3: $i] :
                                            ( ( X1 @ X3 )
                                           => ( X2 = X3 ) ) ) ) )
                         => ( ! [X1: $i > $o] :
                                ( ~ ! [X2: $i] :
                                      ~ ! [X3: $i] :
                                          ( ( X1 @ X3 )
                                          = ( X3 = X2 ) )
                               => ~ ! [X2: $i] :
                                      ( ( X1 @ X2 )
                                     => ~ ! [X3: $i] :
                                            ( ( X1 @ X3 )
                                           => ( X2 = X3 ) ) ) )
                           => ( ! [X1: $i,X2: $i] :
                                  ( ( X1 = X2 )
                                 => ! [X3: $i,X4: $i] :
                                      ( ( X3 = X4 )
                                     => ( ( in @ X3 @ X1 )
                                       => ( in @ X4 @ X2 ) ) ) )
                             => ( ! [X1: $i,X2: $i] :
                                    ( ( X1 = X2 )
                                   => ! [X3: $i,X4: $i] :
                                        ( ( X3 = X4 )
                                       => ( ( in @ X3 @ X1 )
                                          = ( in @ X4 @ X2 ) ) ) )
                               => ( ! [X1: $i > $o] :
                                      ( ~ ! [X2: $i] :
                                            ( ( X1 @ X2 )
                                           => ~ ! [X3: $i] :
                                                  ( ( X1 @ X3 )
                                                 => ( X2 = X3 ) ) )
                                     => ! [X2: $i,X3: $i] :
                                          ( ( X1 @ X2 )
                                         => ( ( X1 @ X3 )
                                           => ( X2 = X3 ) ) ) )
                                 => ( ! [X1: $i > $o,X2: $i > $o] :
                                        ( ! [X3: $i,X4: $i] :
                                            ( ( X3 = X4 )
                                           => ( ( X1 @ X3 )
                                              = ( X2 @ X4 ) ) )
                                       => ( ( ~ ! [X3: $i] :
                                                  ( ( X1 @ X3 )
                                                 => ~ ! [X4: $i] :
                                                        ( ( X1 @ X4 )
                                                       => ( X3 = X4 ) ) ) )
                                          = ( ~ ! [X3: $i] :
                                                  ( ( X2 @ X3 )
                                                 => ~ ! [X4: $i] :
                                                        ( ( X2 @ X4 )
                                                       => ( X3 = X4 ) ) ) ) ) )
                                   => ( ! [X1: $i,X2: $i] :
                                          ( ( X1 = X2 )
                                         => ! [X3: $i,X4: $i] :
                                              ( ( X3 = X4 )
                                             => ( ( setadjoin @ X1 @ X3 )
                                                = ( setadjoin @ X2 @ X4 ) ) ) )
                                     => ( ! [X1: $i,X2: $i] :
                                            ( ( X1 = X2 )
                                           => ( ( powerset @ X1 )
                                              = ( powerset @ X2 ) ) )
                                       => ( ! [X1: $i,X2: $i] :
                                              ( ( X1 = X2 )
                                             => ( ( setunion @ X1 )
                                                = ( setunion @ X2 ) ) )
                                         => ( ! [X1: $i > $o] :
                                                ( ~ ! [X2: $i] :
                                                      ( ( X1 @ X2 )
                                                     => ~ ! [X3: $i] :
                                                            ( ( X1 @ X3 )
                                                           => ( X2 = X3 ) ) )
                                               => ! [X2: $i,X3: $i] :
                                                    ( ( X1 @ X2 )
                                                   => ( ( X1 @ X3 )
                                                     => ( X2 = X3 ) ) ) )
                                           => ( ! [X1: $i > $o,X2: $i > $o] :
                                                  ( ! [X3: $i,X4: $i] :
                                                      ( ( X3 = X4 )
                                                     => ( ( X1 @ X3 )
                                                        = ( X2 @ X4 ) ) )
                                                 => ( ~ ! [X3: $i] :
                                                          ( ( X1 @ X3 )
                                                         => ~ ! [X4: $i] :
                                                                ( ( X1 @ X4 )
                                                               => ( X3 = X4 ) ) )
                                                   => ( ~ ! [X3: $i] :
                                                            ( ( X2 @ X3 )
                                                           => ~ ! [X4: $i] :
                                                                  ( ( X2 @ X4 )
                                                                 => ( X3 = X4 ) ) )
                                                     => ( ( descr @ X1 )
                                                        = ( descr @ X2 ) ) ) ) )
                                             => ( ! [X1: $i,X2: $i] :
                                                    ( ( X1 = X2 )
                                                   => ! [X3: $i > $o,X4: $i > $o] :
                                                        ( ! [X5: $i] :
                                                            ( ( in @ X5 @ X1 )
                                                           => ! [X6: $i] :
                                                                ( ( in @ X6 @ X2 )
                                                               => ( ( X5 = X6 )
                                                                 => ( ( X3 @ X5 )
                                                                    = ( X4 @ X6 ) ) ) ) )
                                                       => ( ( dsetconstr @ X1 @ X3 )
                                                          = ( dsetconstr @ X2 @ X4 ) ) ) )
                                               => ( ! [X1: $i,X2: $i] :
                                                      ( ! [X3: $i] :
                                                          ( ( in @ X3 @ X1 )
                                                         => ( in @ X3 @ X2 ) )
                                                     => ( subset @ X1 @ X2 ) )
                                                 => ( ! [X1: $i,X2: $i] :
                                                        ( ( X1 = X2 )
                                                       => ( subset @ X2 @ X1 ) )
                                                   => ( ! [X1: $i,X2: $i] :
                                                          ( ( X1 = X2 )
                                                         => ( subset @ X1 @ X2 ) )
                                                     => ( ! [X1: $i,X2: $i] :
                                                            ( ! [X3: $i] :
                                                                ( ( in @ X3 @ X1 )
                                                               => ( in @ X3 @ X2 ) )
                                                           => ( subset @ X1 @ X2 ) )
                                                       => ( ! [X1: $i] : ( subset @ emptyset @ X1 )
                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                ( ( subset @ X1 @ X2 )
                                                               => ( ( in @ X3 @ X1 )
                                                                 => ( in @ X3 @ X2 ) ) )
                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                  ( ( subset @ X1 @ X2 )
                                                                 => ( ~ ( in @ X3 @ X2 )
                                                                   => ~ ( in @ X3 @ X1 ) ) )
                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                    ( ( in @ X3 @ X1 )
                                                                   => ( ~ ( in @ X3 @ X2 )
                                                                     => ~ ( subset @ X1 @ X2 ) ) )
                                                               => ( ! [X1: $i,X2: $i] :
                                                                      ( ~ ( subset @ X1 @ X2 )
                                                                     => ( X1 != X2 ) )
                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                        ( ( in @ X3 @ X1 )
                                                                       => ( ~ ( in @ X3 @ X2 )
                                                                         => ( X1 != X2 ) ) )
                                                                   => ( ! [X1: $i] : ( subset @ X1 @ X1 )
                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                            ( ( subset @ X1 @ X2 )
                                                                           => ( ( subset @ X2 @ X3 )
                                                                             => ( subset @ X1 @ X3 ) ) )
                                                                       => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) )
                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                ( ( subset @ X1 @ X3 )
                                                                               => ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                  ( ( subset @ X1 @ X2 )
                                                                                 => ( in @ X1 @ ( powerset @ X2 ) ) )
                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                    ( ( subset @ X1 @ X2 )
                                                                                   => ( ( subset @ X2 @ X1 )
                                                                                     => ( X1 = X2 ) ) )
                                                                               => ( ! [X1: $i] :
                                                                                      ( ( subset @ X1 @ emptyset )
                                                                                     => ( X1 = emptyset ) )
                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                        ( ( subset @ X2 @ X1 )
                                                                                       => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                          ( ( in @ X2 @ ( powerset @ X1 ) )
                                                                                         => ( subset @ X2 @ X1 ) )
                                                                                     => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                              ( ( subset @ X1 @ X2 )
                                                                                             => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
                                                                                         => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                                                                                           => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                   => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                               => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                        ( ( in @ X3 @ X2 )
                                                                                                       => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                                                                                          ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                         => ( ( ( in @ X3 @ X1 )
                                                                                                             => X4 )
                                                                                                           => ( ( ( in @ X3 @ X2 )
                                                                                                               => X4 )
                                                                                                             => X4 ) ) )
                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                            ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                           => ( ~ ( in @ X3 @ X1 )
                                                                                                             => ( in @ X3 @ X2 ) ) )
                                                                                                       => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                                                                                                         => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                 => ( ( in @ X3 @ X2 )
                                                                                                                   => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                    ( ( subset @ X3 @ X1 )
                                                                                                                   => ( ( subset @ X3 @ X2 )
                                                                                                                     => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                      ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                     => ( in @ X3 @ X1 ) )
                                                                                                                 => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                          ( ( subset @ X1 @ X2 )
                                                                                                                         => ( ( binintersect @ X1 @ X2 )
                                                                                                                            = X1 ) )
                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                            ( ( ( binintersect @ X1 @ X2 )
                                                                                                                              = X2 )
                                                                                                                           => ( subset @ X2 @ X1 ) )
                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                              ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                             => ( in @ X3 @ X2 ) )
                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                ( ! [X3: $i] :
                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                   => ~ ( in @ X3 @ X2 ) )
                                                                                                                               => ( ( binintersect @ X1 @ X2 )
                                                                                                                                  = emptyset ) )
                                                                                                                           => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                    ( ( subset @ X2 @ X1 )
                                                                                                                                   => ( ( binintersect @ X1 @ X2 )
                                                                                                                                      = X2 ) )
                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                      ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                        = X1 )
                                                                                                                                     => ( subset @ X1 @ X2 ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                        ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                                                                                                        = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                         => ( ~ ( in @ X3 @ X2 )
                                                                                                                                           => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                            ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                           => ( in @ X3 @ X1 ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                              ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                             => ~ ( in @ X3 @ X2 ) )
                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                ( ( subset @ X1 @ X2 )
                                                                                                                                               => ( ( setminus @ X1 @ X2 )
                                                                                                                                                  = emptyset ) )
                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                  ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                 => ( ( in @ X3 @ X1 )
                                                                                                                                                   => ( in @ X3 @ X2 ) ) )
                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                    ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                   => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                     => ~ ( in @ X3 @ X1 ) ) )
                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                      ( ~ ( in @ X3 @ X1 )
                                                                                                                                                     => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                        ( ( in @ X3 @ X2 )
                                                                                                                                                       => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                   => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                            ( ( ( setminus @ X1 @ X2 )
                                                                                                                                                              = emptyset )
                                                                                                                                                           => ( subset @ X1 @ X2 ) )
                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                              ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                                                                                             => ! [X4: $o] :
                                                                                                                                                                  ( ( ( in @ X3 @ X1 )
                                                                                                                                                                   => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                     => X4 ) )
                                                                                                                                                                 => ( ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                     => ( ( in @ X3 @ X2 )
                                                                                                                                                                       => X4 ) )
                                                                                                                                                                   => X4 ) ) )
                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                               => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                 => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                  ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                 => ( ( in @ X3 @ X2 )
                                                                                                                                                                   => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                   => ( ( in @ X3 @ X2 )
                                                                                                                                                                     => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                      ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                     => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                       => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                 => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                   => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                     => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                       => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                         => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                  ( ( in @ X2 @ X1 )
                                                                                                                                                                                 => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                    ( ( in @ X2 @ X1 )
                                                                                                                                                                                   => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                     => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                        ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                       => ( ( X3 != X1 )
                                                                                                                                                                                         => ( X3 = X2 ) ) )
                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                                                                                             => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                                                                                               => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                                                                                 => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                                                                                   => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                                                                                     => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                                                                                       => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                      ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                     => ~ ! [X4: $i] :
                                                                                                                                                                                                            ( ( in @ X4 @ X1 )
                                                                                                                                                                                                           => ! [X5: $i] :
                                                                                                                                                                                                                ( ( in @ X5 @ X2 )
                                                                                                                                                                                                               => ( X3
                                                                                                                                                                                                                 != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                                                                                                 => ( sP5
                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                          ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                                                                                                         => ~ ! [X3: $i] :
                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                               => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                                                                                                     => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                                                                                                       => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                         => ( ! [X1: $i] :
                                                                                                                                                                                                                ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                                                                                                = X1 )
                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                  ( ! [X3: $i] :
                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                                                                          ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                         => ( ( X2 @ X3 )
                                                                                                                                                                                                                           => ( ( X2 @ X4 )
                                                                                                                                                                                                                             => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                 => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                         => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                   => ~ ! [X3: $i] :
                                                                                                                                                                                                                          ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                         => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                           != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                    ( ~ ! [X3: $i] :
                                                                                                                                                                                                                          ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                         => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                           != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                                                                                                   => ~ ! [X3: $i] :
                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                         => ~ ( X2 @ X3 ) ) )
                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                     => ( ( X2 @ X3 )
                                                                                                                                                                                                                       => ( ! [X4: $i] :
                                                                                                                                                                                                                              ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                             => ( ( X2 @ X4 )
                                                                                                                                                                                                                               => ( X4 = X3 ) ) )
                                                                                                                                                                                                                         => ~ ! [X4: $i] :
                                                                                                                                                                                                                                ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                               => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                 != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                        ( ! [X3: $i] :
                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                                                                                ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                               => ( ( X2 @ X3 )
                                                                                                                                                                                                                                 => ( ( X2 @ X4 )
                                                                                                                                                                                                                                   => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                       => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                               => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                         => ~ ! [X3: $i] :
                                                                                                                                                                                                                                ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                               => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                 != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                          ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                                                                                            = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                         => ( X1 = X2 ) )
                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                            ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                           => ( X1 = X3 ) )
                                                                                                                                                                                                                       => ( ! [X1: $i] :
                                                                                                                                                                                                                              ( ( iskpair @ X1 )
                                                                                                                                                                                                                             => ~ ! [X2: $i] :
                                                                                                                                                                                                                                    ( ( in @ X2
                                                                                                                                                                                                                                      @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                        @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                                                                                                   => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                        @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                                     != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                         => ( ! [X1: $i] :
                                                                                                                                                                                                                                ( ~ ! [X2: $i] :
                                                                                                                                                                                                                                      ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                     => ( X1
                                                                                                                                                                                                                                       != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                               => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                  ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                  = X1 )
                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                    ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                   => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                      ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                        = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                     => ( X1 = X3 ) )
                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                        ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                          = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                       => ( X1 = X3 ) )
                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                          ( ( X1 = X2 )
                                                                                                                                                                                                                                         => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                            = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                            ( ( X1 = X2 )
                                                                                                                                                                                                                                           => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                              = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                              ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                             => ( ( X3 = X4 )
                                                                                                                                                                                                                                               => ( X2 = X4 ) ) )
                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                  = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                                                                                               => ( X1 = X2 ) )
                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                  ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                    = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                 => ( X2 = X4 ) )
                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                    ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                      = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                   => ( X2 = X4 ) )
                                                                                                                                                                                                                                               => ( ! [X1: $i] :
                                                                                                                                                                                                                                                      ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                     => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                            ( ( in @ X2
                                                                                                                                                                                                                                                              @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                    ( X1
                                                                                                                                                                                                                                                                    = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                                                                                           => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                    ( X1
                                                                                                                                                                                                                                                                    = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                                                                                             != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                        ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                        = X2 )
                                                                                                                                                                                                                                                   => ( sP8
                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                            ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                           => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                              ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                             => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                               => ( in @ X4 @ X2 ) )
                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                     => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                        = X3 ) ) )
                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                       => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                          = X4 ) ) )
                                                                                                                                                                                                                                                               => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                    ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                   => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                                                                                                      = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h82,assumption,
    ! [X1: $i,X2: $i] :
      ( ( X1 != X2 )
     => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) ),
    introduced(assumption,[]) ).

thf(h83,assumption,
    ~ ( ! [X1: $i,X2: $i] :
          ( ( X1 = X2 )
         => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
     => ( ! [X1: $i,X2: $i] :
            ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
           => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
       => ( ! [X1: $i,X2: $i,X3: $i] :
              ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
             => ( ( X3 != X1 )
               => ( X3 = X2 ) ) )
         => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
           => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
             => ( ! [X1: $i,X2: $i > $o] :
                    ( ~ ! [X3: $i] :
                          ( ( in @ X3 @ X1 )
                         => ~ ( X2 @ X3 ) )
                   => ( ( dsetconstr @ X1 @ X2 )
                     != emptyset ) )
               => ( ! [X1: $i > $o,X2: $i] :
                      ( ( in @ X2 @ emptyset )
                     => ( X1 @ X2 ) )
                 => ( ! [X1: $o] :
                        ( X1
                       => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                   => ( ! [X1: $o] :
                          ( X1
                         => ( set2prop @ ( prop2set @ X1 ) ) )
                     => ( ! [X1: $i > $o] :
                            ( ~ ! [X2: $i] :
                                  ~ ( X1 @ X2 )
                           => ( ! [X2: $i,X3: $i] :
                                  ( ( X1 @ X2 )
                                 => ( ( X1 @ X3 )
                                   => ( X2 = X3 ) ) )
                             => ~ ! [X2: $i] :
                                    ( ( X1 @ X2 )
                                   => ~ ! [X3: $i] :
                                          ( ( X1 @ X3 )
                                         => ( X2 = X3 ) ) ) ) )
                       => ( ! [X1: $i > $o] :
                              ( ~ ! [X2: $i] :
                                    ~ ! [X3: $i] :
                                        ( ( X1 @ X3 )
                                        = ( X3 = X2 ) )
                             => ~ ! [X2: $i] :
                                    ( ( X1 @ X2 )
                                   => ~ ! [X3: $i] :
                                          ( ( X1 @ X3 )
                                         => ( X2 = X3 ) ) ) )
                         => ( ! [X1: $i,X2: $i] :
                                ( ( X1 = X2 )
                               => ! [X3: $i,X4: $i] :
                                    ( ( X3 = X4 )
                                   => ( ( in @ X3 @ X1 )
                                     => ( in @ X4 @ X2 ) ) ) )
                           => ( ! [X1: $i,X2: $i] :
                                  ( ( X1 = X2 )
                                 => ! [X3: $i,X4: $i] :
                                      ( ( X3 = X4 )
                                     => ( ( in @ X3 @ X1 )
                                        = ( in @ X4 @ X2 ) ) ) )
                             => ( ! [X1: $i > $o] :
                                    ( ~ ! [X2: $i] :
                                          ( ( X1 @ X2 )
                                         => ~ ! [X3: $i] :
                                                ( ( X1 @ X3 )
                                               => ( X2 = X3 ) ) )
                                   => ! [X2: $i,X3: $i] :
                                        ( ( X1 @ X2 )
                                       => ( ( X1 @ X3 )
                                         => ( X2 = X3 ) ) ) )
                               => ( ! [X1: $i > $o,X2: $i > $o] :
                                      ( ! [X3: $i,X4: $i] :
                                          ( ( X3 = X4 )
                                         => ( ( X1 @ X3 )
                                            = ( X2 @ X4 ) ) )
                                     => ( ( ~ ! [X3: $i] :
                                                ( ( X1 @ X3 )
                                               => ~ ! [X4: $i] :
                                                      ( ( X1 @ X4 )
                                                     => ( X3 = X4 ) ) ) )
                                        = ( ~ ! [X3: $i] :
                                                ( ( X2 @ X3 )
                                               => ~ ! [X4: $i] :
                                                      ( ( X2 @ X4 )
                                                     => ( X3 = X4 ) ) ) ) ) )
                                 => ( ! [X1: $i,X2: $i] :
                                        ( ( X1 = X2 )
                                       => ! [X3: $i,X4: $i] :
                                            ( ( X3 = X4 )
                                           => ( ( setadjoin @ X1 @ X3 )
                                              = ( setadjoin @ X2 @ X4 ) ) ) )
                                   => ( ! [X1: $i,X2: $i] :
                                          ( ( X1 = X2 )
                                         => ( ( powerset @ X1 )
                                            = ( powerset @ X2 ) ) )
                                     => ( ! [X1: $i,X2: $i] :
                                            ( ( X1 = X2 )
                                           => ( ( setunion @ X1 )
                                              = ( setunion @ X2 ) ) )
                                       => ( ! [X1: $i > $o] :
                                              ( ~ ! [X2: $i] :
                                                    ( ( X1 @ X2 )
                                                   => ~ ! [X3: $i] :
                                                          ( ( X1 @ X3 )
                                                         => ( X2 = X3 ) ) )
                                             => ! [X2: $i,X3: $i] :
                                                  ( ( X1 @ X2 )
                                                 => ( ( X1 @ X3 )
                                                   => ( X2 = X3 ) ) ) )
                                         => ( ! [X1: $i > $o,X2: $i > $o] :
                                                ( ! [X3: $i,X4: $i] :
                                                    ( ( X3 = X4 )
                                                   => ( ( X1 @ X3 )
                                                      = ( X2 @ X4 ) ) )
                                               => ( ~ ! [X3: $i] :
                                                        ( ( X1 @ X3 )
                                                       => ~ ! [X4: $i] :
                                                              ( ( X1 @ X4 )
                                                             => ( X3 = X4 ) ) )
                                                 => ( ~ ! [X3: $i] :
                                                          ( ( X2 @ X3 )
                                                         => ~ ! [X4: $i] :
                                                                ( ( X2 @ X4 )
                                                               => ( X3 = X4 ) ) )
                                                   => ( ( descr @ X1 )
                                                      = ( descr @ X2 ) ) ) ) )
                                           => ( ! [X1: $i,X2: $i] :
                                                  ( ( X1 = X2 )
                                                 => ! [X3: $i > $o,X4: $i > $o] :
                                                      ( ! [X5: $i] :
                                                          ( ( in @ X5 @ X1 )
                                                         => ! [X6: $i] :
                                                              ( ( in @ X6 @ X2 )
                                                             => ( ( X5 = X6 )
                                                               => ( ( X3 @ X5 )
                                                                  = ( X4 @ X6 ) ) ) ) )
                                                     => ( ( dsetconstr @ X1 @ X3 )
                                                        = ( dsetconstr @ X2 @ X4 ) ) ) )
                                             => ( ! [X1: $i,X2: $i] :
                                                    ( ! [X3: $i] :
                                                        ( ( in @ X3 @ X1 )
                                                       => ( in @ X3 @ X2 ) )
                                                   => ( subset @ X1 @ X2 ) )
                                               => ( ! [X1: $i,X2: $i] :
                                                      ( ( X1 = X2 )
                                                     => ( subset @ X2 @ X1 ) )
                                                 => ( ! [X1: $i,X2: $i] :
                                                        ( ( X1 = X2 )
                                                       => ( subset @ X1 @ X2 ) )
                                                   => ( ! [X1: $i,X2: $i] :
                                                          ( ! [X3: $i] :
                                                              ( ( in @ X3 @ X1 )
                                                             => ( in @ X3 @ X2 ) )
                                                         => ( subset @ X1 @ X2 ) )
                                                     => ( ! [X1: $i] : ( subset @ emptyset @ X1 )
                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                              ( ( subset @ X1 @ X2 )
                                                             => ( ( in @ X3 @ X1 )
                                                               => ( in @ X3 @ X2 ) ) )
                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                ( ( subset @ X1 @ X2 )
                                                               => ( ~ ( in @ X3 @ X2 )
                                                                 => ~ ( in @ X3 @ X1 ) ) )
                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                  ( ( in @ X3 @ X1 )
                                                                 => ( ~ ( in @ X3 @ X2 )
                                                                   => ~ ( subset @ X1 @ X2 ) ) )
                                                             => ( ! [X1: $i,X2: $i] :
                                                                    ( ~ ( subset @ X1 @ X2 )
                                                                   => ( X1 != X2 ) )
                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                      ( ( in @ X3 @ X1 )
                                                                     => ( ~ ( in @ X3 @ X2 )
                                                                       => ( X1 != X2 ) ) )
                                                                 => ( ! [X1: $i] : ( subset @ X1 @ X1 )
                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                          ( ( subset @ X1 @ X2 )
                                                                         => ( ( subset @ X2 @ X3 )
                                                                           => ( subset @ X1 @ X3 ) ) )
                                                                     => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) )
                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                              ( ( subset @ X1 @ X3 )
                                                                             => ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                ( ( subset @ X1 @ X2 )
                                                                               => ( in @ X1 @ ( powerset @ X2 ) ) )
                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                  ( ( subset @ X1 @ X2 )
                                                                                 => ( ( subset @ X2 @ X1 )
                                                                                   => ( X1 = X2 ) ) )
                                                                             => ( ! [X1: $i] :
                                                                                    ( ( subset @ X1 @ emptyset )
                                                                                   => ( X1 = emptyset ) )
                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                      ( ( subset @ X2 @ X1 )
                                                                                     => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                        ( ( in @ X2 @ ( powerset @ X1 ) )
                                                                                       => ( subset @ X2 @ X1 ) )
                                                                                   => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                            ( ( subset @ X1 @ X2 )
                                                                                           => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
                                                                                       => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                                                                                         => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                 => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                             => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                      ( ( in @ X3 @ X2 )
                                                                                                     => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                                                                                        ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                       => ( ( ( in @ X3 @ X1 )
                                                                                                           => X4 )
                                                                                                         => ( ( ( in @ X3 @ X2 )
                                                                                                             => X4 )
                                                                                                           => X4 ) ) )
                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                          ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                         => ( ~ ( in @ X3 @ X1 )
                                                                                                           => ( in @ X3 @ X2 ) ) )
                                                                                                     => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                                                                                                       => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                               => ( ( in @ X3 @ X2 )
                                                                                                                 => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                  ( ( subset @ X3 @ X1 )
                                                                                                                 => ( ( subset @ X3 @ X2 )
                                                                                                                   => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                    ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                   => ( in @ X3 @ X1 ) )
                                                                                                               => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                        ( ( subset @ X1 @ X2 )
                                                                                                                       => ( ( binintersect @ X1 @ X2 )
                                                                                                                          = X1 ) )
                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                          ( ( ( binintersect @ X1 @ X2 )
                                                                                                                            = X2 )
                                                                                                                         => ( subset @ X2 @ X1 ) )
                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                            ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                           => ( in @ X3 @ X2 ) )
                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                              ( ! [X3: $i] :
                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                 => ~ ( in @ X3 @ X2 ) )
                                                                                                                             => ( ( binintersect @ X1 @ X2 )
                                                                                                                                = emptyset ) )
                                                                                                                         => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                  ( ( subset @ X2 @ X1 )
                                                                                                                                 => ( ( binintersect @ X1 @ X2 )
                                                                                                                                    = X2 ) )
                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                    ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                      = X1 )
                                                                                                                                   => ( subset @ X1 @ X2 ) )
                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                      ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                                                                                                      = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                       => ( ~ ( in @ X3 @ X2 )
                                                                                                                                         => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                          ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                         => ( in @ X3 @ X1 ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                            ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                           => ~ ( in @ X3 @ X2 ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                              ( ( subset @ X1 @ X2 )
                                                                                                                                             => ( ( setminus @ X1 @ X2 )
                                                                                                                                                = emptyset ) )
                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                               => ( ( in @ X3 @ X1 )
                                                                                                                                                 => ( in @ X3 @ X2 ) ) )
                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                  ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                 => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                   => ~ ( in @ X3 @ X1 ) ) )
                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                    ( ~ ( in @ X3 @ X1 )
                                                                                                                                                   => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                      ( ( in @ X3 @ X2 )
                                                                                                                                                     => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                 => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                          ( ( ( setminus @ X1 @ X2 )
                                                                                                                                                            = emptyset )
                                                                                                                                                         => ( subset @ X1 @ X2 ) )
                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                            ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                                                                                           => ! [X4: $o] :
                                                                                                                                                                ( ( ( in @ X3 @ X1 )
                                                                                                                                                                 => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                   => X4 ) )
                                                                                                                                                               => ( ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                   => ( ( in @ X3 @ X2 )
                                                                                                                                                                     => X4 ) )
                                                                                                                                                                 => X4 ) ) )
                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                             => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                               => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                ( ~ ( in @ X3 @ X1 )
                                                                                                                                                               => ( ( in @ X3 @ X2 )
                                                                                                                                                                 => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                 => ( ( in @ X3 @ X2 )
                                                                                                                                                                   => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                    ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                   => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                     => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                               => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                 => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                   => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                     => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                       => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                ( ( in @ X2 @ X1 )
                                                                                                                                                                               => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                  ( ( in @ X2 @ X1 )
                                                                                                                                                                                 => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                   => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                      ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                     => ( ( X3 != X1 )
                                                                                                                                                                                       => ( X3 = X2 ) ) )
                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                                                                           => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                                                                                             => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                                                                                               => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                                                                                 => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                                                                                   => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                                                                                     => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                    ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                   => ~ ! [X4: $i] :
                                                                                                                                                                                                          ( ( in @ X4 @ X1 )
                                                                                                                                                                                                         => ! [X5: $i] :
                                                                                                                                                                                                              ( ( in @ X5 @ X2 )
                                                                                                                                                                                                             => ( X3
                                                                                                                                                                                                               != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                                                                                               => ( sP5
                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                        ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                                                                                                       => ~ ! [X3: $i] :
                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                             => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                                                                                                   => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                                                                                                     => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                       => ( ! [X1: $i] :
                                                                                                                                                                                                              ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                                                                                              = X1 )
                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                ( ! [X3: $i] :
                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                                                                        ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                       => ( ( X2 @ X3 )
                                                                                                                                                                                                                         => ( ( X2 @ X4 )
                                                                                                                                                                                                                           => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                               => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                       => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                 => ~ ! [X3: $i] :
                                                                                                                                                                                                                        ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                       => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                         != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                  ( ~ ! [X3: $i] :
                                                                                                                                                                                                                        ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                       => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                         != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                                                                                                 => ~ ! [X3: $i] :
                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                       => ~ ( X2 @ X3 ) ) )
                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                   => ( ( X2 @ X3 )
                                                                                                                                                                                                                     => ( ! [X4: $i] :
                                                                                                                                                                                                                            ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                           => ( ( X2 @ X4 )
                                                                                                                                                                                                                             => ( X4 = X3 ) ) )
                                                                                                                                                                                                                       => ~ ! [X4: $i] :
                                                                                                                                                                                                                              ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                             => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                               != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                      ( ! [X3: $i] :
                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                                                                              ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                             => ( ( X2 @ X3 )
                                                                                                                                                                                                                               => ( ( X2 @ X4 )
                                                                                                                                                                                                                                 => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                     => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                             => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                       => ~ ! [X3: $i] :
                                                                                                                                                                                                                              ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                             => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                               != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                        ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                                                                                          = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                       => ( X1 = X2 ) )
                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                          ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                         => ( X1 = X3 ) )
                                                                                                                                                                                                                     => ( ! [X1: $i] :
                                                                                                                                                                                                                            ( ( iskpair @ X1 )
                                                                                                                                                                                                                           => ~ ! [X2: $i] :
                                                                                                                                                                                                                                  ( ( in @ X2
                                                                                                                                                                                                                                    @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                      @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                                                                                                 => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                      @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                                   != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                       => ( ! [X1: $i] :
                                                                                                                                                                                                                              ( ~ ! [X2: $i] :
                                                                                                                                                                                                                                    ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                   => ( X1
                                                                                                                                                                                                                                     != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                             => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                = X1 )
                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                  ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                 => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                    ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                      = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                   => ( X1 = X3 ) )
                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                      ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                        = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                     => ( X1 = X3 ) )
                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                        ( ( X1 = X2 )
                                                                                                                                                                                                                                       => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                          = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                          ( ( X1 = X2 )
                                                                                                                                                                                                                                         => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                            = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                            ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                              = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                           => ( ( X3 = X4 )
                                                                                                                                                                                                                                             => ( X2 = X4 ) ) )
                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                              ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                                                                                             => ( X1 = X2 ) )
                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                  = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                               => ( X2 = X4 ) )
                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                  ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                    = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                 => ( X2 = X4 ) )
                                                                                                                                                                                                                                             => ( ! [X1: $i] :
                                                                                                                                                                                                                                                    ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                   => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                          ( ( in @ X2
                                                                                                                                                                                                                                                            @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                              @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                  ( X1
                                                                                                                                                                                                                                                                  = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                                                                                         => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                              @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                  ( X1
                                                                                                                                                                                                                                                                  = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                                                                                           != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                      ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                      = X2 )
                                                                                                                                                                                                                                                 => ( sP8
                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                         => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                            ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                           => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                              ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                             => ( in @ X4 @ X2 ) )
                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                   => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                      = X3 ) ) )
                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                     => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                        = X4 ) ) )
                                                                                                                                                                                                                                                             => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                  ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                 => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                                                                                                    = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h84,assumption,
    ! [X1: $i,X2: $i] :
      ( ( X1 = X2 )
     => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ),
    introduced(assumption,[]) ).

thf(h85,assumption,
    ~ ( ! [X1: $i,X2: $i] :
          ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
         => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
     => ( ! [X1: $i,X2: $i,X3: $i] :
            ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
           => ( ( X3 != X1 )
             => ( X3 = X2 ) ) )
       => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
         => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
           => ( ! [X1: $i,X2: $i > $o] :
                  ( ~ ! [X3: $i] :
                        ( ( in @ X3 @ X1 )
                       => ~ ( X2 @ X3 ) )
                 => ( ( dsetconstr @ X1 @ X2 )
                   != emptyset ) )
             => ( ! [X1: $i > $o,X2: $i] :
                    ( ( in @ X2 @ emptyset )
                   => ( X1 @ X2 ) )
               => ( ! [X1: $o] :
                      ( X1
                     => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                 => ( ! [X1: $o] :
                        ( X1
                       => ( set2prop @ ( prop2set @ X1 ) ) )
                   => ( ! [X1: $i > $o] :
                          ( ~ ! [X2: $i] :
                                ~ ( X1 @ X2 )
                         => ( ! [X2: $i,X3: $i] :
                                ( ( X1 @ X2 )
                               => ( ( X1 @ X3 )
                                 => ( X2 = X3 ) ) )
                           => ~ ! [X2: $i] :
                                  ( ( X1 @ X2 )
                                 => ~ ! [X3: $i] :
                                        ( ( X1 @ X3 )
                                       => ( X2 = X3 ) ) ) ) )
                     => ( ! [X1: $i > $o] :
                            ( ~ ! [X2: $i] :
                                  ~ ! [X3: $i] :
                                      ( ( X1 @ X3 )
                                      = ( X3 = X2 ) )
                           => ~ ! [X2: $i] :
                                  ( ( X1 @ X2 )
                                 => ~ ! [X3: $i] :
                                        ( ( X1 @ X3 )
                                       => ( X2 = X3 ) ) ) )
                       => ( ! [X1: $i,X2: $i] :
                              ( ( X1 = X2 )
                             => ! [X3: $i,X4: $i] :
                                  ( ( X3 = X4 )
                                 => ( ( in @ X3 @ X1 )
                                   => ( in @ X4 @ X2 ) ) ) )
                         => ( ! [X1: $i,X2: $i] :
                                ( ( X1 = X2 )
                               => ! [X3: $i,X4: $i] :
                                    ( ( X3 = X4 )
                                   => ( ( in @ X3 @ X1 )
                                      = ( in @ X4 @ X2 ) ) ) )
                           => ( ! [X1: $i > $o] :
                                  ( ~ ! [X2: $i] :
                                        ( ( X1 @ X2 )
                                       => ~ ! [X3: $i] :
                                              ( ( X1 @ X3 )
                                             => ( X2 = X3 ) ) )
                                 => ! [X2: $i,X3: $i] :
                                      ( ( X1 @ X2 )
                                     => ( ( X1 @ X3 )
                                       => ( X2 = X3 ) ) ) )
                             => ( ! [X1: $i > $o,X2: $i > $o] :
                                    ( ! [X3: $i,X4: $i] :
                                        ( ( X3 = X4 )
                                       => ( ( X1 @ X3 )
                                          = ( X2 @ X4 ) ) )
                                   => ( ( ~ ! [X3: $i] :
                                              ( ( X1 @ X3 )
                                             => ~ ! [X4: $i] :
                                                    ( ( X1 @ X4 )
                                                   => ( X3 = X4 ) ) ) )
                                      = ( ~ ! [X3: $i] :
                                              ( ( X2 @ X3 )
                                             => ~ ! [X4: $i] :
                                                    ( ( X2 @ X4 )
                                                   => ( X3 = X4 ) ) ) ) ) )
                               => ( ! [X1: $i,X2: $i] :
                                      ( ( X1 = X2 )
                                     => ! [X3: $i,X4: $i] :
                                          ( ( X3 = X4 )
                                         => ( ( setadjoin @ X1 @ X3 )
                                            = ( setadjoin @ X2 @ X4 ) ) ) )
                                 => ( ! [X1: $i,X2: $i] :
                                        ( ( X1 = X2 )
                                       => ( ( powerset @ X1 )
                                          = ( powerset @ X2 ) ) )
                                   => ( ! [X1: $i,X2: $i] :
                                          ( ( X1 = X2 )
                                         => ( ( setunion @ X1 )
                                            = ( setunion @ X2 ) ) )
                                     => ( ! [X1: $i > $o] :
                                            ( ~ ! [X2: $i] :
                                                  ( ( X1 @ X2 )
                                                 => ~ ! [X3: $i] :
                                                        ( ( X1 @ X3 )
                                                       => ( X2 = X3 ) ) )
                                           => ! [X2: $i,X3: $i] :
                                                ( ( X1 @ X2 )
                                               => ( ( X1 @ X3 )
                                                 => ( X2 = X3 ) ) ) )
                                       => ( ! [X1: $i > $o,X2: $i > $o] :
                                              ( ! [X3: $i,X4: $i] :
                                                  ( ( X3 = X4 )
                                                 => ( ( X1 @ X3 )
                                                    = ( X2 @ X4 ) ) )
                                             => ( ~ ! [X3: $i] :
                                                      ( ( X1 @ X3 )
                                                     => ~ ! [X4: $i] :
                                                            ( ( X1 @ X4 )
                                                           => ( X3 = X4 ) ) )
                                               => ( ~ ! [X3: $i] :
                                                        ( ( X2 @ X3 )
                                                       => ~ ! [X4: $i] :
                                                              ( ( X2 @ X4 )
                                                             => ( X3 = X4 ) ) )
                                                 => ( ( descr @ X1 )
                                                    = ( descr @ X2 ) ) ) ) )
                                         => ( ! [X1: $i,X2: $i] :
                                                ( ( X1 = X2 )
                                               => ! [X3: $i > $o,X4: $i > $o] :
                                                    ( ! [X5: $i] :
                                                        ( ( in @ X5 @ X1 )
                                                       => ! [X6: $i] :
                                                            ( ( in @ X6 @ X2 )
                                                           => ( ( X5 = X6 )
                                                             => ( ( X3 @ X5 )
                                                                = ( X4 @ X6 ) ) ) ) )
                                                   => ( ( dsetconstr @ X1 @ X3 )
                                                      = ( dsetconstr @ X2 @ X4 ) ) ) )
                                           => ( ! [X1: $i,X2: $i] :
                                                  ( ! [X3: $i] :
                                                      ( ( in @ X3 @ X1 )
                                                     => ( in @ X3 @ X2 ) )
                                                 => ( subset @ X1 @ X2 ) )
                                             => ( ! [X1: $i,X2: $i] :
                                                    ( ( X1 = X2 )
                                                   => ( subset @ X2 @ X1 ) )
                                               => ( ! [X1: $i,X2: $i] :
                                                      ( ( X1 = X2 )
                                                     => ( subset @ X1 @ X2 ) )
                                                 => ( ! [X1: $i,X2: $i] :
                                                        ( ! [X3: $i] :
                                                            ( ( in @ X3 @ X1 )
                                                           => ( in @ X3 @ X2 ) )
                                                       => ( subset @ X1 @ X2 ) )
                                                   => ( ! [X1: $i] : ( subset @ emptyset @ X1 )
                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                            ( ( subset @ X1 @ X2 )
                                                           => ( ( in @ X3 @ X1 )
                                                             => ( in @ X3 @ X2 ) ) )
                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                              ( ( subset @ X1 @ X2 )
                                                             => ( ~ ( in @ X3 @ X2 )
                                                               => ~ ( in @ X3 @ X1 ) ) )
                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                ( ( in @ X3 @ X1 )
                                                               => ( ~ ( in @ X3 @ X2 )
                                                                 => ~ ( subset @ X1 @ X2 ) ) )
                                                           => ( ! [X1: $i,X2: $i] :
                                                                  ( ~ ( subset @ X1 @ X2 )
                                                                 => ( X1 != X2 ) )
                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                    ( ( in @ X3 @ X1 )
                                                                   => ( ~ ( in @ X3 @ X2 )
                                                                     => ( X1 != X2 ) ) )
                                                               => ( ! [X1: $i] : ( subset @ X1 @ X1 )
                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                        ( ( subset @ X1 @ X2 )
                                                                       => ( ( subset @ X2 @ X3 )
                                                                         => ( subset @ X1 @ X3 ) ) )
                                                                   => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) )
                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                            ( ( subset @ X1 @ X3 )
                                                                           => ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
                                                                       => ( ! [X1: $i,X2: $i] :
                                                                              ( ( subset @ X1 @ X2 )
                                                                             => ( in @ X1 @ ( powerset @ X2 ) ) )
                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                ( ( subset @ X1 @ X2 )
                                                                               => ( ( subset @ X2 @ X1 )
                                                                                 => ( X1 = X2 ) ) )
                                                                           => ( ! [X1: $i] :
                                                                                  ( ( subset @ X1 @ emptyset )
                                                                                 => ( X1 = emptyset ) )
                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                    ( ( subset @ X2 @ X1 )
                                                                                   => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                      ( ( in @ X2 @ ( powerset @ X1 ) )
                                                                                     => ( subset @ X2 @ X1 ) )
                                                                                 => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                          ( ( subset @ X1 @ X2 )
                                                                                         => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
                                                                                     => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                                                                                       => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                ( ( in @ X3 @ X1 )
                                                                                               => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                           => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                    ( ( in @ X3 @ X2 )
                                                                                                   => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                                                                                      ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                     => ( ( ( in @ X3 @ X1 )
                                                                                                         => X4 )
                                                                                                       => ( ( ( in @ X3 @ X2 )
                                                                                                           => X4 )
                                                                                                         => X4 ) ) )
                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                        ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                       => ( ~ ( in @ X3 @ X1 )
                                                                                                         => ( in @ X3 @ X2 ) ) )
                                                                                                   => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                                                                                                     => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                             => ( ( in @ X3 @ X2 )
                                                                                                               => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                ( ( subset @ X3 @ X1 )
                                                                                                               => ( ( subset @ X3 @ X2 )
                                                                                                                 => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                  ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                 => ( in @ X3 @ X1 ) )
                                                                                                             => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                      ( ( subset @ X1 @ X2 )
                                                                                                                     => ( ( binintersect @ X1 @ X2 )
                                                                                                                        = X1 ) )
                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                        ( ( ( binintersect @ X1 @ X2 )
                                                                                                                          = X2 )
                                                                                                                       => ( subset @ X2 @ X1 ) )
                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                          ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                         => ( in @ X3 @ X2 ) )
                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                            ( ! [X3: $i] :
                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                               => ~ ( in @ X3 @ X2 ) )
                                                                                                                           => ( ( binintersect @ X1 @ X2 )
                                                                                                                              = emptyset ) )
                                                                                                                       => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                ( ( subset @ X2 @ X1 )
                                                                                                                               => ( ( binintersect @ X1 @ X2 )
                                                                                                                                  = X2 ) )
                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                  ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                    = X1 )
                                                                                                                                 => ( subset @ X1 @ X2 ) )
                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                    ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                                                                                                    = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                     => ( ~ ( in @ X3 @ X2 )
                                                                                                                                       => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                        ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                       => ( in @ X3 @ X1 ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                          ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                         => ~ ( in @ X3 @ X2 ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                            ( ( subset @ X1 @ X2 )
                                                                                                                                           => ( ( setminus @ X1 @ X2 )
                                                                                                                                              = emptyset ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                              ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                             => ( ( in @ X3 @ X1 )
                                                                                                                                               => ( in @ X3 @ X2 ) ) )
                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                               => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                 => ~ ( in @ X3 @ X1 ) ) )
                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                  ( ~ ( in @ X3 @ X1 )
                                                                                                                                                 => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                    ( ( in @ X3 @ X2 )
                                                                                                                                                   => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                               => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                        ( ( ( setminus @ X1 @ X2 )
                                                                                                                                                          = emptyset )
                                                                                                                                                       => ( subset @ X1 @ X2 ) )
                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                          ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                                                                                         => ! [X4: $o] :
                                                                                                                                                              ( ( ( in @ X3 @ X1 )
                                                                                                                                                               => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                 => X4 ) )
                                                                                                                                                             => ( ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                 => ( ( in @ X3 @ X2 )
                                                                                                                                                                   => X4 ) )
                                                                                                                                                               => X4 ) ) )
                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                           => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                             => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                              ( ~ ( in @ X3 @ X1 )
                                                                                                                                                             => ( ( in @ X3 @ X2 )
                                                                                                                                                               => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                               => ( ( in @ X3 @ X2 )
                                                                                                                                                                 => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                  ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                 => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                   => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                             => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                               => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                 => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                   => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                     => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                              ( ( in @ X2 @ X1 )
                                                                                                                                                                             => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                ( ( in @ X2 @ X1 )
                                                                                                                                                                               => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                 => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                    ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                   => ( ( X3 != X1 )
                                                                                                                                                                                     => ( X3 = X2 ) ) )
                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                                                                         => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                                                                           => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                                                                                             => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                                                                                               => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                                                                                 => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                                                                                   => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                  ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                 => ~ ! [X4: $i] :
                                                                                                                                                                                                        ( ( in @ X4 @ X1 )
                                                                                                                                                                                                       => ! [X5: $i] :
                                                                                                                                                                                                            ( ( in @ X5 @ X2 )
                                                                                                                                                                                                           => ( X3
                                                                                                                                                                                                             != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                                                                                             => ( sP5
                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                      ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                                                                                                     => ~ ! [X3: $i] :
                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                           => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                                                                                                 => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                                                                                                   => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                     => ( ! [X1: $i] :
                                                                                                                                                                                                            ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                                                                                            = X1 )
                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                              ( ! [X3: $i] :
                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                                                                      ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                     => ( ( X2 @ X3 )
                                                                                                                                                                                                                       => ( ( X2 @ X4 )
                                                                                                                                                                                                                         => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                             => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                     => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                               => ~ ! [X3: $i] :
                                                                                                                                                                                                                      ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                     => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                       != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                ( ~ ! [X3: $i] :
                                                                                                                                                                                                                      ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                     => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                       != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                                                                                               => ~ ! [X3: $i] :
                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                     => ~ ( X2 @ X3 ) ) )
                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                 => ( ( X2 @ X3 )
                                                                                                                                                                                                                   => ( ! [X4: $i] :
                                                                                                                                                                                                                          ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                         => ( ( X2 @ X4 )
                                                                                                                                                                                                                           => ( X4 = X3 ) ) )
                                                                                                                                                                                                                     => ~ ! [X4: $i] :
                                                                                                                                                                                                                            ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                           => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                             != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                    ( ! [X3: $i] :
                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                                                                            ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                           => ( ( X2 @ X3 )
                                                                                                                                                                                                                             => ( ( X2 @ X4 )
                                                                                                                                                                                                                               => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                   => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                           => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                     => ~ ! [X3: $i] :
                                                                                                                                                                                                                            ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                           => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                             != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                      ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                                                                                        = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                     => ( X1 = X2 ) )
                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                        ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                       => ( X1 = X3 ) )
                                                                                                                                                                                                                   => ( ! [X1: $i] :
                                                                                                                                                                                                                          ( ( iskpair @ X1 )
                                                                                                                                                                                                                         => ~ ! [X2: $i] :
                                                                                                                                                                                                                                ( ( in @ X2
                                                                                                                                                                                                                                  @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                    @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                                                                                               => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                    @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                                 != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                     => ( ! [X1: $i] :
                                                                                                                                                                                                                            ( ~ ! [X2: $i] :
                                                                                                                                                                                                                                  ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                 => ( X1
                                                                                                                                                                                                                                   != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                           => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                              ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                              = X1 )
                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                               => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                  ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                    = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                 => ( X1 = X3 ) )
                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                    ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                      = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                   => ( X1 = X3 ) )
                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                      ( ( X1 = X2 )
                                                                                                                                                                                                                                     => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                        = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                        ( ( X1 = X2 )
                                                                                                                                                                                                                                       => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                          = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                          ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                            = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                         => ( ( X3 = X4 )
                                                                                                                                                                                                                                           => ( X2 = X4 ) ) )
                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                            ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                              = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                                                                                           => ( X1 = X2 ) )
                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                              ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                             => ( X2 = X4 ) )
                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                  = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                               => ( X2 = X4 ) )
                                                                                                                                                                                                                                           => ( ! [X1: $i] :
                                                                                                                                                                                                                                                  ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                 => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                        ( ( in @ X2
                                                                                                                                                                                                                                                          @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                            @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                ( X1
                                                                                                                                                                                                                                                                = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                                                                                       => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                            @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                ( X1
                                                                                                                                                                                                                                                                = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                                                                                         != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                    ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                    = X2 )
                                                                                                                                                                                                                                               => ( sP8
                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                       => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                          ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                         => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                            ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                           => ( in @ X4 @ X2 ) )
                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                 => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                    = X3 ) ) )
                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                   => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                      = X4 ) ) )
                                                                                                                                                                                                                                                           => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                               => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                                                                                                  = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h86,assumption,
    ! [X1: $i,X2: $i] :
      ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
     => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) ),
    introduced(assumption,[]) ).

thf(h87,assumption,
    ~ ( ! [X1: $i,X2: $i,X3: $i] :
          ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
         => ( ( X3 != X1 )
           => ( X3 = X2 ) ) )
     => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
       => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
         => ( ! [X1: $i,X2: $i > $o] :
                ( ~ ! [X3: $i] :
                      ( ( in @ X3 @ X1 )
                     => ~ ( X2 @ X3 ) )
               => ( ( dsetconstr @ X1 @ X2 )
                 != emptyset ) )
           => ( ! [X1: $i > $o,X2: $i] :
                  ( ( in @ X2 @ emptyset )
                 => ( X1 @ X2 ) )
             => ( ! [X1: $o] :
                    ( X1
                   => ( in @ emptyset @ ( prop2set @ X1 ) ) )
               => ( ! [X1: $o] :
                      ( X1
                     => ( set2prop @ ( prop2set @ X1 ) ) )
                 => ( ! [X1: $i > $o] :
                        ( ~ ! [X2: $i] :
                              ~ ( X1 @ X2 )
                       => ( ! [X2: $i,X3: $i] :
                              ( ( X1 @ X2 )
                             => ( ( X1 @ X3 )
                               => ( X2 = X3 ) ) )
                         => ~ ! [X2: $i] :
                                ( ( X1 @ X2 )
                               => ~ ! [X3: $i] :
                                      ( ( X1 @ X3 )
                                     => ( X2 = X3 ) ) ) ) )
                   => ( ! [X1: $i > $o] :
                          ( ~ ! [X2: $i] :
                                ~ ! [X3: $i] :
                                    ( ( X1 @ X3 )
                                    = ( X3 = X2 ) )
                         => ~ ! [X2: $i] :
                                ( ( X1 @ X2 )
                               => ~ ! [X3: $i] :
                                      ( ( X1 @ X3 )
                                     => ( X2 = X3 ) ) ) )
                     => ( ! [X1: $i,X2: $i] :
                            ( ( X1 = X2 )
                           => ! [X3: $i,X4: $i] :
                                ( ( X3 = X4 )
                               => ( ( in @ X3 @ X1 )
                                 => ( in @ X4 @ X2 ) ) ) )
                       => ( ! [X1: $i,X2: $i] :
                              ( ( X1 = X2 )
                             => ! [X3: $i,X4: $i] :
                                  ( ( X3 = X4 )
                                 => ( ( in @ X3 @ X1 )
                                    = ( in @ X4 @ X2 ) ) ) )
                         => ( ! [X1: $i > $o] :
                                ( ~ ! [X2: $i] :
                                      ( ( X1 @ X2 )
                                     => ~ ! [X3: $i] :
                                            ( ( X1 @ X3 )
                                           => ( X2 = X3 ) ) )
                               => ! [X2: $i,X3: $i] :
                                    ( ( X1 @ X2 )
                                   => ( ( X1 @ X3 )
                                     => ( X2 = X3 ) ) ) )
                           => ( ! [X1: $i > $o,X2: $i > $o] :
                                  ( ! [X3: $i,X4: $i] :
                                      ( ( X3 = X4 )
                                     => ( ( X1 @ X3 )
                                        = ( X2 @ X4 ) ) )
                                 => ( ( ~ ! [X3: $i] :
                                            ( ( X1 @ X3 )
                                           => ~ ! [X4: $i] :
                                                  ( ( X1 @ X4 )
                                                 => ( X3 = X4 ) ) ) )
                                    = ( ~ ! [X3: $i] :
                                            ( ( X2 @ X3 )
                                           => ~ ! [X4: $i] :
                                                  ( ( X2 @ X4 )
                                                 => ( X3 = X4 ) ) ) ) ) )
                             => ( ! [X1: $i,X2: $i] :
                                    ( ( X1 = X2 )
                                   => ! [X3: $i,X4: $i] :
                                        ( ( X3 = X4 )
                                       => ( ( setadjoin @ X1 @ X3 )
                                          = ( setadjoin @ X2 @ X4 ) ) ) )
                               => ( ! [X1: $i,X2: $i] :
                                      ( ( X1 = X2 )
                                     => ( ( powerset @ X1 )
                                        = ( powerset @ X2 ) ) )
                                 => ( ! [X1: $i,X2: $i] :
                                        ( ( X1 = X2 )
                                       => ( ( setunion @ X1 )
                                          = ( setunion @ X2 ) ) )
                                   => ( ! [X1: $i > $o] :
                                          ( ~ ! [X2: $i] :
                                                ( ( X1 @ X2 )
                                               => ~ ! [X3: $i] :
                                                      ( ( X1 @ X3 )
                                                     => ( X2 = X3 ) ) )
                                         => ! [X2: $i,X3: $i] :
                                              ( ( X1 @ X2 )
                                             => ( ( X1 @ X3 )
                                               => ( X2 = X3 ) ) ) )
                                     => ( ! [X1: $i > $o,X2: $i > $o] :
                                            ( ! [X3: $i,X4: $i] :
                                                ( ( X3 = X4 )
                                               => ( ( X1 @ X3 )
                                                  = ( X2 @ X4 ) ) )
                                           => ( ~ ! [X3: $i] :
                                                    ( ( X1 @ X3 )
                                                   => ~ ! [X4: $i] :
                                                          ( ( X1 @ X4 )
                                                         => ( X3 = X4 ) ) )
                                             => ( ~ ! [X3: $i] :
                                                      ( ( X2 @ X3 )
                                                     => ~ ! [X4: $i] :
                                                            ( ( X2 @ X4 )
                                                           => ( X3 = X4 ) ) )
                                               => ( ( descr @ X1 )
                                                  = ( descr @ X2 ) ) ) ) )
                                       => ( ! [X1: $i,X2: $i] :
                                              ( ( X1 = X2 )
                                             => ! [X3: $i > $o,X4: $i > $o] :
                                                  ( ! [X5: $i] :
                                                      ( ( in @ X5 @ X1 )
                                                     => ! [X6: $i] :
                                                          ( ( in @ X6 @ X2 )
                                                         => ( ( X5 = X6 )
                                                           => ( ( X3 @ X5 )
                                                              = ( X4 @ X6 ) ) ) ) )
                                                 => ( ( dsetconstr @ X1 @ X3 )
                                                    = ( dsetconstr @ X2 @ X4 ) ) ) )
                                         => ( ! [X1: $i,X2: $i] :
                                                ( ! [X3: $i] :
                                                    ( ( in @ X3 @ X1 )
                                                   => ( in @ X3 @ X2 ) )
                                               => ( subset @ X1 @ X2 ) )
                                           => ( ! [X1: $i,X2: $i] :
                                                  ( ( X1 = X2 )
                                                 => ( subset @ X2 @ X1 ) )
                                             => ( ! [X1: $i,X2: $i] :
                                                    ( ( X1 = X2 )
                                                   => ( subset @ X1 @ X2 ) )
                                               => ( ! [X1: $i,X2: $i] :
                                                      ( ! [X3: $i] :
                                                          ( ( in @ X3 @ X1 )
                                                         => ( in @ X3 @ X2 ) )
                                                     => ( subset @ X1 @ X2 ) )
                                                 => ( ! [X1: $i] : ( subset @ emptyset @ X1 )
                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                          ( ( subset @ X1 @ X2 )
                                                         => ( ( in @ X3 @ X1 )
                                                           => ( in @ X3 @ X2 ) ) )
                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                            ( ( subset @ X1 @ X2 )
                                                           => ( ~ ( in @ X3 @ X2 )
                                                             => ~ ( in @ X3 @ X1 ) ) )
                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                              ( ( in @ X3 @ X1 )
                                                             => ( ~ ( in @ X3 @ X2 )
                                                               => ~ ( subset @ X1 @ X2 ) ) )
                                                         => ( ! [X1: $i,X2: $i] :
                                                                ( ~ ( subset @ X1 @ X2 )
                                                               => ( X1 != X2 ) )
                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                  ( ( in @ X3 @ X1 )
                                                                 => ( ~ ( in @ X3 @ X2 )
                                                                   => ( X1 != X2 ) ) )
                                                             => ( ! [X1: $i] : ( subset @ X1 @ X1 )
                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                      ( ( subset @ X1 @ X2 )
                                                                     => ( ( subset @ X2 @ X3 )
                                                                       => ( subset @ X1 @ X3 ) ) )
                                                                 => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) )
                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                          ( ( subset @ X1 @ X3 )
                                                                         => ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
                                                                     => ( ! [X1: $i,X2: $i] :
                                                                            ( ( subset @ X1 @ X2 )
                                                                           => ( in @ X1 @ ( powerset @ X2 ) ) )
                                                                       => ( ! [X1: $i,X2: $i] :
                                                                              ( ( subset @ X1 @ X2 )
                                                                             => ( ( subset @ X2 @ X1 )
                                                                               => ( X1 = X2 ) ) )
                                                                         => ( ! [X1: $i] :
                                                                                ( ( subset @ X1 @ emptyset )
                                                                               => ( X1 = emptyset ) )
                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                  ( ( subset @ X2 @ X1 )
                                                                                 => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                    ( ( in @ X2 @ ( powerset @ X1 ) )
                                                                                   => ( subset @ X2 @ X1 ) )
                                                                               => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                        ( ( subset @ X1 @ X2 )
                                                                                       => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
                                                                                   => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                                                                                     => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                              ( ( in @ X3 @ X1 )
                                                                                             => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                         => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                  ( ( in @ X3 @ X2 )
                                                                                                 => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                                                                                    ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                   => ( ( ( in @ X3 @ X1 )
                                                                                                       => X4 )
                                                                                                     => ( ( ( in @ X3 @ X2 )
                                                                                                         => X4 )
                                                                                                       => X4 ) ) )
                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                      ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                     => ( ~ ( in @ X3 @ X1 )
                                                                                                       => ( in @ X3 @ X2 ) ) )
                                                                                                 => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                                                                                                   => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                           => ( ( in @ X3 @ X2 )
                                                                                                             => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                              ( ( subset @ X3 @ X1 )
                                                                                                             => ( ( subset @ X3 @ X2 )
                                                                                                               => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                               => ( in @ X3 @ X1 ) )
                                                                                                           => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                    ( ( subset @ X1 @ X2 )
                                                                                                                   => ( ( binintersect @ X1 @ X2 )
                                                                                                                      = X1 ) )
                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                      ( ( ( binintersect @ X1 @ X2 )
                                                                                                                        = X2 )
                                                                                                                     => ( subset @ X2 @ X1 ) )
                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                        ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                       => ( in @ X3 @ X2 ) )
                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                          ( ! [X3: $i] :
                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                             => ~ ( in @ X3 @ X2 ) )
                                                                                                                         => ( ( binintersect @ X1 @ X2 )
                                                                                                                            = emptyset ) )
                                                                                                                     => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                              ( ( subset @ X2 @ X1 )
                                                                                                                             => ( ( binintersect @ X1 @ X2 )
                                                                                                                                = X2 ) )
                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                  = X1 )
                                                                                                                               => ( subset @ X1 @ X2 ) )
                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                  ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                                                                                                  = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                   => ( ~ ( in @ X3 @ X2 )
                                                                                                                                     => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                      ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                     => ( in @ X3 @ X1 ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                        ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                       => ~ ( in @ X3 @ X2 ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                          ( ( subset @ X1 @ X2 )
                                                                                                                                         => ( ( setminus @ X1 @ X2 )
                                                                                                                                            = emptyset ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                            ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                           => ( ( in @ X3 @ X1 )
                                                                                                                                             => ( in @ X3 @ X2 ) ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                              ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                             => ( ~ ( in @ X3 @ X2 )
                                                                                                                                               => ~ ( in @ X3 @ X1 ) ) )
                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                ( ~ ( in @ X3 @ X1 )
                                                                                                                                               => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                  ( ( in @ X3 @ X2 )
                                                                                                                                                 => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                             => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                      ( ( ( setminus @ X1 @ X2 )
                                                                                                                                                        = emptyset )
                                                                                                                                                     => ( subset @ X1 @ X2 ) )
                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                        ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                                                                                       => ! [X4: $o] :
                                                                                                                                                            ( ( ( in @ X3 @ X1 )
                                                                                                                                                             => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                               => X4 ) )
                                                                                                                                                           => ( ( ~ ( in @ X3 @ X1 )
                                                                                                                                                               => ( ( in @ X3 @ X2 )
                                                                                                                                                                 => X4 ) )
                                                                                                                                                             => X4 ) ) )
                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                         => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                           => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                            ( ~ ( in @ X3 @ X1 )
                                                                                                                                                           => ( ( in @ X3 @ X2 )
                                                                                                                                                             => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                             => ( ( in @ X3 @ X2 )
                                                                                                                                                               => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                ( ~ ( in @ X3 @ X1 )
                                                                                                                                                               => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                 => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                           => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                             => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                               => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                 => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                   => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                            ( ( in @ X2 @ X1 )
                                                                                                                                                                           => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                              ( ( in @ X2 @ X1 )
                                                                                                                                                                             => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                               => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                  ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                 => ( ( X3 != X1 )
                                                                                                                                                                                   => ( X3 = X2 ) ) )
                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                                                                       => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                                                                         => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                                                                           => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                                                                                             => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                                                                                               => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                                                                                 => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                               => ~ ! [X4: $i] :
                                                                                                                                                                                                      ( ( in @ X4 @ X1 )
                                                                                                                                                                                                     => ! [X5: $i] :
                                                                                                                                                                                                          ( ( in @ X5 @ X2 )
                                                                                                                                                                                                         => ( X3
                                                                                                                                                                                                           != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                                                                                           => ( sP5
                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                    ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                                                                                                   => ~ ! [X3: $i] :
                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                         => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                                                                                               => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                                                                                                 => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                   => ( ! [X1: $i] :
                                                                                                                                                                                                          ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                                                                                          = X1 )
                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                            ( ! [X3: $i] :
                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                                                    ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                   => ( ( X2 @ X3 )
                                                                                                                                                                                                                     => ( ( X2 @ X4 )
                                                                                                                                                                                                                       => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                           => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                   => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                             => ~ ! [X3: $i] :
                                                                                                                                                                                                                    ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                   => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                     != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                              ( ~ ! [X3: $i] :
                                                                                                                                                                                                                    ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                   => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                     != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                                                                                             => ~ ! [X3: $i] :
                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                   => ~ ( X2 @ X3 ) ) )
                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                               => ( ( X2 @ X3 )
                                                                                                                                                                                                                 => ( ! [X4: $i] :
                                                                                                                                                                                                                        ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                       => ( ( X2 @ X4 )
                                                                                                                                                                                                                         => ( X4 = X3 ) ) )
                                                                                                                                                                                                                   => ~ ! [X4: $i] :
                                                                                                                                                                                                                          ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                         => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                           != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                  ( ! [X3: $i] :
                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                                                                          ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                         => ( ( X2 @ X3 )
                                                                                                                                                                                                                           => ( ( X2 @ X4 )
                                                                                                                                                                                                                             => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                 => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                         => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                   => ~ ! [X3: $i] :
                                                                                                                                                                                                                          ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                         => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                           != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                    ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                                                                                      = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                   => ( X1 = X2 ) )
                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                      ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                     => ( X1 = X3 ) )
                                                                                                                                                                                                                 => ( ! [X1: $i] :
                                                                                                                                                                                                                        ( ( iskpair @ X1 )
                                                                                                                                                                                                                       => ~ ! [X2: $i] :
                                                                                                                                                                                                                              ( ( in @ X2
                                                                                                                                                                                                                                @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                  @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                                                                                             => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                  @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                               != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                   => ( ! [X1: $i] :
                                                                                                                                                                                                                          ( ~ ! [X2: $i] :
                                                                                                                                                                                                                                ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                               => ( X1
                                                                                                                                                                                                                                 != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                         => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                            ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                            = X1 )
                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                              ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                             => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                  = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                               => ( X1 = X3 ) )
                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                  ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                    = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                 => ( X1 = X3 ) )
                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                    ( ( X1 = X2 )
                                                                                                                                                                                                                                   => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                      = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                      ( ( X1 = X2 )
                                                                                                                                                                                                                                     => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                        = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                        ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                          = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                       => ( ( X3 = X4 )
                                                                                                                                                                                                                                         => ( X2 = X4 ) ) )
                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                          ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                            = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                                                                                         => ( X1 = X2 ) )
                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                            ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                              = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                           => ( X2 = X4 ) )
                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                              ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                             => ( X2 = X4 ) )
                                                                                                                                                                                                                                         => ( ! [X1: $i] :
                                                                                                                                                                                                                                                ( ( iskpair @ X1 )
                                                                                                                                                                                                                                               => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                      ( ( in @ X2
                                                                                                                                                                                                                                                        @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                          @ ^ [X3: $i] :
                                                                                                                                                                                                                                                              ( X1
                                                                                                                                                                                                                                                              = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                                                                                     => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                          @ ^ [X3: $i] :
                                                                                                                                                                                                                                                              ( X1
                                                                                                                                                                                                                                                              = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                                                                                       != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                  ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                  = X2 )
                                                                                                                                                                                                                                             => ( sP8
                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                      ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                     => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                        ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                       => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                          ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                         => ( in @ X4 @ X2 ) )
                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                               => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                  = X3 ) ) )
                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                 => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                    = X4 ) ) )
                                                                                                                                                                                                                                                         => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                              ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                             => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                                                                                                = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h88,assumption,
    ! [X1: $i,X2: $i,X3: $i] :
      ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
     => ( ( X3 != X1 )
       => ( X3 = X2 ) ) ),
    introduced(assumption,[]) ).

thf(h89,assumption,
    ~ ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
     => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
       => ( ! [X1: $i,X2: $i > $o] :
              ( ~ ! [X3: $i] :
                    ( ( in @ X3 @ X1 )
                   => ~ ( X2 @ X3 ) )
             => ( ( dsetconstr @ X1 @ X2 )
               != emptyset ) )
         => ( ! [X1: $i > $o,X2: $i] :
                ( ( in @ X2 @ emptyset )
               => ( X1 @ X2 ) )
           => ( ! [X1: $o] :
                  ( X1
                 => ( in @ emptyset @ ( prop2set @ X1 ) ) )
             => ( ! [X1: $o] :
                    ( X1
                   => ( set2prop @ ( prop2set @ X1 ) ) )
               => ( ! [X1: $i > $o] :
                      ( ~ ! [X2: $i] :
                            ~ ( X1 @ X2 )
                     => ( ! [X2: $i,X3: $i] :
                            ( ( X1 @ X2 )
                           => ( ( X1 @ X3 )
                             => ( X2 = X3 ) ) )
                       => ~ ! [X2: $i] :
                              ( ( X1 @ X2 )
                             => ~ ! [X3: $i] :
                                    ( ( X1 @ X3 )
                                   => ( X2 = X3 ) ) ) ) )
                 => ( ! [X1: $i > $o] :
                        ( ~ ! [X2: $i] :
                              ~ ! [X3: $i] :
                                  ( ( X1 @ X3 )
                                  = ( X3 = X2 ) )
                       => ~ ! [X2: $i] :
                              ( ( X1 @ X2 )
                             => ~ ! [X3: $i] :
                                    ( ( X1 @ X3 )
                                   => ( X2 = X3 ) ) ) )
                   => ( ! [X1: $i,X2: $i] :
                          ( ( X1 = X2 )
                         => ! [X3: $i,X4: $i] :
                              ( ( X3 = X4 )
                             => ( ( in @ X3 @ X1 )
                               => ( in @ X4 @ X2 ) ) ) )
                     => ( ! [X1: $i,X2: $i] :
                            ( ( X1 = X2 )
                           => ! [X3: $i,X4: $i] :
                                ( ( X3 = X4 )
                               => ( ( in @ X3 @ X1 )
                                  = ( in @ X4 @ X2 ) ) ) )
                       => ( ! [X1: $i > $o] :
                              ( ~ ! [X2: $i] :
                                    ( ( X1 @ X2 )
                                   => ~ ! [X3: $i] :
                                          ( ( X1 @ X3 )
                                         => ( X2 = X3 ) ) )
                             => ! [X2: $i,X3: $i] :
                                  ( ( X1 @ X2 )
                                 => ( ( X1 @ X3 )
                                   => ( X2 = X3 ) ) ) )
                         => ( ! [X1: $i > $o,X2: $i > $o] :
                                ( ! [X3: $i,X4: $i] :
                                    ( ( X3 = X4 )
                                   => ( ( X1 @ X3 )
                                      = ( X2 @ X4 ) ) )
                               => ( ( ~ ! [X3: $i] :
                                          ( ( X1 @ X3 )
                                         => ~ ! [X4: $i] :
                                                ( ( X1 @ X4 )
                                               => ( X3 = X4 ) ) ) )
                                  = ( ~ ! [X3: $i] :
                                          ( ( X2 @ X3 )
                                         => ~ ! [X4: $i] :
                                                ( ( X2 @ X4 )
                                               => ( X3 = X4 ) ) ) ) ) )
                           => ( ! [X1: $i,X2: $i] :
                                  ( ( X1 = X2 )
                                 => ! [X3: $i,X4: $i] :
                                      ( ( X3 = X4 )
                                     => ( ( setadjoin @ X1 @ X3 )
                                        = ( setadjoin @ X2 @ X4 ) ) ) )
                             => ( ! [X1: $i,X2: $i] :
                                    ( ( X1 = X2 )
                                   => ( ( powerset @ X1 )
                                      = ( powerset @ X2 ) ) )
                               => ( ! [X1: $i,X2: $i] :
                                      ( ( X1 = X2 )
                                     => ( ( setunion @ X1 )
                                        = ( setunion @ X2 ) ) )
                                 => ( ! [X1: $i > $o] :
                                        ( ~ ! [X2: $i] :
                                              ( ( X1 @ X2 )
                                             => ~ ! [X3: $i] :
                                                    ( ( X1 @ X3 )
                                                   => ( X2 = X3 ) ) )
                                       => ! [X2: $i,X3: $i] :
                                            ( ( X1 @ X2 )
                                           => ( ( X1 @ X3 )
                                             => ( X2 = X3 ) ) ) )
                                   => ( ! [X1: $i > $o,X2: $i > $o] :
                                          ( ! [X3: $i,X4: $i] :
                                              ( ( X3 = X4 )
                                             => ( ( X1 @ X3 )
                                                = ( X2 @ X4 ) ) )
                                         => ( ~ ! [X3: $i] :
                                                  ( ( X1 @ X3 )
                                                 => ~ ! [X4: $i] :
                                                        ( ( X1 @ X4 )
                                                       => ( X3 = X4 ) ) )
                                           => ( ~ ! [X3: $i] :
                                                    ( ( X2 @ X3 )
                                                   => ~ ! [X4: $i] :
                                                          ( ( X2 @ X4 )
                                                         => ( X3 = X4 ) ) )
                                             => ( ( descr @ X1 )
                                                = ( descr @ X2 ) ) ) ) )
                                     => ( ! [X1: $i,X2: $i] :
                                            ( ( X1 = X2 )
                                           => ! [X3: $i > $o,X4: $i > $o] :
                                                ( ! [X5: $i] :
                                                    ( ( in @ X5 @ X1 )
                                                   => ! [X6: $i] :
                                                        ( ( in @ X6 @ X2 )
                                                       => ( ( X5 = X6 )
                                                         => ( ( X3 @ X5 )
                                                            = ( X4 @ X6 ) ) ) ) )
                                               => ( ( dsetconstr @ X1 @ X3 )
                                                  = ( dsetconstr @ X2 @ X4 ) ) ) )
                                       => ( ! [X1: $i,X2: $i] :
                                              ( ! [X3: $i] :
                                                  ( ( in @ X3 @ X1 )
                                                 => ( in @ X3 @ X2 ) )
                                             => ( subset @ X1 @ X2 ) )
                                         => ( ! [X1: $i,X2: $i] :
                                                ( ( X1 = X2 )
                                               => ( subset @ X2 @ X1 ) )
                                           => ( ! [X1: $i,X2: $i] :
                                                  ( ( X1 = X2 )
                                                 => ( subset @ X1 @ X2 ) )
                                             => ( ! [X1: $i,X2: $i] :
                                                    ( ! [X3: $i] :
                                                        ( ( in @ X3 @ X1 )
                                                       => ( in @ X3 @ X2 ) )
                                                   => ( subset @ X1 @ X2 ) )
                                               => ( ! [X1: $i] : ( subset @ emptyset @ X1 )
                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                        ( ( subset @ X1 @ X2 )
                                                       => ( ( in @ X3 @ X1 )
                                                         => ( in @ X3 @ X2 ) ) )
                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                          ( ( subset @ X1 @ X2 )
                                                         => ( ~ ( in @ X3 @ X2 )
                                                           => ~ ( in @ X3 @ X1 ) ) )
                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                            ( ( in @ X3 @ X1 )
                                                           => ( ~ ( in @ X3 @ X2 )
                                                             => ~ ( subset @ X1 @ X2 ) ) )
                                                       => ( ! [X1: $i,X2: $i] :
                                                              ( ~ ( subset @ X1 @ X2 )
                                                             => ( X1 != X2 ) )
                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                ( ( in @ X3 @ X1 )
                                                               => ( ~ ( in @ X3 @ X2 )
                                                                 => ( X1 != X2 ) ) )
                                                           => ( ! [X1: $i] : ( subset @ X1 @ X1 )
                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                    ( ( subset @ X1 @ X2 )
                                                                   => ( ( subset @ X2 @ X3 )
                                                                     => ( subset @ X1 @ X3 ) ) )
                                                               => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) )
                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                        ( ( subset @ X1 @ X3 )
                                                                       => ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
                                                                   => ( ! [X1: $i,X2: $i] :
                                                                          ( ( subset @ X1 @ X2 )
                                                                         => ( in @ X1 @ ( powerset @ X2 ) ) )
                                                                     => ( ! [X1: $i,X2: $i] :
                                                                            ( ( subset @ X1 @ X2 )
                                                                           => ( ( subset @ X2 @ X1 )
                                                                             => ( X1 = X2 ) ) )
                                                                       => ( ! [X1: $i] :
                                                                              ( ( subset @ X1 @ emptyset )
                                                                             => ( X1 = emptyset ) )
                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                ( ( subset @ X2 @ X1 )
                                                                               => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                  ( ( in @ X2 @ ( powerset @ X1 ) )
                                                                                 => ( subset @ X2 @ X1 ) )
                                                                             => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                      ( ( subset @ X1 @ X2 )
                                                                                     => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
                                                                                 => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                                                                                   => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                            ( ( in @ X3 @ X1 )
                                                                                           => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                       => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                ( ( in @ X3 @ X2 )
                                                                                               => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                                                                                  ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                 => ( ( ( in @ X3 @ X1 )
                                                                                                     => X4 )
                                                                                                   => ( ( ( in @ X3 @ X2 )
                                                                                                       => X4 )
                                                                                                     => X4 ) ) )
                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                    ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                   => ( ~ ( in @ X3 @ X1 )
                                                                                                     => ( in @ X3 @ X2 ) ) )
                                                                                               => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                                                                                                 => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                         => ( ( in @ X3 @ X2 )
                                                                                                           => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                            ( ( subset @ X3 @ X1 )
                                                                                                           => ( ( subset @ X3 @ X2 )
                                                                                                             => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                              ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                             => ( in @ X3 @ X1 ) )
                                                                                                         => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                  ( ( subset @ X1 @ X2 )
                                                                                                                 => ( ( binintersect @ X1 @ X2 )
                                                                                                                    = X1 ) )
                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                    ( ( ( binintersect @ X1 @ X2 )
                                                                                                                      = X2 )
                                                                                                                   => ( subset @ X2 @ X1 ) )
                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                      ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                     => ( in @ X3 @ X2 ) )
                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                        ( ! [X3: $i] :
                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                           => ~ ( in @ X3 @ X2 ) )
                                                                                                                       => ( ( binintersect @ X1 @ X2 )
                                                                                                                          = emptyset ) )
                                                                                                                   => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                            ( ( subset @ X2 @ X1 )
                                                                                                                           => ( ( binintersect @ X1 @ X2 )
                                                                                                                              = X2 ) )
                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                              ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                = X1 )
                                                                                                                             => ( subset @ X1 @ X2 ) )
                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                                                                                                = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                 => ( ~ ( in @ X3 @ X2 )
                                                                                                                                   => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                    ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                   => ( in @ X3 @ X1 ) )
                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                      ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                     => ~ ( in @ X3 @ X2 ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                        ( ( subset @ X1 @ X2 )
                                                                                                                                       => ( ( setminus @ X1 @ X2 )
                                                                                                                                          = emptyset ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                          ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                         => ( ( in @ X3 @ X1 )
                                                                                                                                           => ( in @ X3 @ X2 ) ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                            ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                           => ( ~ ( in @ X3 @ X2 )
                                                                                                                                             => ~ ( in @ X3 @ X1 ) ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                              ( ~ ( in @ X3 @ X1 )
                                                                                                                                             => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                ( ( in @ X3 @ X2 )
                                                                                                                                               => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                           => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                    ( ( ( setminus @ X1 @ X2 )
                                                                                                                                                      = emptyset )
                                                                                                                                                   => ( subset @ X1 @ X2 ) )
                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                      ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                                                                                     => ! [X4: $o] :
                                                                                                                                                          ( ( ( in @ X3 @ X1 )
                                                                                                                                                           => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                             => X4 ) )
                                                                                                                                                         => ( ( ~ ( in @ X3 @ X1 )
                                                                                                                                                             => ( ( in @ X3 @ X2 )
                                                                                                                                                               => X4 ) )
                                                                                                                                                           => X4 ) ) )
                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                       => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                         => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                          ( ~ ( in @ X3 @ X1 )
                                                                                                                                                         => ( ( in @ X3 @ X2 )
                                                                                                                                                           => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                           => ( ( in @ X3 @ X2 )
                                                                                                                                                             => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                              ( ~ ( in @ X3 @ X1 )
                                                                                                                                                             => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                               => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                         => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                           => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                             => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                               => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                 => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                          ( ( in @ X2 @ X1 )
                                                                                                                                                                         => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                            ( ( in @ X2 @ X1 )
                                                                                                                                                                           => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                             => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                               => ( ( X3 != X1 )
                                                                                                                                                                                 => ( X3 = X2 ) ) )
                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                                                                     => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                                                                       => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                                                                         => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                                                                           => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                                                                                             => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                                                                                               => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                              ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                             => ~ ! [X4: $i] :
                                                                                                                                                                                                    ( ( in @ X4 @ X1 )
                                                                                                                                                                                                   => ! [X5: $i] :
                                                                                                                                                                                                        ( ( in @ X5 @ X2 )
                                                                                                                                                                                                       => ( X3
                                                                                                                                                                                                         != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                                                                                         => ( sP5
                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                  ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                                                                                                 => ~ ! [X3: $i] :
                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                       => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                                                                                             => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                                                                                               => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                 => ( ! [X1: $i] :
                                                                                                                                                                                                        ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                                                                                        = X1 )
                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                          ( ! [X3: $i] :
                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                                                  ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                 => ( ( X2 @ X3 )
                                                                                                                                                                                                                   => ( ( X2 @ X4 )
                                                                                                                                                                                                                     => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                         => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                 => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                           => ~ ! [X3: $i] :
                                                                                                                                                                                                                  ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                 => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                   != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                            ( ~ ! [X3: $i] :
                                                                                                                                                                                                                  ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                 => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                   != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                                                                                           => ~ ! [X3: $i] :
                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                 => ~ ( X2 @ X3 ) ) )
                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                             => ( ( X2 @ X3 )
                                                                                                                                                                                                               => ( ! [X4: $i] :
                                                                                                                                                                                                                      ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                     => ( ( X2 @ X4 )
                                                                                                                                                                                                                       => ( X4 = X3 ) ) )
                                                                                                                                                                                                                 => ~ ! [X4: $i] :
                                                                                                                                                                                                                        ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                       => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                         != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                ( ! [X3: $i] :
                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                                                                        ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                       => ( ( X2 @ X3 )
                                                                                                                                                                                                                         => ( ( X2 @ X4 )
                                                                                                                                                                                                                           => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                               => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                       => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                 => ~ ! [X3: $i] :
                                                                                                                                                                                                                        ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                       => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                         != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                  ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                                                                                    = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                 => ( X1 = X2 ) )
                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                    ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                   => ( X1 = X3 ) )
                                                                                                                                                                                                               => ( ! [X1: $i] :
                                                                                                                                                                                                                      ( ( iskpair @ X1 )
                                                                                                                                                                                                                     => ~ ! [X2: $i] :
                                                                                                                                                                                                                            ( ( in @ X2
                                                                                                                                                                                                                              @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                                                                                           => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                             != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                 => ( ! [X1: $i] :
                                                                                                                                                                                                                        ( ~ ! [X2: $i] :
                                                                                                                                                                                                                              ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                             => ( X1
                                                                                                                                                                                                                               != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                       => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                          ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                          = X1 )
                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                            ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                           => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                              ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                             => ( X1 = X3 ) )
                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                  = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                               => ( X1 = X3 ) )
                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                  ( ( X1 = X2 )
                                                                                                                                                                                                                                 => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                    = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                    ( ( X1 = X2 )
                                                                                                                                                                                                                                   => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                      = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                      ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                        = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                     => ( ( X3 = X4 )
                                                                                                                                                                                                                                       => ( X2 = X4 ) ) )
                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                        ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                          = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                                                                                       => ( X1 = X2 ) )
                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                          ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                            = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                         => ( X2 = X4 ) )
                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                            ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                              = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                           => ( X2 = X4 ) )
                                                                                                                                                                                                                                       => ( ! [X1: $i] :
                                                                                                                                                                                                                                              ( ( iskpair @ X1 )
                                                                                                                                                                                                                                             => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                    ( ( in @ X2
                                                                                                                                                                                                                                                      @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                        @ ^ [X3: $i] :
                                                                                                                                                                                                                                                            ( X1
                                                                                                                                                                                                                                                            = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                                                                                   => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                        @ ^ [X3: $i] :
                                                                                                                                                                                                                                                            ( X1
                                                                                                                                                                                                                                                            = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                                                                                     != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                = X2 )
                                                                                                                                                                                                                                           => ( sP8
                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                    ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                   => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                      ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                     => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                        ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                       => ( in @ X4 @ X2 ) )
                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                             => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                = X3 ) ) )
                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                               => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                  = X4 ) ) )
                                                                                                                                                                                                                                                       => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                            ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                           => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                                                                                              = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h90,assumption,
    ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ),
    introduced(assumption,[]) ).

thf(h91,assumption,
    ~ ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
     => ( ! [X1: $i,X2: $i > $o] :
            ( ~ ! [X3: $i] :
                  ( ( in @ X3 @ X1 )
                 => ~ ( X2 @ X3 ) )
           => ( ( dsetconstr @ X1 @ X2 )
             != emptyset ) )
       => ( ! [X1: $i > $o,X2: $i] :
              ( ( in @ X2 @ emptyset )
             => ( X1 @ X2 ) )
         => ( ! [X1: $o] :
                ( X1
               => ( in @ emptyset @ ( prop2set @ X1 ) ) )
           => ( ! [X1: $o] :
                  ( X1
                 => ( set2prop @ ( prop2set @ X1 ) ) )
             => ( ! [X1: $i > $o] :
                    ( ~ ! [X2: $i] :
                          ~ ( X1 @ X2 )
                   => ( ! [X2: $i,X3: $i] :
                          ( ( X1 @ X2 )
                         => ( ( X1 @ X3 )
                           => ( X2 = X3 ) ) )
                     => ~ ! [X2: $i] :
                            ( ( X1 @ X2 )
                           => ~ ! [X3: $i] :
                                  ( ( X1 @ X3 )
                                 => ( X2 = X3 ) ) ) ) )
               => ( ! [X1: $i > $o] :
                      ( ~ ! [X2: $i] :
                            ~ ! [X3: $i] :
                                ( ( X1 @ X3 )
                                = ( X3 = X2 ) )
                     => ~ ! [X2: $i] :
                            ( ( X1 @ X2 )
                           => ~ ! [X3: $i] :
                                  ( ( X1 @ X3 )
                                 => ( X2 = X3 ) ) ) )
                 => ( ! [X1: $i,X2: $i] :
                        ( ( X1 = X2 )
                       => ! [X3: $i,X4: $i] :
                            ( ( X3 = X4 )
                           => ( ( in @ X3 @ X1 )
                             => ( in @ X4 @ X2 ) ) ) )
                   => ( ! [X1: $i,X2: $i] :
                          ( ( X1 = X2 )
                         => ! [X3: $i,X4: $i] :
                              ( ( X3 = X4 )
                             => ( ( in @ X3 @ X1 )
                                = ( in @ X4 @ X2 ) ) ) )
                     => ( ! [X1: $i > $o] :
                            ( ~ ! [X2: $i] :
                                  ( ( X1 @ X2 )
                                 => ~ ! [X3: $i] :
                                        ( ( X1 @ X3 )
                                       => ( X2 = X3 ) ) )
                           => ! [X2: $i,X3: $i] :
                                ( ( X1 @ X2 )
                               => ( ( X1 @ X3 )
                                 => ( X2 = X3 ) ) ) )
                       => ( ! [X1: $i > $o,X2: $i > $o] :
                              ( ! [X3: $i,X4: $i] :
                                  ( ( X3 = X4 )
                                 => ( ( X1 @ X3 )
                                    = ( X2 @ X4 ) ) )
                             => ( ( ~ ! [X3: $i] :
                                        ( ( X1 @ X3 )
                                       => ~ ! [X4: $i] :
                                              ( ( X1 @ X4 )
                                             => ( X3 = X4 ) ) ) )
                                = ( ~ ! [X3: $i] :
                                        ( ( X2 @ X3 )
                                       => ~ ! [X4: $i] :
                                              ( ( X2 @ X4 )
                                             => ( X3 = X4 ) ) ) ) ) )
                         => ( ! [X1: $i,X2: $i] :
                                ( ( X1 = X2 )
                               => ! [X3: $i,X4: $i] :
                                    ( ( X3 = X4 )
                                   => ( ( setadjoin @ X1 @ X3 )
                                      = ( setadjoin @ X2 @ X4 ) ) ) )
                           => ( ! [X1: $i,X2: $i] :
                                  ( ( X1 = X2 )
                                 => ( ( powerset @ X1 )
                                    = ( powerset @ X2 ) ) )
                             => ( ! [X1: $i,X2: $i] :
                                    ( ( X1 = X2 )
                                   => ( ( setunion @ X1 )
                                      = ( setunion @ X2 ) ) )
                               => ( ! [X1: $i > $o] :
                                      ( ~ ! [X2: $i] :
                                            ( ( X1 @ X2 )
                                           => ~ ! [X3: $i] :
                                                  ( ( X1 @ X3 )
                                                 => ( X2 = X3 ) ) )
                                     => ! [X2: $i,X3: $i] :
                                          ( ( X1 @ X2 )
                                         => ( ( X1 @ X3 )
                                           => ( X2 = X3 ) ) ) )
                                 => ( ! [X1: $i > $o,X2: $i > $o] :
                                        ( ! [X3: $i,X4: $i] :
                                            ( ( X3 = X4 )
                                           => ( ( X1 @ X3 )
                                              = ( X2 @ X4 ) ) )
                                       => ( ~ ! [X3: $i] :
                                                ( ( X1 @ X3 )
                                               => ~ ! [X4: $i] :
                                                      ( ( X1 @ X4 )
                                                     => ( X3 = X4 ) ) )
                                         => ( ~ ! [X3: $i] :
                                                  ( ( X2 @ X3 )
                                                 => ~ ! [X4: $i] :
                                                        ( ( X2 @ X4 )
                                                       => ( X3 = X4 ) ) )
                                           => ( ( descr @ X1 )
                                              = ( descr @ X2 ) ) ) ) )
                                   => ( ! [X1: $i,X2: $i] :
                                          ( ( X1 = X2 )
                                         => ! [X3: $i > $o,X4: $i > $o] :
                                              ( ! [X5: $i] :
                                                  ( ( in @ X5 @ X1 )
                                                 => ! [X6: $i] :
                                                      ( ( in @ X6 @ X2 )
                                                     => ( ( X5 = X6 )
                                                       => ( ( X3 @ X5 )
                                                          = ( X4 @ X6 ) ) ) ) )
                                             => ( ( dsetconstr @ X1 @ X3 )
                                                = ( dsetconstr @ X2 @ X4 ) ) ) )
                                     => ( ! [X1: $i,X2: $i] :
                                            ( ! [X3: $i] :
                                                ( ( in @ X3 @ X1 )
                                               => ( in @ X3 @ X2 ) )
                                           => ( subset @ X1 @ X2 ) )
                                       => ( ! [X1: $i,X2: $i] :
                                              ( ( X1 = X2 )
                                             => ( subset @ X2 @ X1 ) )
                                         => ( ! [X1: $i,X2: $i] :
                                                ( ( X1 = X2 )
                                               => ( subset @ X1 @ X2 ) )
                                           => ( ! [X1: $i,X2: $i] :
                                                  ( ! [X3: $i] :
                                                      ( ( in @ X3 @ X1 )
                                                     => ( in @ X3 @ X2 ) )
                                                 => ( subset @ X1 @ X2 ) )
                                             => ( ! [X1: $i] : ( subset @ emptyset @ X1 )
                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                      ( ( subset @ X1 @ X2 )
                                                     => ( ( in @ X3 @ X1 )
                                                       => ( in @ X3 @ X2 ) ) )
                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                        ( ( subset @ X1 @ X2 )
                                                       => ( ~ ( in @ X3 @ X2 )
                                                         => ~ ( in @ X3 @ X1 ) ) )
                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                          ( ( in @ X3 @ X1 )
                                                         => ( ~ ( in @ X3 @ X2 )
                                                           => ~ ( subset @ X1 @ X2 ) ) )
                                                     => ( ! [X1: $i,X2: $i] :
                                                            ( ~ ( subset @ X1 @ X2 )
                                                           => ( X1 != X2 ) )
                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                              ( ( in @ X3 @ X1 )
                                                             => ( ~ ( in @ X3 @ X2 )
                                                               => ( X1 != X2 ) ) )
                                                         => ( ! [X1: $i] : ( subset @ X1 @ X1 )
                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                  ( ( subset @ X1 @ X2 )
                                                                 => ( ( subset @ X2 @ X3 )
                                                                   => ( subset @ X1 @ X3 ) ) )
                                                             => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) )
                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                      ( ( subset @ X1 @ X3 )
                                                                     => ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
                                                                 => ( ! [X1: $i,X2: $i] :
                                                                        ( ( subset @ X1 @ X2 )
                                                                       => ( in @ X1 @ ( powerset @ X2 ) ) )
                                                                   => ( ! [X1: $i,X2: $i] :
                                                                          ( ( subset @ X1 @ X2 )
                                                                         => ( ( subset @ X2 @ X1 )
                                                                           => ( X1 = X2 ) ) )
                                                                     => ( ! [X1: $i] :
                                                                            ( ( subset @ X1 @ emptyset )
                                                                           => ( X1 = emptyset ) )
                                                                       => ( ! [X1: $i,X2: $i] :
                                                                              ( ( subset @ X2 @ X1 )
                                                                             => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                ( ( in @ X2 @ ( powerset @ X1 ) )
                                                                               => ( subset @ X2 @ X1 ) )
                                                                           => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                    ( ( subset @ X1 @ X2 )
                                                                                   => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
                                                                               => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                                                                                 => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                          ( ( in @ X3 @ X1 )
                                                                                         => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                     => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                              ( ( in @ X3 @ X2 )
                                                                                             => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                                                                                ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                               => ( ( ( in @ X3 @ X1 )
                                                                                                   => X4 )
                                                                                                 => ( ( ( in @ X3 @ X2 )
                                                                                                     => X4 )
                                                                                                   => X4 ) ) )
                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                  ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                 => ( ~ ( in @ X3 @ X1 )
                                                                                                   => ( in @ X3 @ X2 ) ) )
                                                                                             => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                                                                                               => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                       => ( ( in @ X3 @ X2 )
                                                                                                         => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                          ( ( subset @ X3 @ X1 )
                                                                                                         => ( ( subset @ X3 @ X2 )
                                                                                                           => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                            ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                           => ( in @ X3 @ X1 ) )
                                                                                                       => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                ( ( subset @ X1 @ X2 )
                                                                                                               => ( ( binintersect @ X1 @ X2 )
                                                                                                                  = X1 ) )
                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                  ( ( ( binintersect @ X1 @ X2 )
                                                                                                                    = X2 )
                                                                                                                 => ( subset @ X2 @ X1 ) )
                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                    ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                   => ( in @ X3 @ X2 ) )
                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                      ( ! [X3: $i] :
                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                         => ~ ( in @ X3 @ X2 ) )
                                                                                                                     => ( ( binintersect @ X1 @ X2 )
                                                                                                                        = emptyset ) )
                                                                                                                 => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                          ( ( subset @ X2 @ X1 )
                                                                                                                         => ( ( binintersect @ X1 @ X2 )
                                                                                                                            = X2 ) )
                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                            ( ( ( binintersect @ X1 @ X2 )
                                                                                                                              = X1 )
                                                                                                                           => ( subset @ X1 @ X2 ) )
                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                              ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                                                                                              = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                               => ( ~ ( in @ X3 @ X2 )
                                                                                                                                 => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                  ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                 => ( in @ X3 @ X1 ) )
                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                    ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                   => ~ ( in @ X3 @ X2 ) )
                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                      ( ( subset @ X1 @ X2 )
                                                                                                                                     => ( ( setminus @ X1 @ X2 )
                                                                                                                                        = emptyset ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                        ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                       => ( ( in @ X3 @ X1 )
                                                                                                                                         => ( in @ X3 @ X2 ) ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                          ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                         => ( ~ ( in @ X3 @ X2 )
                                                                                                                                           => ~ ( in @ X3 @ X1 ) ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                            ( ~ ( in @ X3 @ X1 )
                                                                                                                                           => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                              ( ( in @ X3 @ X2 )
                                                                                                                                             => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                         => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                  ( ( ( setminus @ X1 @ X2 )
                                                                                                                                                    = emptyset )
                                                                                                                                                 => ( subset @ X1 @ X2 ) )
                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                    ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                                                                                   => ! [X4: $o] :
                                                                                                                                                        ( ( ( in @ X3 @ X1 )
                                                                                                                                                         => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                           => X4 ) )
                                                                                                                                                       => ( ( ~ ( in @ X3 @ X1 )
                                                                                                                                                           => ( ( in @ X3 @ X2 )
                                                                                                                                                             => X4 ) )
                                                                                                                                                         => X4 ) ) )
                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                     => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                       => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                        ( ~ ( in @ X3 @ X1 )
                                                                                                                                                       => ( ( in @ X3 @ X2 )
                                                                                                                                                         => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                         => ( ( in @ X3 @ X2 )
                                                                                                                                                           => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                            ( ~ ( in @ X3 @ X1 )
                                                                                                                                                           => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                             => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                       => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                         => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                           => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                             => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                               => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                        ( ( in @ X2 @ X1 )
                                                                                                                                                                       => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                          ( ( in @ X2 @ X1 )
                                                                                                                                                                         => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                           => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                              ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                             => ( ( X3 != X1 )
                                                                                                                                                                               => ( X3 = X2 ) ) )
                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                                                                   => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                                                                     => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                                                                       => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                                                                         => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                                                                           => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                                                                                             => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                            ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                           => ~ ! [X4: $i] :
                                                                                                                                                                                                  ( ( in @ X4 @ X1 )
                                                                                                                                                                                                 => ! [X5: $i] :
                                                                                                                                                                                                      ( ( in @ X5 @ X2 )
                                                                                                                                                                                                     => ( X3
                                                                                                                                                                                                       != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                                                                                       => ( sP5
                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                                                                                               => ~ ! [X3: $i] :
                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                     => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                                                                                           => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                                                                                             => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                               => ( ! [X1: $i] :
                                                                                                                                                                                                      ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                                                                                      = X1 )
                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                        ( ! [X3: $i] :
                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                                                                ( ( in @ X4 @ X1 )
                                                                                                                                                                                                               => ( ( X2 @ X3 )
                                                                                                                                                                                                                 => ( ( X2 @ X4 )
                                                                                                                                                                                                                   => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                       => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                               => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                         => ~ ! [X3: $i] :
                                                                                                                                                                                                                ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                               => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                 != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                          ( ~ ! [X3: $i] :
                                                                                                                                                                                                                ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                               => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                 != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                                                                                         => ~ ! [X3: $i] :
                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                               => ~ ( X2 @ X3 ) ) )
                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                           => ( ( X2 @ X3 )
                                                                                                                                                                                                             => ( ! [X4: $i] :
                                                                                                                                                                                                                    ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                   => ( ( X2 @ X4 )
                                                                                                                                                                                                                     => ( X4 = X3 ) ) )
                                                                                                                                                                                                               => ~ ! [X4: $i] :
                                                                                                                                                                                                                      ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                     => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                       != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                              ( ! [X3: $i] :
                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                                                                      ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                     => ( ( X2 @ X3 )
                                                                                                                                                                                                                       => ( ( X2 @ X4 )
                                                                                                                                                                                                                         => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                             => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                     => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                               => ~ ! [X3: $i] :
                                                                                                                                                                                                                      ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                     => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                       != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                                                                                  = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                               => ( X1 = X2 ) )
                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                  ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                 => ( X1 = X3 ) )
                                                                                                                                                                                                             => ( ! [X1: $i] :
                                                                                                                                                                                                                    ( ( iskpair @ X1 )
                                                                                                                                                                                                                   => ~ ! [X2: $i] :
                                                                                                                                                                                                                          ( ( in @ X2
                                                                                                                                                                                                                            @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                              @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                                                                                         => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                              @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                           != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                               => ( ! [X1: $i] :
                                                                                                                                                                                                                      ( ~ ! [X2: $i] :
                                                                                                                                                                                                                            ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                           => ( X1
                                                                                                                                                                                                                             != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                     => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                        ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                        = X1 )
                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                         => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                            ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                              = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                           => ( X1 = X3 ) )
                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                              ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                             => ( X1 = X3 ) )
                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                ( ( X1 = X2 )
                                                                                                                                                                                                                               => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                  = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                  ( ( X1 = X2 )
                                                                                                                                                                                                                                 => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                    = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                    ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                      = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                   => ( ( X3 = X4 )
                                                                                                                                                                                                                                     => ( X2 = X4 ) ) )
                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                      ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                        = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                                                                                     => ( X1 = X2 ) )
                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                        ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                          = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                       => ( X2 = X4 ) )
                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                          ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                            = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                         => ( X2 = X4 ) )
                                                                                                                                                                                                                                     => ( ! [X1: $i] :
                                                                                                                                                                                                                                            ( ( iskpair @ X1 )
                                                                                                                                                                                                                                           => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                  ( ( in @ X2
                                                                                                                                                                                                                                                    @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                      @ ^ [X3: $i] :
                                                                                                                                                                                                                                                          ( X1
                                                                                                                                                                                                                                                          = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                                                                                 => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                      @ ^ [X3: $i] :
                                                                                                                                                                                                                                                          ( X1
                                                                                                                                                                                                                                                          = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                                                                                   != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                              ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                              = X2 )
                                                                                                                                                                                                                                         => ( sP8
                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                  ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                 => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                    ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                   => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                      ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                     => ( in @ X4 @ X2 ) )
                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                           => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                              = X3 ) ) )
                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                             => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                = X4 ) ) )
                                                                                                                                                                                                                                                     => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                         => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                                                                                            = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h92,assumption,
    ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ),
    introduced(assumption,[]) ).

thf(h93,assumption,
    ~ ( ! [X1: $i,X2: $i > $o] :
          ( ~ ! [X3: $i] :
                ( ( in @ X3 @ X1 )
               => ~ ( X2 @ X3 ) )
         => ( ( dsetconstr @ X1 @ X2 )
           != emptyset ) )
     => ( ! [X1: $i > $o,X2: $i] :
            ( ( in @ X2 @ emptyset )
           => ( X1 @ X2 ) )
       => ( ! [X1: $o] :
              ( X1
             => ( in @ emptyset @ ( prop2set @ X1 ) ) )
         => ( ! [X1: $o] :
                ( X1
               => ( set2prop @ ( prop2set @ X1 ) ) )
           => ( ! [X1: $i > $o] :
                  ( ~ ! [X2: $i] :
                        ~ ( X1 @ X2 )
                 => ( ! [X2: $i,X3: $i] :
                        ( ( X1 @ X2 )
                       => ( ( X1 @ X3 )
                         => ( X2 = X3 ) ) )
                   => ~ ! [X2: $i] :
                          ( ( X1 @ X2 )
                         => ~ ! [X3: $i] :
                                ( ( X1 @ X3 )
                               => ( X2 = X3 ) ) ) ) )
             => ( ! [X1: $i > $o] :
                    ( ~ ! [X2: $i] :
                          ~ ! [X3: $i] :
                              ( ( X1 @ X3 )
                              = ( X3 = X2 ) )
                   => ~ ! [X2: $i] :
                          ( ( X1 @ X2 )
                         => ~ ! [X3: $i] :
                                ( ( X1 @ X3 )
                               => ( X2 = X3 ) ) ) )
               => ( ! [X1: $i,X2: $i] :
                      ( ( X1 = X2 )
                     => ! [X3: $i,X4: $i] :
                          ( ( X3 = X4 )
                         => ( ( in @ X3 @ X1 )
                           => ( in @ X4 @ X2 ) ) ) )
                 => ( ! [X1: $i,X2: $i] :
                        ( ( X1 = X2 )
                       => ! [X3: $i,X4: $i] :
                            ( ( X3 = X4 )
                           => ( ( in @ X3 @ X1 )
                              = ( in @ X4 @ X2 ) ) ) )
                   => ( ! [X1: $i > $o] :
                          ( ~ ! [X2: $i] :
                                ( ( X1 @ X2 )
                               => ~ ! [X3: $i] :
                                      ( ( X1 @ X3 )
                                     => ( X2 = X3 ) ) )
                         => ! [X2: $i,X3: $i] :
                              ( ( X1 @ X2 )
                             => ( ( X1 @ X3 )
                               => ( X2 = X3 ) ) ) )
                     => ( ! [X1: $i > $o,X2: $i > $o] :
                            ( ! [X3: $i,X4: $i] :
                                ( ( X3 = X4 )
                               => ( ( X1 @ X3 )
                                  = ( X2 @ X4 ) ) )
                           => ( ( ~ ! [X3: $i] :
                                      ( ( X1 @ X3 )
                                     => ~ ! [X4: $i] :
                                            ( ( X1 @ X4 )
                                           => ( X3 = X4 ) ) ) )
                              = ( ~ ! [X3: $i] :
                                      ( ( X2 @ X3 )
                                     => ~ ! [X4: $i] :
                                            ( ( X2 @ X4 )
                                           => ( X3 = X4 ) ) ) ) ) )
                       => ( ! [X1: $i,X2: $i] :
                              ( ( X1 = X2 )
                             => ! [X3: $i,X4: $i] :
                                  ( ( X3 = X4 )
                                 => ( ( setadjoin @ X1 @ X3 )
                                    = ( setadjoin @ X2 @ X4 ) ) ) )
                         => ( ! [X1: $i,X2: $i] :
                                ( ( X1 = X2 )
                               => ( ( powerset @ X1 )
                                  = ( powerset @ X2 ) ) )
                           => ( ! [X1: $i,X2: $i] :
                                  ( ( X1 = X2 )
                                 => ( ( setunion @ X1 )
                                    = ( setunion @ X2 ) ) )
                             => ( ! [X1: $i > $o] :
                                    ( ~ ! [X2: $i] :
                                          ( ( X1 @ X2 )
                                         => ~ ! [X3: $i] :
                                                ( ( X1 @ X3 )
                                               => ( X2 = X3 ) ) )
                                   => ! [X2: $i,X3: $i] :
                                        ( ( X1 @ X2 )
                                       => ( ( X1 @ X3 )
                                         => ( X2 = X3 ) ) ) )
                               => ( ! [X1: $i > $o,X2: $i > $o] :
                                      ( ! [X3: $i,X4: $i] :
                                          ( ( X3 = X4 )
                                         => ( ( X1 @ X3 )
                                            = ( X2 @ X4 ) ) )
                                     => ( ~ ! [X3: $i] :
                                              ( ( X1 @ X3 )
                                             => ~ ! [X4: $i] :
                                                    ( ( X1 @ X4 )
                                                   => ( X3 = X4 ) ) )
                                       => ( ~ ! [X3: $i] :
                                                ( ( X2 @ X3 )
                                               => ~ ! [X4: $i] :
                                                      ( ( X2 @ X4 )
                                                     => ( X3 = X4 ) ) )
                                         => ( ( descr @ X1 )
                                            = ( descr @ X2 ) ) ) ) )
                                 => ( ! [X1: $i,X2: $i] :
                                        ( ( X1 = X2 )
                                       => ! [X3: $i > $o,X4: $i > $o] :
                                            ( ! [X5: $i] :
                                                ( ( in @ X5 @ X1 )
                                               => ! [X6: $i] :
                                                    ( ( in @ X6 @ X2 )
                                                   => ( ( X5 = X6 )
                                                     => ( ( X3 @ X5 )
                                                        = ( X4 @ X6 ) ) ) ) )
                                           => ( ( dsetconstr @ X1 @ X3 )
                                              = ( dsetconstr @ X2 @ X4 ) ) ) )
                                   => ( ! [X1: $i,X2: $i] :
                                          ( ! [X3: $i] :
                                              ( ( in @ X3 @ X1 )
                                             => ( in @ X3 @ X2 ) )
                                         => ( subset @ X1 @ X2 ) )
                                     => ( ! [X1: $i,X2: $i] :
                                            ( ( X1 = X2 )
                                           => ( subset @ X2 @ X1 ) )
                                       => ( ! [X1: $i,X2: $i] :
                                              ( ( X1 = X2 )
                                             => ( subset @ X1 @ X2 ) )
                                         => ( ! [X1: $i,X2: $i] :
                                                ( ! [X3: $i] :
                                                    ( ( in @ X3 @ X1 )
                                                   => ( in @ X3 @ X2 ) )
                                               => ( subset @ X1 @ X2 ) )
                                           => ( ! [X1: $i] : ( subset @ emptyset @ X1 )
                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                    ( ( subset @ X1 @ X2 )
                                                   => ( ( in @ X3 @ X1 )
                                                     => ( in @ X3 @ X2 ) ) )
                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                      ( ( subset @ X1 @ X2 )
                                                     => ( ~ ( in @ X3 @ X2 )
                                                       => ~ ( in @ X3 @ X1 ) ) )
                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                        ( ( in @ X3 @ X1 )
                                                       => ( ~ ( in @ X3 @ X2 )
                                                         => ~ ( subset @ X1 @ X2 ) ) )
                                                   => ( ! [X1: $i,X2: $i] :
                                                          ( ~ ( subset @ X1 @ X2 )
                                                         => ( X1 != X2 ) )
                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                            ( ( in @ X3 @ X1 )
                                                           => ( ~ ( in @ X3 @ X2 )
                                                             => ( X1 != X2 ) ) )
                                                       => ( ! [X1: $i] : ( subset @ X1 @ X1 )
                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                ( ( subset @ X1 @ X2 )
                                                               => ( ( subset @ X2 @ X3 )
                                                                 => ( subset @ X1 @ X3 ) ) )
                                                           => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) )
                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                    ( ( subset @ X1 @ X3 )
                                                                   => ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
                                                               => ( ! [X1: $i,X2: $i] :
                                                                      ( ( subset @ X1 @ X2 )
                                                                     => ( in @ X1 @ ( powerset @ X2 ) ) )
                                                                 => ( ! [X1: $i,X2: $i] :
                                                                        ( ( subset @ X1 @ X2 )
                                                                       => ( ( subset @ X2 @ X1 )
                                                                         => ( X1 = X2 ) ) )
                                                                   => ( ! [X1: $i] :
                                                                          ( ( subset @ X1 @ emptyset )
                                                                         => ( X1 = emptyset ) )
                                                                     => ( ! [X1: $i,X2: $i] :
                                                                            ( ( subset @ X2 @ X1 )
                                                                           => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                                       => ( ! [X1: $i,X2: $i] :
                                                                              ( ( in @ X2 @ ( powerset @ X1 ) )
                                                                             => ( subset @ X2 @ X1 ) )
                                                                         => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                  ( ( subset @ X1 @ X2 )
                                                                                 => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
                                                                             => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                                                                               => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                        ( ( in @ X3 @ X1 )
                                                                                       => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                   => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                            ( ( in @ X3 @ X2 )
                                                                                           => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                                                                              ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                             => ( ( ( in @ X3 @ X1 )
                                                                                                 => X4 )
                                                                                               => ( ( ( in @ X3 @ X2 )
                                                                                                   => X4 )
                                                                                                 => X4 ) ) )
                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                               => ( ~ ( in @ X3 @ X1 )
                                                                                                 => ( in @ X3 @ X2 ) ) )
                                                                                           => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                                                                                             => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                     => ( ( in @ X3 @ X2 )
                                                                                                       => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                        ( ( subset @ X3 @ X1 )
                                                                                                       => ( ( subset @ X3 @ X2 )
                                                                                                         => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                          ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                         => ( in @ X3 @ X1 ) )
                                                                                                     => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                              ( ( subset @ X1 @ X2 )
                                                                                                             => ( ( binintersect @ X1 @ X2 )
                                                                                                                = X1 ) )
                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                ( ( ( binintersect @ X1 @ X2 )
                                                                                                                  = X2 )
                                                                                                               => ( subset @ X2 @ X1 ) )
                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                  ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                 => ( in @ X3 @ X2 ) )
                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                    ( ! [X3: $i] :
                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                       => ~ ( in @ X3 @ X2 ) )
                                                                                                                   => ( ( binintersect @ X1 @ X2 )
                                                                                                                      = emptyset ) )
                                                                                                               => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                        ( ( subset @ X2 @ X1 )
                                                                                                                       => ( ( binintersect @ X1 @ X2 )
                                                                                                                          = X2 ) )
                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                          ( ( ( binintersect @ X1 @ X2 )
                                                                                                                            = X1 )
                                                                                                                         => ( subset @ X1 @ X2 ) )
                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                            ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                                                                                            = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                             => ( ~ ( in @ X3 @ X2 )
                                                                                                                               => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                               => ( in @ X3 @ X1 ) )
                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                  ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                 => ~ ( in @ X3 @ X2 ) )
                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                    ( ( subset @ X1 @ X2 )
                                                                                                                                   => ( ( setminus @ X1 @ X2 )
                                                                                                                                      = emptyset ) )
                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                      ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                     => ( ( in @ X3 @ X1 )
                                                                                                                                       => ( in @ X3 @ X2 ) ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                        ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                       => ( ~ ( in @ X3 @ X2 )
                                                                                                                                         => ~ ( in @ X3 @ X1 ) ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                          ( ~ ( in @ X3 @ X1 )
                                                                                                                                         => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                            ( ( in @ X3 @ X2 )
                                                                                                                                           => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                ( ( ( setminus @ X1 @ X2 )
                                                                                                                                                  = emptyset )
                                                                                                                                               => ( subset @ X1 @ X2 ) )
                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                  ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                                                                                 => ! [X4: $o] :
                                                                                                                                                      ( ( ( in @ X3 @ X1 )
                                                                                                                                                       => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                         => X4 ) )
                                                                                                                                                     => ( ( ~ ( in @ X3 @ X1 )
                                                                                                                                                         => ( ( in @ X3 @ X2 )
                                                                                                                                                           => X4 ) )
                                                                                                                                                       => X4 ) ) )
                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                   => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                     => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                      ( ~ ( in @ X3 @ X1 )
                                                                                                                                                     => ( ( in @ X3 @ X2 )
                                                                                                                                                       => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                       => ( ( in @ X3 @ X2 )
                                                                                                                                                         => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                          ( ~ ( in @ X3 @ X1 )
                                                                                                                                                         => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                           => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                     => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                       => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                         => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                           => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                             => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                      ( ( in @ X2 @ X1 )
                                                                                                                                                                     => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                        ( ( in @ X2 @ X1 )
                                                                                                                                                                       => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                         => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                            ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                           => ( ( X3 != X1 )
                                                                                                                                                                             => ( X3 = X2 ) ) )
                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                                                                 => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                                                                   => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                                                                     => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                                                                       => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                                                                         => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                                                                           => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                         => ~ ! [X4: $i] :
                                                                                                                                                                                                ( ( in @ X4 @ X1 )
                                                                                                                                                                                               => ! [X5: $i] :
                                                                                                                                                                                                    ( ( in @ X5 @ X2 )
                                                                                                                                                                                                   => ( X3
                                                                                                                                                                                                     != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                                                                                     => ( sP5
                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                              ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                                                                                             => ~ ! [X3: $i] :
                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                   => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                                                                                         => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                                                                                           => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                             => ( ! [X1: $i] :
                                                                                                                                                                                                    ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                                                                                    = X1 )
                                                                                                                                                                                               => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                      ( ! [X3: $i] :
                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                                                              ( ( in @ X4 @ X1 )
                                                                                                                                                                                                             => ( ( X2 @ X3 )
                                                                                                                                                                                                               => ( ( X2 @ X4 )
                                                                                                                                                                                                                 => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                     => ( ~ ! [X3: $i] :
                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                             => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                       => ~ ! [X3: $i] :
                                                                                                                                                                                                              ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                             => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                               != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                        ( ~ ! [X3: $i] :
                                                                                                                                                                                                              ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                             => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                               != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                                                                                       => ~ ! [X3: $i] :
                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                             => ~ ( X2 @ X3 ) ) )
                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                         => ( ( X2 @ X3 )
                                                                                                                                                                                                           => ( ! [X4: $i] :
                                                                                                                                                                                                                  ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                 => ( ( X2 @ X4 )
                                                                                                                                                                                                                   => ( X4 = X3 ) ) )
                                                                                                                                                                                                             => ~ ! [X4: $i] :
                                                                                                                                                                                                                    ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                   => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                     != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                            ( ! [X3: $i] :
                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                                                    ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                   => ( ( X2 @ X3 )
                                                                                                                                                                                                                     => ( ( X2 @ X4 )
                                                                                                                                                                                                                       => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                           => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                   => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                             => ~ ! [X3: $i] :
                                                                                                                                                                                                                    ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                   => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                     != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                              ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                                                                                = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                             => ( X1 = X2 ) )
                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                               => ( X1 = X3 ) )
                                                                                                                                                                                                           => ( ! [X1: $i] :
                                                                                                                                                                                                                  ( ( iskpair @ X1 )
                                                                                                                                                                                                                 => ~ ! [X2: $i] :
                                                                                                                                                                                                                        ( ( in @ X2
                                                                                                                                                                                                                          @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                            @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                                                                                       => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                            @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                         != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                             => ( ! [X1: $i] :
                                                                                                                                                                                                                    ( ~ ! [X2: $i] :
                                                                                                                                                                                                                          ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                         => ( X1
                                                                                                                                                                                                                           != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                   => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                      ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                      = X1 )
                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                       => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                          ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                            = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                         => ( X1 = X3 ) )
                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                            ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                              = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                           => ( X1 = X3 ) )
                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                              ( ( X1 = X2 )
                                                                                                                                                                                                                             => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                ( ( X1 = X2 )
                                                                                                                                                                                                                               => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                  = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                  ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                    = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                 => ( ( X3 = X4 )
                                                                                                                                                                                                                                   => ( X2 = X4 ) ) )
                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                    ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                      = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                                                                                   => ( X1 = X2 ) )
                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                      ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                        = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                     => ( X2 = X4 ) )
                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                        ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                          = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                       => ( X2 = X4 ) )
                                                                                                                                                                                                                                   => ( ! [X1: $i] :
                                                                                                                                                                                                                                          ( ( iskpair @ X1 )
                                                                                                                                                                                                                                         => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                ( ( in @ X2
                                                                                                                                                                                                                                                  @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                    @ ^ [X3: $i] :
                                                                                                                                                                                                                                                        ( X1
                                                                                                                                                                                                                                                        = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                                                                               => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                    @ ^ [X3: $i] :
                                                                                                                                                                                                                                                        ( X1
                                                                                                                                                                                                                                                        = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                                                                                 != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                            ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                            = X2 )
                                                                                                                                                                                                                                       => ( sP8
                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                               => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                  ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                 => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                    ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                   => ( in @ X4 @ X2 ) )
                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                         => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                            = X3 ) ) )
                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                           => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                              = X4 ) ) )
                                                                                                                                                                                                                                                   => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                       => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                                                                                          = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h94,assumption,
    ! [X1: $i,X2: $i > $o] :
      ( ~ ! [X3: $i] :
            ( ( in @ X3 @ X1 )
           => ~ ( X2 @ X3 ) )
     => ( ( dsetconstr @ X1 @ X2 )
       != emptyset ) ),
    introduced(assumption,[]) ).

thf(h95,assumption,
    ~ ( ! [X1: $i > $o,X2: $i] :
          ( ( in @ X2 @ emptyset )
         => ( X1 @ X2 ) )
     => ( ! [X1: $o] :
            ( X1
           => ( in @ emptyset @ ( prop2set @ X1 ) ) )
       => ( ! [X1: $o] :
              ( X1
             => ( set2prop @ ( prop2set @ X1 ) ) )
         => ( ! [X1: $i > $o] :
                ( ~ ! [X2: $i] :
                      ~ ( X1 @ X2 )
               => ( ! [X2: $i,X3: $i] :
                      ( ( X1 @ X2 )
                     => ( ( X1 @ X3 )
                       => ( X2 = X3 ) ) )
                 => ~ ! [X2: $i] :
                        ( ( X1 @ X2 )
                       => ~ ! [X3: $i] :
                              ( ( X1 @ X3 )
                             => ( X2 = X3 ) ) ) ) )
           => ( ! [X1: $i > $o] :
                  ( ~ ! [X2: $i] :
                        ~ ! [X3: $i] :
                            ( ( X1 @ X3 )
                            = ( X3 = X2 ) )
                 => ~ ! [X2: $i] :
                        ( ( X1 @ X2 )
                       => ~ ! [X3: $i] :
                              ( ( X1 @ X3 )
                             => ( X2 = X3 ) ) ) )
             => ( ! [X1: $i,X2: $i] :
                    ( ( X1 = X2 )
                   => ! [X3: $i,X4: $i] :
                        ( ( X3 = X4 )
                       => ( ( in @ X3 @ X1 )
                         => ( in @ X4 @ X2 ) ) ) )
               => ( ! [X1: $i,X2: $i] :
                      ( ( X1 = X2 )
                     => ! [X3: $i,X4: $i] :
                          ( ( X3 = X4 )
                         => ( ( in @ X3 @ X1 )
                            = ( in @ X4 @ X2 ) ) ) )
                 => ( ! [X1: $i > $o] :
                        ( ~ ! [X2: $i] :
                              ( ( X1 @ X2 )
                             => ~ ! [X3: $i] :
                                    ( ( X1 @ X3 )
                                   => ( X2 = X3 ) ) )
                       => ! [X2: $i,X3: $i] :
                            ( ( X1 @ X2 )
                           => ( ( X1 @ X3 )
                             => ( X2 = X3 ) ) ) )
                   => ( ! [X1: $i > $o,X2: $i > $o] :
                          ( ! [X3: $i,X4: $i] :
                              ( ( X3 = X4 )
                             => ( ( X1 @ X3 )
                                = ( X2 @ X4 ) ) )
                         => ( ( ~ ! [X3: $i] :
                                    ( ( X1 @ X3 )
                                   => ~ ! [X4: $i] :
                                          ( ( X1 @ X4 )
                                         => ( X3 = X4 ) ) ) )
                            = ( ~ ! [X3: $i] :
                                    ( ( X2 @ X3 )
                                   => ~ ! [X4: $i] :
                                          ( ( X2 @ X4 )
                                         => ( X3 = X4 ) ) ) ) ) )
                     => ( ! [X1: $i,X2: $i] :
                            ( ( X1 = X2 )
                           => ! [X3: $i,X4: $i] :
                                ( ( X3 = X4 )
                               => ( ( setadjoin @ X1 @ X3 )
                                  = ( setadjoin @ X2 @ X4 ) ) ) )
                       => ( ! [X1: $i,X2: $i] :
                              ( ( X1 = X2 )
                             => ( ( powerset @ X1 )
                                = ( powerset @ X2 ) ) )
                         => ( ! [X1: $i,X2: $i] :
                                ( ( X1 = X2 )
                               => ( ( setunion @ X1 )
                                  = ( setunion @ X2 ) ) )
                           => ( ! [X1: $i > $o] :
                                  ( ~ ! [X2: $i] :
                                        ( ( X1 @ X2 )
                                       => ~ ! [X3: $i] :
                                              ( ( X1 @ X3 )
                                             => ( X2 = X3 ) ) )
                                 => ! [X2: $i,X3: $i] :
                                      ( ( X1 @ X2 )
                                     => ( ( X1 @ X3 )
                                       => ( X2 = X3 ) ) ) )
                             => ( ! [X1: $i > $o,X2: $i > $o] :
                                    ( ! [X3: $i,X4: $i] :
                                        ( ( X3 = X4 )
                                       => ( ( X1 @ X3 )
                                          = ( X2 @ X4 ) ) )
                                   => ( ~ ! [X3: $i] :
                                            ( ( X1 @ X3 )
                                           => ~ ! [X4: $i] :
                                                  ( ( X1 @ X4 )
                                                 => ( X3 = X4 ) ) )
                                     => ( ~ ! [X3: $i] :
                                              ( ( X2 @ X3 )
                                             => ~ ! [X4: $i] :
                                                    ( ( X2 @ X4 )
                                                   => ( X3 = X4 ) ) )
                                       => ( ( descr @ X1 )
                                          = ( descr @ X2 ) ) ) ) )
                               => ( ! [X1: $i,X2: $i] :
                                      ( ( X1 = X2 )
                                     => ! [X3: $i > $o,X4: $i > $o] :
                                          ( ! [X5: $i] :
                                              ( ( in @ X5 @ X1 )
                                             => ! [X6: $i] :
                                                  ( ( in @ X6 @ X2 )
                                                 => ( ( X5 = X6 )
                                                   => ( ( X3 @ X5 )
                                                      = ( X4 @ X6 ) ) ) ) )
                                         => ( ( dsetconstr @ X1 @ X3 )
                                            = ( dsetconstr @ X2 @ X4 ) ) ) )
                                 => ( ! [X1: $i,X2: $i] :
                                        ( ! [X3: $i] :
                                            ( ( in @ X3 @ X1 )
                                           => ( in @ X3 @ X2 ) )
                                       => ( subset @ X1 @ X2 ) )
                                   => ( ! [X1: $i,X2: $i] :
                                          ( ( X1 = X2 )
                                         => ( subset @ X2 @ X1 ) )
                                     => ( ! [X1: $i,X2: $i] :
                                            ( ( X1 = X2 )
                                           => ( subset @ X1 @ X2 ) )
                                       => ( ! [X1: $i,X2: $i] :
                                              ( ! [X3: $i] :
                                                  ( ( in @ X3 @ X1 )
                                                 => ( in @ X3 @ X2 ) )
                                             => ( subset @ X1 @ X2 ) )
                                         => ( ! [X1: $i] : ( subset @ emptyset @ X1 )
                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                  ( ( subset @ X1 @ X2 )
                                                 => ( ( in @ X3 @ X1 )
                                                   => ( in @ X3 @ X2 ) ) )
                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                    ( ( subset @ X1 @ X2 )
                                                   => ( ~ ( in @ X3 @ X2 )
                                                     => ~ ( in @ X3 @ X1 ) ) )
                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                      ( ( in @ X3 @ X1 )
                                                     => ( ~ ( in @ X3 @ X2 )
                                                       => ~ ( subset @ X1 @ X2 ) ) )
                                                 => ( ! [X1: $i,X2: $i] :
                                                        ( ~ ( subset @ X1 @ X2 )
                                                       => ( X1 != X2 ) )
                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                          ( ( in @ X3 @ X1 )
                                                         => ( ~ ( in @ X3 @ X2 )
                                                           => ( X1 != X2 ) ) )
                                                     => ( ! [X1: $i] : ( subset @ X1 @ X1 )
                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                              ( ( subset @ X1 @ X2 )
                                                             => ( ( subset @ X2 @ X3 )
                                                               => ( subset @ X1 @ X3 ) ) )
                                                         => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) )
                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                  ( ( subset @ X1 @ X3 )
                                                                 => ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
                                                             => ( ! [X1: $i,X2: $i] :
                                                                    ( ( subset @ X1 @ X2 )
                                                                   => ( in @ X1 @ ( powerset @ X2 ) ) )
                                                               => ( ! [X1: $i,X2: $i] :
                                                                      ( ( subset @ X1 @ X2 )
                                                                     => ( ( subset @ X2 @ X1 )
                                                                       => ( X1 = X2 ) ) )
                                                                 => ( ! [X1: $i] :
                                                                        ( ( subset @ X1 @ emptyset )
                                                                       => ( X1 = emptyset ) )
                                                                   => ( ! [X1: $i,X2: $i] :
                                                                          ( ( subset @ X2 @ X1 )
                                                                         => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                                     => ( ! [X1: $i,X2: $i] :
                                                                            ( ( in @ X2 @ ( powerset @ X1 ) )
                                                                           => ( subset @ X2 @ X1 ) )
                                                                       => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                ( ( subset @ X1 @ X2 )
                                                                               => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
                                                                           => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                                                                             => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                      ( ( in @ X3 @ X1 )
                                                                                     => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                 => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                          ( ( in @ X3 @ X2 )
                                                                                         => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                                                                            ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                           => ( ( ( in @ X3 @ X1 )
                                                                                               => X4 )
                                                                                             => ( ( ( in @ X3 @ X2 )
                                                                                                 => X4 )
                                                                                               => X4 ) ) )
                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                              ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                             => ( ~ ( in @ X3 @ X1 )
                                                                                               => ( in @ X3 @ X2 ) ) )
                                                                                         => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                                                                                           => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                   => ( ( in @ X3 @ X2 )
                                                                                                     => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                      ( ( subset @ X3 @ X1 )
                                                                                                     => ( ( subset @ X3 @ X2 )
                                                                                                       => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                        ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                       => ( in @ X3 @ X1 ) )
                                                                                                   => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                            ( ( subset @ X1 @ X2 )
                                                                                                           => ( ( binintersect @ X1 @ X2 )
                                                                                                              = X1 ) )
                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                              ( ( ( binintersect @ X1 @ X2 )
                                                                                                                = X2 )
                                                                                                             => ( subset @ X2 @ X1 ) )
                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                               => ( in @ X3 @ X2 ) )
                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                  ( ! [X3: $i] :
                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                     => ~ ( in @ X3 @ X2 ) )
                                                                                                                 => ( ( binintersect @ X1 @ X2 )
                                                                                                                    = emptyset ) )
                                                                                                             => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                      ( ( subset @ X2 @ X1 )
                                                                                                                     => ( ( binintersect @ X1 @ X2 )
                                                                                                                        = X2 ) )
                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                        ( ( ( binintersect @ X1 @ X2 )
                                                                                                                          = X1 )
                                                                                                                       => ( subset @ X1 @ X2 ) )
                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                          ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                                                                                          = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                           => ( ~ ( in @ X3 @ X2 )
                                                                                                                             => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                              ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                             => ( in @ X3 @ X1 ) )
                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                               => ~ ( in @ X3 @ X2 ) )
                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                  ( ( subset @ X1 @ X2 )
                                                                                                                                 => ( ( setminus @ X1 @ X2 )
                                                                                                                                    = emptyset ) )
                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                    ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                   => ( ( in @ X3 @ X1 )
                                                                                                                                     => ( in @ X3 @ X2 ) ) )
                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                      ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                     => ( ~ ( in @ X3 @ X2 )
                                                                                                                                       => ~ ( in @ X3 @ X1 ) ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                        ( ~ ( in @ X3 @ X1 )
                                                                                                                                       => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                          ( ( in @ X3 @ X2 )
                                                                                                                                         => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                              ( ( ( setminus @ X1 @ X2 )
                                                                                                                                                = emptyset )
                                                                                                                                             => ( subset @ X1 @ X2 ) )
                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                                                                               => ! [X4: $o] :
                                                                                                                                                    ( ( ( in @ X3 @ X1 )
                                                                                                                                                     => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                       => X4 ) )
                                                                                                                                                   => ( ( ~ ( in @ X3 @ X1 )
                                                                                                                                                       => ( ( in @ X3 @ X2 )
                                                                                                                                                         => X4 ) )
                                                                                                                                                     => X4 ) ) )
                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                 => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                   => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                    ( ~ ( in @ X3 @ X1 )
                                                                                                                                                   => ( ( in @ X3 @ X2 )
                                                                                                                                                     => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                     => ( ( in @ X3 @ X2 )
                                                                                                                                                       => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                        ( ~ ( in @ X3 @ X1 )
                                                                                                                                                       => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                         => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                   => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                     => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                       => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                         => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                           => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                    ( ( in @ X2 @ X1 )
                                                                                                                                                                   => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                      ( ( in @ X2 @ X1 )
                                                                                                                                                                     => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                       => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                          ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                         => ( ( X3 != X1 )
                                                                                                                                                                           => ( X3 = X2 ) ) )
                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                                                                               => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                                                                 => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                                                                   => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                                                                     => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                                                                       => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                                                                         => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                       => ~ ! [X4: $i] :
                                                                                                                                                                                              ( ( in @ X4 @ X1 )
                                                                                                                                                                                             => ! [X5: $i] :
                                                                                                                                                                                                  ( ( in @ X5 @ X2 )
                                                                                                                                                                                                 => ( X3
                                                                                                                                                                                                   != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                                                                                   => ( sP5
                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                            ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                                                                                           => ~ ! [X3: $i] :
                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                 => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                                                                                       => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                                                                                         => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                           => ( ! [X1: $i] :
                                                                                                                                                                                                  ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                                                                                  = X1 )
                                                                                                                                                                                             => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                    ( ! [X3: $i] :
                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                                                            ( ( in @ X4 @ X1 )
                                                                                                                                                                                                           => ( ( X2 @ X3 )
                                                                                                                                                                                                             => ( ( X2 @ X4 )
                                                                                                                                                                                                               => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                   => ( ~ ! [X3: $i] :
                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                           => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                     => ~ ! [X3: $i] :
                                                                                                                                                                                                            ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                           => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                             != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                               => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                      ( ~ ! [X3: $i] :
                                                                                                                                                                                                            ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                           => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                             != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                                                                                     => ~ ! [X3: $i] :
                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                           => ~ ( X2 @ X3 ) ) )
                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                       => ( ( X2 @ X3 )
                                                                                                                                                                                                         => ( ! [X4: $i] :
                                                                                                                                                                                                                ( ( in @ X4 @ X1 )
                                                                                                                                                                                                               => ( ( X2 @ X4 )
                                                                                                                                                                                                                 => ( X4 = X3 ) ) )
                                                                                                                                                                                                           => ~ ! [X4: $i] :
                                                                                                                                                                                                                  ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                 => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                   != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                          ( ! [X3: $i] :
                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                                                  ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                 => ( ( X2 @ X3 )
                                                                                                                                                                                                                   => ( ( X2 @ X4 )
                                                                                                                                                                                                                     => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                         => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                 => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                           => ~ ! [X3: $i] :
                                                                                                                                                                                                                  ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                 => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                   != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                            ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                                                                              = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                           => ( X1 = X2 ) )
                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                              ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                             => ( X1 = X3 ) )
                                                                                                                                                                                                         => ( ! [X1: $i] :
                                                                                                                                                                                                                ( ( iskpair @ X1 )
                                                                                                                                                                                                               => ~ ! [X2: $i] :
                                                                                                                                                                                                                      ( ( in @ X2
                                                                                                                                                                                                                        @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                          @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                                                                                     => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                          @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                       != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                           => ( ! [X1: $i] :
                                                                                                                                                                                                                  ( ~ ! [X2: $i] :
                                                                                                                                                                                                                        ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                       => ( X1
                                                                                                                                                                                                                         != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                 => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                    ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                    = X1 )
                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                      ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                     => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                        ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                          = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                       => ( X1 = X3 ) )
                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                          ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                            = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                         => ( X1 = X3 ) )
                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                            ( ( X1 = X2 )
                                                                                                                                                                                                                           => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                              = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                              ( ( X1 = X2 )
                                                                                                                                                                                                                             => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                  = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                               => ( ( X3 = X4 )
                                                                                                                                                                                                                                 => ( X2 = X4 ) ) )
                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                  ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                    = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                                                                                 => ( X1 = X2 ) )
                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                    ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                      = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                   => ( X2 = X4 ) )
                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                      ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                        = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                     => ( X2 = X4 ) )
                                                                                                                                                                                                                                 => ( ! [X1: $i] :
                                                                                                                                                                                                                                        ( ( iskpair @ X1 )
                                                                                                                                                                                                                                       => ~ ! [X2: $i] :
                                                                                                                                                                                                                                              ( ( in @ X2
                                                                                                                                                                                                                                                @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                  @ ^ [X3: $i] :
                                                                                                                                                                                                                                                      ( X1
                                                                                                                                                                                                                                                      = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                                                                             => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                  @ ^ [X3: $i] :
                                                                                                                                                                                                                                                      ( X1
                                                                                                                                                                                                                                                      = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                                                                               != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                          ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                          = X2 )
                                                                                                                                                                                                                                     => ( sP8
                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                              ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                             => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                               => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                  ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                 => ( in @ X4 @ X2 ) )
                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                       => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                          = X3 ) ) )
                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                         => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                            = X4 ) ) )
                                                                                                                                                                                                                                                 => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                      ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                     => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                                                                                        = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h96,assumption,
    ! [X1: $i > $o,X2: $i] :
      ( ( in @ X2 @ emptyset )
     => ( X1 @ X2 ) ),
    introduced(assumption,[]) ).

thf(h97,assumption,
    ~ ( ! [X1: $o] :
          ( X1
         => ( in @ emptyset @ ( prop2set @ X1 ) ) )
     => ( ! [X1: $o] :
            ( X1
           => ( set2prop @ ( prop2set @ X1 ) ) )
       => ( ! [X1: $i > $o] :
              ( ~ ! [X2: $i] :
                    ~ ( X1 @ X2 )
             => ( ! [X2: $i,X3: $i] :
                    ( ( X1 @ X2 )
                   => ( ( X1 @ X3 )
                     => ( X2 = X3 ) ) )
               => ~ ! [X2: $i] :
                      ( ( X1 @ X2 )
                     => ~ ! [X3: $i] :
                            ( ( X1 @ X3 )
                           => ( X2 = X3 ) ) ) ) )
         => ( ! [X1: $i > $o] :
                ( ~ ! [X2: $i] :
                      ~ ! [X3: $i] :
                          ( ( X1 @ X3 )
                          = ( X3 = X2 ) )
               => ~ ! [X2: $i] :
                      ( ( X1 @ X2 )
                     => ~ ! [X3: $i] :
                            ( ( X1 @ X3 )
                           => ( X2 = X3 ) ) ) )
           => ( ! [X1: $i,X2: $i] :
                  ( ( X1 = X2 )
                 => ! [X3: $i,X4: $i] :
                      ( ( X3 = X4 )
                     => ( ( in @ X3 @ X1 )
                       => ( in @ X4 @ X2 ) ) ) )
             => ( ! [X1: $i,X2: $i] :
                    ( ( X1 = X2 )
                   => ! [X3: $i,X4: $i] :
                        ( ( X3 = X4 )
                       => ( ( in @ X3 @ X1 )
                          = ( in @ X4 @ X2 ) ) ) )
               => ( ! [X1: $i > $o] :
                      ( ~ ! [X2: $i] :
                            ( ( X1 @ X2 )
                           => ~ ! [X3: $i] :
                                  ( ( X1 @ X3 )
                                 => ( X2 = X3 ) ) )
                     => ! [X2: $i,X3: $i] :
                          ( ( X1 @ X2 )
                         => ( ( X1 @ X3 )
                           => ( X2 = X3 ) ) ) )
                 => ( ! [X1: $i > $o,X2: $i > $o] :
                        ( ! [X3: $i,X4: $i] :
                            ( ( X3 = X4 )
                           => ( ( X1 @ X3 )
                              = ( X2 @ X4 ) ) )
                       => ( ( ~ ! [X3: $i] :
                                  ( ( X1 @ X3 )
                                 => ~ ! [X4: $i] :
                                        ( ( X1 @ X4 )
                                       => ( X3 = X4 ) ) ) )
                          = ( ~ ! [X3: $i] :
                                  ( ( X2 @ X3 )
                                 => ~ ! [X4: $i] :
                                        ( ( X2 @ X4 )
                                       => ( X3 = X4 ) ) ) ) ) )
                   => ( ! [X1: $i,X2: $i] :
                          ( ( X1 = X2 )
                         => ! [X3: $i,X4: $i] :
                              ( ( X3 = X4 )
                             => ( ( setadjoin @ X1 @ X3 )
                                = ( setadjoin @ X2 @ X4 ) ) ) )
                     => ( ! [X1: $i,X2: $i] :
                            ( ( X1 = X2 )
                           => ( ( powerset @ X1 )
                              = ( powerset @ X2 ) ) )
                       => ( ! [X1: $i,X2: $i] :
                              ( ( X1 = X2 )
                             => ( ( setunion @ X1 )
                                = ( setunion @ X2 ) ) )
                         => ( ! [X1: $i > $o] :
                                ( ~ ! [X2: $i] :
                                      ( ( X1 @ X2 )
                                     => ~ ! [X3: $i] :
                                            ( ( X1 @ X3 )
                                           => ( X2 = X3 ) ) )
                               => ! [X2: $i,X3: $i] :
                                    ( ( X1 @ X2 )
                                   => ( ( X1 @ X3 )
                                     => ( X2 = X3 ) ) ) )
                           => ( ! [X1: $i > $o,X2: $i > $o] :
                                  ( ! [X3: $i,X4: $i] :
                                      ( ( X3 = X4 )
                                     => ( ( X1 @ X3 )
                                        = ( X2 @ X4 ) ) )
                                 => ( ~ ! [X3: $i] :
                                          ( ( X1 @ X3 )
                                         => ~ ! [X4: $i] :
                                                ( ( X1 @ X4 )
                                               => ( X3 = X4 ) ) )
                                   => ( ~ ! [X3: $i] :
                                            ( ( X2 @ X3 )
                                           => ~ ! [X4: $i] :
                                                  ( ( X2 @ X4 )
                                                 => ( X3 = X4 ) ) )
                                     => ( ( descr @ X1 )
                                        = ( descr @ X2 ) ) ) ) )
                             => ( ! [X1: $i,X2: $i] :
                                    ( ( X1 = X2 )
                                   => ! [X3: $i > $o,X4: $i > $o] :
                                        ( ! [X5: $i] :
                                            ( ( in @ X5 @ X1 )
                                           => ! [X6: $i] :
                                                ( ( in @ X6 @ X2 )
                                               => ( ( X5 = X6 )
                                                 => ( ( X3 @ X5 )
                                                    = ( X4 @ X6 ) ) ) ) )
                                       => ( ( dsetconstr @ X1 @ X3 )
                                          = ( dsetconstr @ X2 @ X4 ) ) ) )
                               => ( ! [X1: $i,X2: $i] :
                                      ( ! [X3: $i] :
                                          ( ( in @ X3 @ X1 )
                                         => ( in @ X3 @ X2 ) )
                                     => ( subset @ X1 @ X2 ) )
                                 => ( ! [X1: $i,X2: $i] :
                                        ( ( X1 = X2 )
                                       => ( subset @ X2 @ X1 ) )
                                   => ( ! [X1: $i,X2: $i] :
                                          ( ( X1 = X2 )
                                         => ( subset @ X1 @ X2 ) )
                                     => ( ! [X1: $i,X2: $i] :
                                            ( ! [X3: $i] :
                                                ( ( in @ X3 @ X1 )
                                               => ( in @ X3 @ X2 ) )
                                           => ( subset @ X1 @ X2 ) )
                                       => ( ! [X1: $i] : ( subset @ emptyset @ X1 )
                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                ( ( subset @ X1 @ X2 )
                                               => ( ( in @ X3 @ X1 )
                                                 => ( in @ X3 @ X2 ) ) )
                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                  ( ( subset @ X1 @ X2 )
                                                 => ( ~ ( in @ X3 @ X2 )
                                                   => ~ ( in @ X3 @ X1 ) ) )
                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                    ( ( in @ X3 @ X1 )
                                                   => ( ~ ( in @ X3 @ X2 )
                                                     => ~ ( subset @ X1 @ X2 ) ) )
                                               => ( ! [X1: $i,X2: $i] :
                                                      ( ~ ( subset @ X1 @ X2 )
                                                     => ( X1 != X2 ) )
                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                        ( ( in @ X3 @ X1 )
                                                       => ( ~ ( in @ X3 @ X2 )
                                                         => ( X1 != X2 ) ) )
                                                   => ( ! [X1: $i] : ( subset @ X1 @ X1 )
                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                            ( ( subset @ X1 @ X2 )
                                                           => ( ( subset @ X2 @ X3 )
                                                             => ( subset @ X1 @ X3 ) ) )
                                                       => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) )
                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                ( ( subset @ X1 @ X3 )
                                                               => ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
                                                           => ( ! [X1: $i,X2: $i] :
                                                                  ( ( subset @ X1 @ X2 )
                                                                 => ( in @ X1 @ ( powerset @ X2 ) ) )
                                                             => ( ! [X1: $i,X2: $i] :
                                                                    ( ( subset @ X1 @ X2 )
                                                                   => ( ( subset @ X2 @ X1 )
                                                                     => ( X1 = X2 ) ) )
                                                               => ( ! [X1: $i] :
                                                                      ( ( subset @ X1 @ emptyset )
                                                                     => ( X1 = emptyset ) )
                                                                 => ( ! [X1: $i,X2: $i] :
                                                                        ( ( subset @ X2 @ X1 )
                                                                       => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                                   => ( ! [X1: $i,X2: $i] :
                                                                          ( ( in @ X2 @ ( powerset @ X1 ) )
                                                                         => ( subset @ X2 @ X1 ) )
                                                                     => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
                                                                       => ( ! [X1: $i,X2: $i] :
                                                                              ( ( subset @ X1 @ X2 )
                                                                             => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
                                                                         => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                                                                           => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                    ( ( in @ X3 @ X1 )
                                                                                   => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                               => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                        ( ( in @ X3 @ X2 )
                                                                                       => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                                                                          ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                         => ( ( ( in @ X3 @ X1 )
                                                                                             => X4 )
                                                                                           => ( ( ( in @ X3 @ X2 )
                                                                                               => X4 )
                                                                                             => X4 ) ) )
                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                            ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                           => ( ~ ( in @ X3 @ X1 )
                                                                                             => ( in @ X3 @ X2 ) ) )
                                                                                       => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                                                                                         => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                 => ( ( in @ X3 @ X2 )
                                                                                                   => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                    ( ( subset @ X3 @ X1 )
                                                                                                   => ( ( subset @ X3 @ X2 )
                                                                                                     => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                      ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                     => ( in @ X3 @ X1 ) )
                                                                                                 => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                          ( ( subset @ X1 @ X2 )
                                                                                                         => ( ( binintersect @ X1 @ X2 )
                                                                                                            = X1 ) )
                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                            ( ( ( binintersect @ X1 @ X2 )
                                                                                                              = X2 )
                                                                                                           => ( subset @ X2 @ X1 ) )
                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                              ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                             => ( in @ X3 @ X2 ) )
                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                ( ! [X3: $i] :
                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                   => ~ ( in @ X3 @ X2 ) )
                                                                                                               => ( ( binintersect @ X1 @ X2 )
                                                                                                                  = emptyset ) )
                                                                                                           => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                    ( ( subset @ X2 @ X1 )
                                                                                                                   => ( ( binintersect @ X1 @ X2 )
                                                                                                                      = X2 ) )
                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                      ( ( ( binintersect @ X1 @ X2 )
                                                                                                                        = X1 )
                                                                                                                     => ( subset @ X1 @ X2 ) )
                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                        ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                                                                                        = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                         => ( ~ ( in @ X3 @ X2 )
                                                                                                                           => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                            ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                           => ( in @ X3 @ X1 ) )
                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                              ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                             => ~ ( in @ X3 @ X2 ) )
                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                ( ( subset @ X1 @ X2 )
                                                                                                                               => ( ( setminus @ X1 @ X2 )
                                                                                                                                  = emptyset ) )
                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                  ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                 => ( ( in @ X3 @ X1 )
                                                                                                                                   => ( in @ X3 @ X2 ) ) )
                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                    ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                   => ( ~ ( in @ X3 @ X2 )
                                                                                                                                     => ~ ( in @ X3 @ X1 ) ) )
                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                      ( ~ ( in @ X3 @ X1 )
                                                                                                                                     => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                        ( ( in @ X3 @ X2 )
                                                                                                                                       => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                            ( ( ( setminus @ X1 @ X2 )
                                                                                                                                              = emptyset )
                                                                                                                                           => ( subset @ X1 @ X2 ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                              ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                                                                             => ! [X4: $o] :
                                                                                                                                                  ( ( ( in @ X3 @ X1 )
                                                                                                                                                   => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                     => X4 ) )
                                                                                                                                                 => ( ( ~ ( in @ X3 @ X1 )
                                                                                                                                                     => ( ( in @ X3 @ X2 )
                                                                                                                                                       => X4 ) )
                                                                                                                                                   => X4 ) ) )
                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                               => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                 => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                  ( ~ ( in @ X3 @ X1 )
                                                                                                                                                 => ( ( in @ X3 @ X2 )
                                                                                                                                                   => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                   => ( ( in @ X3 @ X2 )
                                                                                                                                                     => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                      ( ~ ( in @ X3 @ X1 )
                                                                                                                                                     => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                       => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                 => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                   => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                     => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                       => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                         => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                  ( ( in @ X2 @ X1 )
                                                                                                                                                                 => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                    ( ( in @ X2 @ X1 )
                                                                                                                                                                   => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                     => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                        ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                       => ( ( X3 != X1 )
                                                                                                                                                                         => ( X3 = X2 ) ) )
                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                                                                             => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                                                                               => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                                                                 => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                                                                   => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                                                                     => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                                                                       => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                      ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                     => ~ ! [X4: $i] :
                                                                                                                                                                                            ( ( in @ X4 @ X1 )
                                                                                                                                                                                           => ! [X5: $i] :
                                                                                                                                                                                                ( ( in @ X5 @ X2 )
                                                                                                                                                                                               => ( X3
                                                                                                                                                                                                 != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                                                                                 => ( sP5
                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                          ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                                                                                         => ~ ! [X3: $i] :
                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                               => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                                                                                     => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                                                                                       => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                         => ( ! [X1: $i] :
                                                                                                                                                                                                ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                                                                                = X1 )
                                                                                                                                                                                           => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                  ( ! [X3: $i] :
                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                                                          ( ( in @ X4 @ X1 )
                                                                                                                                                                                                         => ( ( X2 @ X3 )
                                                                                                                                                                                                           => ( ( X2 @ X4 )
                                                                                                                                                                                                             => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                 => ( ~ ! [X3: $i] :
                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                         => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                   => ~ ! [X3: $i] :
                                                                                                                                                                                                          ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                         => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                           != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                             => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                    ( ~ ! [X3: $i] :
                                                                                                                                                                                                          ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                         => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                           != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                                                                                   => ~ ! [X3: $i] :
                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                         => ~ ( X2 @ X3 ) ) )
                                                                                                                                                                                               => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                     => ( ( X2 @ X3 )
                                                                                                                                                                                                       => ( ! [X4: $i] :
                                                                                                                                                                                                              ( ( in @ X4 @ X1 )
                                                                                                                                                                                                             => ( ( X2 @ X4 )
                                                                                                                                                                                                               => ( X4 = X3 ) ) )
                                                                                                                                                                                                         => ~ ! [X4: $i] :
                                                                                                                                                                                                                ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                               => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                 != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                        ( ! [X3: $i] :
                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                                                                ( ( in @ X4 @ X1 )
                                                                                                                                                                                                               => ( ( X2 @ X3 )
                                                                                                                                                                                                                 => ( ( X2 @ X4 )
                                                                                                                                                                                                                   => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                       => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                               => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                         => ~ ! [X3: $i] :
                                                                                                                                                                                                                ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                               => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                 != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                          ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                                                                            = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                         => ( X1 = X2 ) )
                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                            ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                           => ( X1 = X3 ) )
                                                                                                                                                                                                       => ( ! [X1: $i] :
                                                                                                                                                                                                              ( ( iskpair @ X1 )
                                                                                                                                                                                                             => ~ ! [X2: $i] :
                                                                                                                                                                                                                    ( ( in @ X2
                                                                                                                                                                                                                      @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                        @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                                                                                   => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                        @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                     != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                         => ( ! [X1: $i] :
                                                                                                                                                                                                                ( ~ ! [X2: $i] :
                                                                                                                                                                                                                      ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                     => ( X1
                                                                                                                                                                                                                       != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                               => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                  ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                  = X1 )
                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                    ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                   => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                      ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                        = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                     => ( X1 = X3 ) )
                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                        ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                          = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                       => ( X1 = X3 ) )
                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                          ( ( X1 = X2 )
                                                                                                                                                                                                                         => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                            = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                            ( ( X1 = X2 )
                                                                                                                                                                                                                           => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                              = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                              ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                             => ( ( X3 = X4 )
                                                                                                                                                                                                                               => ( X2 = X4 ) ) )
                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                  = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                                                                               => ( X1 = X2 ) )
                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                  ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                    = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                 => ( X2 = X4 ) )
                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                    ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                      = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                   => ( X2 = X4 ) )
                                                                                                                                                                                                                               => ( ! [X1: $i] :
                                                                                                                                                                                                                                      ( ( iskpair @ X1 )
                                                                                                                                                                                                                                     => ~ ! [X2: $i] :
                                                                                                                                                                                                                                            ( ( in @ X2
                                                                                                                                                                                                                                              @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                @ ^ [X3: $i] :
                                                                                                                                                                                                                                                    ( X1
                                                                                                                                                                                                                                                    = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                                                                           => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                @ ^ [X3: $i] :
                                                                                                                                                                                                                                                    ( X1
                                                                                                                                                                                                                                                    = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                                                                             != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                        ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                        = X2 )
                                                                                                                                                                                                                                   => ( sP8
                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                            ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                           => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                              ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                             => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                               => ( in @ X4 @ X2 ) )
                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                     => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                        = X3 ) ) )
                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                       => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                          = X4 ) ) )
                                                                                                                                                                                                                                               => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                    ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                   => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                                                                                      = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h98,assumption,
    ! [X1: $o] :
      ( X1
     => ( in @ emptyset @ ( prop2set @ X1 ) ) ),
    introduced(assumption,[]) ).

thf(h99,assumption,
    ~ ( ! [X1: $o] :
          ( X1
         => ( set2prop @ ( prop2set @ X1 ) ) )
     => ( ! [X1: $i > $o] :
            ( ~ ! [X2: $i] :
                  ~ ( X1 @ X2 )
           => ( ! [X2: $i,X3: $i] :
                  ( ( X1 @ X2 )
                 => ( ( X1 @ X3 )
                   => ( X2 = X3 ) ) )
             => ~ ! [X2: $i] :
                    ( ( X1 @ X2 )
                   => ~ ! [X3: $i] :
                          ( ( X1 @ X3 )
                         => ( X2 = X3 ) ) ) ) )
       => ( ! [X1: $i > $o] :
              ( ~ ! [X2: $i] :
                    ~ ! [X3: $i] :
                        ( ( X1 @ X3 )
                        = ( X3 = X2 ) )
             => ~ ! [X2: $i] :
                    ( ( X1 @ X2 )
                   => ~ ! [X3: $i] :
                          ( ( X1 @ X3 )
                         => ( X2 = X3 ) ) ) )
         => ( ! [X1: $i,X2: $i] :
                ( ( X1 = X2 )
               => ! [X3: $i,X4: $i] :
                    ( ( X3 = X4 )
                   => ( ( in @ X3 @ X1 )
                     => ( in @ X4 @ X2 ) ) ) )
           => ( ! [X1: $i,X2: $i] :
                  ( ( X1 = X2 )
                 => ! [X3: $i,X4: $i] :
                      ( ( X3 = X4 )
                     => ( ( in @ X3 @ X1 )
                        = ( in @ X4 @ X2 ) ) ) )
             => ( ! [X1: $i > $o] :
                    ( ~ ! [X2: $i] :
                          ( ( X1 @ X2 )
                         => ~ ! [X3: $i] :
                                ( ( X1 @ X3 )
                               => ( X2 = X3 ) ) )
                   => ! [X2: $i,X3: $i] :
                        ( ( X1 @ X2 )
                       => ( ( X1 @ X3 )
                         => ( X2 = X3 ) ) ) )
               => ( ! [X1: $i > $o,X2: $i > $o] :
                      ( ! [X3: $i,X4: $i] :
                          ( ( X3 = X4 )
                         => ( ( X1 @ X3 )
                            = ( X2 @ X4 ) ) )
                     => ( ( ~ ! [X3: $i] :
                                ( ( X1 @ X3 )
                               => ~ ! [X4: $i] :
                                      ( ( X1 @ X4 )
                                     => ( X3 = X4 ) ) ) )
                        = ( ~ ! [X3: $i] :
                                ( ( X2 @ X3 )
                               => ~ ! [X4: $i] :
                                      ( ( X2 @ X4 )
                                     => ( X3 = X4 ) ) ) ) ) )
                 => ( ! [X1: $i,X2: $i] :
                        ( ( X1 = X2 )
                       => ! [X3: $i,X4: $i] :
                            ( ( X3 = X4 )
                           => ( ( setadjoin @ X1 @ X3 )
                              = ( setadjoin @ X2 @ X4 ) ) ) )
                   => ( ! [X1: $i,X2: $i] :
                          ( ( X1 = X2 )
                         => ( ( powerset @ X1 )
                            = ( powerset @ X2 ) ) )
                     => ( ! [X1: $i,X2: $i] :
                            ( ( X1 = X2 )
                           => ( ( setunion @ X1 )
                              = ( setunion @ X2 ) ) )
                       => ( ! [X1: $i > $o] :
                              ( ~ ! [X2: $i] :
                                    ( ( X1 @ X2 )
                                   => ~ ! [X3: $i] :
                                          ( ( X1 @ X3 )
                                         => ( X2 = X3 ) ) )
                             => ! [X2: $i,X3: $i] :
                                  ( ( X1 @ X2 )
                                 => ( ( X1 @ X3 )
                                   => ( X2 = X3 ) ) ) )
                         => ( ! [X1: $i > $o,X2: $i > $o] :
                                ( ! [X3: $i,X4: $i] :
                                    ( ( X3 = X4 )
                                   => ( ( X1 @ X3 )
                                      = ( X2 @ X4 ) ) )
                               => ( ~ ! [X3: $i] :
                                        ( ( X1 @ X3 )
                                       => ~ ! [X4: $i] :
                                              ( ( X1 @ X4 )
                                             => ( X3 = X4 ) ) )
                                 => ( ~ ! [X3: $i] :
                                          ( ( X2 @ X3 )
                                         => ~ ! [X4: $i] :
                                                ( ( X2 @ X4 )
                                               => ( X3 = X4 ) ) )
                                   => ( ( descr @ X1 )
                                      = ( descr @ X2 ) ) ) ) )
                           => ( ! [X1: $i,X2: $i] :
                                  ( ( X1 = X2 )
                                 => ! [X3: $i > $o,X4: $i > $o] :
                                      ( ! [X5: $i] :
                                          ( ( in @ X5 @ X1 )
                                         => ! [X6: $i] :
                                              ( ( in @ X6 @ X2 )
                                             => ( ( X5 = X6 )
                                               => ( ( X3 @ X5 )
                                                  = ( X4 @ X6 ) ) ) ) )
                                     => ( ( dsetconstr @ X1 @ X3 )
                                        = ( dsetconstr @ X2 @ X4 ) ) ) )
                             => ( ! [X1: $i,X2: $i] :
                                    ( ! [X3: $i] :
                                        ( ( in @ X3 @ X1 )
                                       => ( in @ X3 @ X2 ) )
                                   => ( subset @ X1 @ X2 ) )
                               => ( ! [X1: $i,X2: $i] :
                                      ( ( X1 = X2 )
                                     => ( subset @ X2 @ X1 ) )
                                 => ( ! [X1: $i,X2: $i] :
                                        ( ( X1 = X2 )
                                       => ( subset @ X1 @ X2 ) )
                                   => ( ! [X1: $i,X2: $i] :
                                          ( ! [X3: $i] :
                                              ( ( in @ X3 @ X1 )
                                             => ( in @ X3 @ X2 ) )
                                         => ( subset @ X1 @ X2 ) )
                                     => ( ! [X1: $i] : ( subset @ emptyset @ X1 )
                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                              ( ( subset @ X1 @ X2 )
                                             => ( ( in @ X3 @ X1 )
                                               => ( in @ X3 @ X2 ) ) )
                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                ( ( subset @ X1 @ X2 )
                                               => ( ~ ( in @ X3 @ X2 )
                                                 => ~ ( in @ X3 @ X1 ) ) )
                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                  ( ( in @ X3 @ X1 )
                                                 => ( ~ ( in @ X3 @ X2 )
                                                   => ~ ( subset @ X1 @ X2 ) ) )
                                             => ( ! [X1: $i,X2: $i] :
                                                    ( ~ ( subset @ X1 @ X2 )
                                                   => ( X1 != X2 ) )
                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                      ( ( in @ X3 @ X1 )
                                                     => ( ~ ( in @ X3 @ X2 )
                                                       => ( X1 != X2 ) ) )
                                                 => ( ! [X1: $i] : ( subset @ X1 @ X1 )
                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                          ( ( subset @ X1 @ X2 )
                                                         => ( ( subset @ X2 @ X3 )
                                                           => ( subset @ X1 @ X3 ) ) )
                                                     => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) )
                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                              ( ( subset @ X1 @ X3 )
                                                             => ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
                                                         => ( ! [X1: $i,X2: $i] :
                                                                ( ( subset @ X1 @ X2 )
                                                               => ( in @ X1 @ ( powerset @ X2 ) ) )
                                                           => ( ! [X1: $i,X2: $i] :
                                                                  ( ( subset @ X1 @ X2 )
                                                                 => ( ( subset @ X2 @ X1 )
                                                                   => ( X1 = X2 ) ) )
                                                             => ( ! [X1: $i] :
                                                                    ( ( subset @ X1 @ emptyset )
                                                                   => ( X1 = emptyset ) )
                                                               => ( ! [X1: $i,X2: $i] :
                                                                      ( ( subset @ X2 @ X1 )
                                                                     => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                                 => ( ! [X1: $i,X2: $i] :
                                                                        ( ( in @ X2 @ ( powerset @ X1 ) )
                                                                       => ( subset @ X2 @ X1 ) )
                                                                   => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
                                                                     => ( ! [X1: $i,X2: $i] :
                                                                            ( ( subset @ X1 @ X2 )
                                                                           => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
                                                                       => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                                                                         => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                  ( ( in @ X3 @ X1 )
                                                                                 => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                             => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                      ( ( in @ X3 @ X2 )
                                                                                     => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                                                                        ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                       => ( ( ( in @ X3 @ X1 )
                                                                                           => X4 )
                                                                                         => ( ( ( in @ X3 @ X2 )
                                                                                             => X4 )
                                                                                           => X4 ) ) )
                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                          ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                         => ( ~ ( in @ X3 @ X1 )
                                                                                           => ( in @ X3 @ X2 ) ) )
                                                                                     => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                                                                                       => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                ( ( in @ X3 @ X1 )
                                                                                               => ( ( in @ X3 @ X2 )
                                                                                                 => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                  ( ( subset @ X3 @ X1 )
                                                                                                 => ( ( subset @ X3 @ X2 )
                                                                                                   => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                    ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                   => ( in @ X3 @ X1 ) )
                                                                                               => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                        ( ( subset @ X1 @ X2 )
                                                                                                       => ( ( binintersect @ X1 @ X2 )
                                                                                                          = X1 ) )
                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                          ( ( ( binintersect @ X1 @ X2 )
                                                                                                            = X2 )
                                                                                                         => ( subset @ X2 @ X1 ) )
                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                            ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                           => ( in @ X3 @ X2 ) )
                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                              ( ! [X3: $i] :
                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                 => ~ ( in @ X3 @ X2 ) )
                                                                                                             => ( ( binintersect @ X1 @ X2 )
                                                                                                                = emptyset ) )
                                                                                                         => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                  ( ( subset @ X2 @ X1 )
                                                                                                                 => ( ( binintersect @ X1 @ X2 )
                                                                                                                    = X2 ) )
                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                    ( ( ( binintersect @ X1 @ X2 )
                                                                                                                      = X1 )
                                                                                                                   => ( subset @ X1 @ X2 ) )
                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                      ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                                                                                      = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                       => ( ~ ( in @ X3 @ X2 )
                                                                                                                         => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                          ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                         => ( in @ X3 @ X1 ) )
                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                            ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                           => ~ ( in @ X3 @ X2 ) )
                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                              ( ( subset @ X1 @ X2 )
                                                                                                                             => ( ( setminus @ X1 @ X2 )
                                                                                                                                = emptyset ) )
                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                               => ( ( in @ X3 @ X1 )
                                                                                                                                 => ( in @ X3 @ X2 ) ) )
                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                  ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                 => ( ~ ( in @ X3 @ X2 )
                                                                                                                                   => ~ ( in @ X3 @ X1 ) ) )
                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                    ( ~ ( in @ X3 @ X1 )
                                                                                                                                   => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                      ( ( in @ X3 @ X2 )
                                                                                                                                     => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                          ( ( ( setminus @ X1 @ X2 )
                                                                                                                                            = emptyset )
                                                                                                                                         => ( subset @ X1 @ X2 ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                            ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                                                                           => ! [X4: $o] :
                                                                                                                                                ( ( ( in @ X3 @ X1 )
                                                                                                                                                 => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                   => X4 ) )
                                                                                                                                               => ( ( ~ ( in @ X3 @ X1 )
                                                                                                                                                   => ( ( in @ X3 @ X2 )
                                                                                                                                                     => X4 ) )
                                                                                                                                                 => X4 ) ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                             => ( ~ ( in @ X3 @ X2 )
                                                                                                                                               => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                ( ~ ( in @ X3 @ X1 )
                                                                                                                                               => ( ( in @ X3 @ X2 )
                                                                                                                                                 => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                 => ( ( in @ X3 @ X2 )
                                                                                                                                                   => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                    ( ~ ( in @ X3 @ X1 )
                                                                                                                                                   => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                     => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                               => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                 => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                   => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                     => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                       => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                ( ( in @ X2 @ X1 )
                                                                                                                                                               => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                  ( ( in @ X2 @ X1 )
                                                                                                                                                                 => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                   => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                      ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                     => ( ( X3 != X1 )
                                                                                                                                                                       => ( X3 = X2 ) ) )
                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                                                           => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                                                                             => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                                                                               => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                                                                 => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                                                                   => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                                                                     => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                    ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                   => ~ ! [X4: $i] :
                                                                                                                                                                                          ( ( in @ X4 @ X1 )
                                                                                                                                                                                         => ! [X5: $i] :
                                                                                                                                                                                              ( ( in @ X5 @ X2 )
                                                                                                                                                                                             => ( X3
                                                                                                                                                                                               != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                                                                               => ( sP5
                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                        ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                                                                                       => ~ ! [X3: $i] :
                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                             => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                                                                                   => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                                                                                     => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                       => ( ! [X1: $i] :
                                                                                                                                                                                              ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                                                                              = X1 )
                                                                                                                                                                                         => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                ( ! [X3: $i] :
                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                                                        ( ( in @ X4 @ X1 )
                                                                                                                                                                                                       => ( ( X2 @ X3 )
                                                                                                                                                                                                         => ( ( X2 @ X4 )
                                                                                                                                                                                                           => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                               => ( ~ ! [X3: $i] :
                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                       => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                 => ~ ! [X3: $i] :
                                                                                                                                                                                                        ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                       => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                         != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                           => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                  ( ~ ! [X3: $i] :
                                                                                                                                                                                                        ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                       => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                         != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                                                                                 => ~ ! [X3: $i] :
                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                       => ~ ( X2 @ X3 ) ) )
                                                                                                                                                                                             => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                   => ( ( X2 @ X3 )
                                                                                                                                                                                                     => ( ! [X4: $i] :
                                                                                                                                                                                                            ( ( in @ X4 @ X1 )
                                                                                                                                                                                                           => ( ( X2 @ X4 )
                                                                                                                                                                                                             => ( X4 = X3 ) ) )
                                                                                                                                                                                                       => ~ ! [X4: $i] :
                                                                                                                                                                                                              ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                             => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                               != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                                                                               => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                      ( ! [X3: $i] :
                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                                                              ( ( in @ X4 @ X1 )
                                                                                                                                                                                                             => ( ( X2 @ X3 )
                                                                                                                                                                                                               => ( ( X2 @ X4 )
                                                                                                                                                                                                                 => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                     => ( ~ ! [X3: $i] :
                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                             => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                       => ~ ! [X3: $i] :
                                                                                                                                                                                                              ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                             => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                               != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                        ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                                                                          = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                       => ( X1 = X2 ) )
                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                          ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                         => ( X1 = X3 ) )
                                                                                                                                                                                                     => ( ! [X1: $i] :
                                                                                                                                                                                                            ( ( iskpair @ X1 )
                                                                                                                                                                                                           => ~ ! [X2: $i] :
                                                                                                                                                                                                                  ( ( in @ X2
                                                                                                                                                                                                                    @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                      @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                                                                                 => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                      @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                   != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                       => ( ! [X1: $i] :
                                                                                                                                                                                                              ( ~ ! [X2: $i] :
                                                                                                                                                                                                                    ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                   => ( X1
                                                                                                                                                                                                                     != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                             => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                = X1 )
                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                  ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                 => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                    ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                      = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                   => ( X1 = X3 ) )
                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                      ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                        = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                     => ( X1 = X3 ) )
                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                        ( ( X1 = X2 )
                                                                                                                                                                                                                       => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                          = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                          ( ( X1 = X2 )
                                                                                                                                                                                                                         => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                            = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                            ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                              = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                           => ( ( X3 = X4 )
                                                                                                                                                                                                                             => ( X2 = X4 ) ) )
                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                              ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                                                                             => ( X1 = X2 ) )
                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                  = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                               => ( X2 = X4 ) )
                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                  ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                    = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                 => ( X2 = X4 ) )
                                                                                                                                                                                                                             => ( ! [X1: $i] :
                                                                                                                                                                                                                                    ( ( iskpair @ X1 )
                                                                                                                                                                                                                                   => ~ ! [X2: $i] :
                                                                                                                                                                                                                                          ( ( in @ X2
                                                                                                                                                                                                                                            @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                              @ ^ [X3: $i] :
                                                                                                                                                                                                                                                  ( X1
                                                                                                                                                                                                                                                  = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                                                                         => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                              @ ^ [X3: $i] :
                                                                                                                                                                                                                                                  ( X1
                                                                                                                                                                                                                                                  = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                                                                           != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                      ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                      = X2 )
                                                                                                                                                                                                                                 => ( sP8
                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                         => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                            ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                           => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                              ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                             => ( in @ X4 @ X2 ) )
                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                   => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                      = X3 ) ) )
                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                     => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                        = X4 ) ) )
                                                                                                                                                                                                                                             => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                  ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                 => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                                                                                    = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h100,assumption,
    ! [X1: $o] :
      ( X1
     => ( set2prop @ ( prop2set @ X1 ) ) ),
    introduced(assumption,[]) ).

thf(h101,assumption,
    ~ ( ! [X1: $i > $o] :
          ( ~ ! [X2: $i] :
                ~ ( X1 @ X2 )
         => ( ! [X2: $i,X3: $i] :
                ( ( X1 @ X2 )
               => ( ( X1 @ X3 )
                 => ( X2 = X3 ) ) )
           => ~ ! [X2: $i] :
                  ( ( X1 @ X2 )
                 => ~ ! [X3: $i] :
                        ( ( X1 @ X3 )
                       => ( X2 = X3 ) ) ) ) )
     => ( ! [X1: $i > $o] :
            ( ~ ! [X2: $i] :
                  ~ ! [X3: $i] :
                      ( ( X1 @ X3 )
                      = ( X3 = X2 ) )
           => ~ ! [X2: $i] :
                  ( ( X1 @ X2 )
                 => ~ ! [X3: $i] :
                        ( ( X1 @ X3 )
                       => ( X2 = X3 ) ) ) )
       => ( ! [X1: $i,X2: $i] :
              ( ( X1 = X2 )
             => ! [X3: $i,X4: $i] :
                  ( ( X3 = X4 )
                 => ( ( in @ X3 @ X1 )
                   => ( in @ X4 @ X2 ) ) ) )
         => ( ! [X1: $i,X2: $i] :
                ( ( X1 = X2 )
               => ! [X3: $i,X4: $i] :
                    ( ( X3 = X4 )
                   => ( ( in @ X3 @ X1 )
                      = ( in @ X4 @ X2 ) ) ) )
           => ( ! [X1: $i > $o] :
                  ( ~ ! [X2: $i] :
                        ( ( X1 @ X2 )
                       => ~ ! [X3: $i] :
                              ( ( X1 @ X3 )
                             => ( X2 = X3 ) ) )
                 => ! [X2: $i,X3: $i] :
                      ( ( X1 @ X2 )
                     => ( ( X1 @ X3 )
                       => ( X2 = X3 ) ) ) )
             => ( ! [X1: $i > $o,X2: $i > $o] :
                    ( ! [X3: $i,X4: $i] :
                        ( ( X3 = X4 )
                       => ( ( X1 @ X3 )
                          = ( X2 @ X4 ) ) )
                   => ( ( ~ ! [X3: $i] :
                              ( ( X1 @ X3 )
                             => ~ ! [X4: $i] :
                                    ( ( X1 @ X4 )
                                   => ( X3 = X4 ) ) ) )
                      = ( ~ ! [X3: $i] :
                              ( ( X2 @ X3 )
                             => ~ ! [X4: $i] :
                                    ( ( X2 @ X4 )
                                   => ( X3 = X4 ) ) ) ) ) )
               => ( ! [X1: $i,X2: $i] :
                      ( ( X1 = X2 )
                     => ! [X3: $i,X4: $i] :
                          ( ( X3 = X4 )
                         => ( ( setadjoin @ X1 @ X3 )
                            = ( setadjoin @ X2 @ X4 ) ) ) )
                 => ( ! [X1: $i,X2: $i] :
                        ( ( X1 = X2 )
                       => ( ( powerset @ X1 )
                          = ( powerset @ X2 ) ) )
                   => ( ! [X1: $i,X2: $i] :
                          ( ( X1 = X2 )
                         => ( ( setunion @ X1 )
                            = ( setunion @ X2 ) ) )
                     => ( ! [X1: $i > $o] :
                            ( ~ ! [X2: $i] :
                                  ( ( X1 @ X2 )
                                 => ~ ! [X3: $i] :
                                        ( ( X1 @ X3 )
                                       => ( X2 = X3 ) ) )
                           => ! [X2: $i,X3: $i] :
                                ( ( X1 @ X2 )
                               => ( ( X1 @ X3 )
                                 => ( X2 = X3 ) ) ) )
                       => ( ! [X1: $i > $o,X2: $i > $o] :
                              ( ! [X3: $i,X4: $i] :
                                  ( ( X3 = X4 )
                                 => ( ( X1 @ X3 )
                                    = ( X2 @ X4 ) ) )
                             => ( ~ ! [X3: $i] :
                                      ( ( X1 @ X3 )
                                     => ~ ! [X4: $i] :
                                            ( ( X1 @ X4 )
                                           => ( X3 = X4 ) ) )
                               => ( ~ ! [X3: $i] :
                                        ( ( X2 @ X3 )
                                       => ~ ! [X4: $i] :
                                              ( ( X2 @ X4 )
                                             => ( X3 = X4 ) ) )
                                 => ( ( descr @ X1 )
                                    = ( descr @ X2 ) ) ) ) )
                         => ( ! [X1: $i,X2: $i] :
                                ( ( X1 = X2 )
                               => ! [X3: $i > $o,X4: $i > $o] :
                                    ( ! [X5: $i] :
                                        ( ( in @ X5 @ X1 )
                                       => ! [X6: $i] :
                                            ( ( in @ X6 @ X2 )
                                           => ( ( X5 = X6 )
                                             => ( ( X3 @ X5 )
                                                = ( X4 @ X6 ) ) ) ) )
                                   => ( ( dsetconstr @ X1 @ X3 )
                                      = ( dsetconstr @ X2 @ X4 ) ) ) )
                           => ( ! [X1: $i,X2: $i] :
                                  ( ! [X3: $i] :
                                      ( ( in @ X3 @ X1 )
                                     => ( in @ X3 @ X2 ) )
                                 => ( subset @ X1 @ X2 ) )
                             => ( ! [X1: $i,X2: $i] :
                                    ( ( X1 = X2 )
                                   => ( subset @ X2 @ X1 ) )
                               => ( ! [X1: $i,X2: $i] :
                                      ( ( X1 = X2 )
                                     => ( subset @ X1 @ X2 ) )
                                 => ( ! [X1: $i,X2: $i] :
                                        ( ! [X3: $i] :
                                            ( ( in @ X3 @ X1 )
                                           => ( in @ X3 @ X2 ) )
                                       => ( subset @ X1 @ X2 ) )
                                   => ( ! [X1: $i] : ( subset @ emptyset @ X1 )
                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                            ( ( subset @ X1 @ X2 )
                                           => ( ( in @ X3 @ X1 )
                                             => ( in @ X3 @ X2 ) ) )
                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                              ( ( subset @ X1 @ X2 )
                                             => ( ~ ( in @ X3 @ X2 )
                                               => ~ ( in @ X3 @ X1 ) ) )
                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                ( ( in @ X3 @ X1 )
                                               => ( ~ ( in @ X3 @ X2 )
                                                 => ~ ( subset @ X1 @ X2 ) ) )
                                           => ( ! [X1: $i,X2: $i] :
                                                  ( ~ ( subset @ X1 @ X2 )
                                                 => ( X1 != X2 ) )
                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                    ( ( in @ X3 @ X1 )
                                                   => ( ~ ( in @ X3 @ X2 )
                                                     => ( X1 != X2 ) ) )
                                               => ( ! [X1: $i] : ( subset @ X1 @ X1 )
                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                        ( ( subset @ X1 @ X2 )
                                                       => ( ( subset @ X2 @ X3 )
                                                         => ( subset @ X1 @ X3 ) ) )
                                                   => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) )
                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                            ( ( subset @ X1 @ X3 )
                                                           => ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
                                                       => ( ! [X1: $i,X2: $i] :
                                                              ( ( subset @ X1 @ X2 )
                                                             => ( in @ X1 @ ( powerset @ X2 ) ) )
                                                         => ( ! [X1: $i,X2: $i] :
                                                                ( ( subset @ X1 @ X2 )
                                                               => ( ( subset @ X2 @ X1 )
                                                                 => ( X1 = X2 ) ) )
                                                           => ( ! [X1: $i] :
                                                                  ( ( subset @ X1 @ emptyset )
                                                                 => ( X1 = emptyset ) )
                                                             => ( ! [X1: $i,X2: $i] :
                                                                    ( ( subset @ X2 @ X1 )
                                                                   => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                               => ( ! [X1: $i,X2: $i] :
                                                                      ( ( in @ X2 @ ( powerset @ X1 ) )
                                                                     => ( subset @ X2 @ X1 ) )
                                                                 => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
                                                                   => ( ! [X1: $i,X2: $i] :
                                                                          ( ( subset @ X1 @ X2 )
                                                                         => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
                                                                     => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                                                                       => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                ( ( in @ X3 @ X1 )
                                                                               => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                           => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                    ( ( in @ X3 @ X2 )
                                                                                   => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                                                                      ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                     => ( ( ( in @ X3 @ X1 )
                                                                                         => X4 )
                                                                                       => ( ( ( in @ X3 @ X2 )
                                                                                           => X4 )
                                                                                         => X4 ) ) )
                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                        ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                       => ( ~ ( in @ X3 @ X1 )
                                                                                         => ( in @ X3 @ X2 ) ) )
                                                                                   => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                                                                                     => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                              ( ( in @ X3 @ X1 )
                                                                                             => ( ( in @ X3 @ X2 )
                                                                                               => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                ( ( subset @ X3 @ X1 )
                                                                                               => ( ( subset @ X3 @ X2 )
                                                                                                 => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                  ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                 => ( in @ X3 @ X1 ) )
                                                                                             => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                      ( ( subset @ X1 @ X2 )
                                                                                                     => ( ( binintersect @ X1 @ X2 )
                                                                                                        = X1 ) )
                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                        ( ( ( binintersect @ X1 @ X2 )
                                                                                                          = X2 )
                                                                                                       => ( subset @ X2 @ X1 ) )
                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                          ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                         => ( in @ X3 @ X2 ) )
                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                            ( ! [X3: $i] :
                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                               => ~ ( in @ X3 @ X2 ) )
                                                                                                           => ( ( binintersect @ X1 @ X2 )
                                                                                                              = emptyset ) )
                                                                                                       => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                ( ( subset @ X2 @ X1 )
                                                                                                               => ( ( binintersect @ X1 @ X2 )
                                                                                                                  = X2 ) )
                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                  ( ( ( binintersect @ X1 @ X2 )
                                                                                                                    = X1 )
                                                                                                                 => ( subset @ X1 @ X2 ) )
                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                    ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                                                                                    = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                     => ( ~ ( in @ X3 @ X2 )
                                                                                                                       => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                        ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                       => ( in @ X3 @ X1 ) )
                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                          ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                         => ~ ( in @ X3 @ X2 ) )
                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                            ( ( subset @ X1 @ X2 )
                                                                                                                           => ( ( setminus @ X1 @ X2 )
                                                                                                                              = emptyset ) )
                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                              ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                             => ( ( in @ X3 @ X1 )
                                                                                                                               => ( in @ X3 @ X2 ) ) )
                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                               => ( ~ ( in @ X3 @ X2 )
                                                                                                                                 => ~ ( in @ X3 @ X1 ) ) )
                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                  ( ~ ( in @ X3 @ X1 )
                                                                                                                                 => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                    ( ( in @ X3 @ X2 )
                                                                                                                                   => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                               => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                        ( ( ( setminus @ X1 @ X2 )
                                                                                                                                          = emptyset )
                                                                                                                                       => ( subset @ X1 @ X2 ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                          ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                                                                         => ! [X4: $o] :
                                                                                                                                              ( ( ( in @ X3 @ X1 )
                                                                                                                                               => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                 => X4 ) )
                                                                                                                                             => ( ( ~ ( in @ X3 @ X1 )
                                                                                                                                                 => ( ( in @ X3 @ X2 )
                                                                                                                                                   => X4 ) )
                                                                                                                                               => X4 ) ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                           => ( ~ ( in @ X3 @ X2 )
                                                                                                                                             => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                              ( ~ ( in @ X3 @ X1 )
                                                                                                                                             => ( ( in @ X3 @ X2 )
                                                                                                                                               => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                               => ( ( in @ X3 @ X2 )
                                                                                                                                                 => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                  ( ~ ( in @ X3 @ X1 )
                                                                                                                                                 => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                   => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                             => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                               => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                 => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                   => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                     => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                              ( ( in @ X2 @ X1 )
                                                                                                                                                             => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                ( ( in @ X2 @ X1 )
                                                                                                                                                               => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                 => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                    ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                   => ( ( X3 != X1 )
                                                                                                                                                                     => ( X3 = X2 ) ) )
                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                                                         => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                                                           => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                                                                             => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                                                                               => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                                                                 => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                                                                   => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                  ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                 => ~ ! [X4: $i] :
                                                                                                                                                                                        ( ( in @ X4 @ X1 )
                                                                                                                                                                                       => ! [X5: $i] :
                                                                                                                                                                                            ( ( in @ X5 @ X2 )
                                                                                                                                                                                           => ( X3
                                                                                                                                                                                             != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                                                                             => ( sP5
                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                      ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                                                                                     => ~ ! [X3: $i] :
                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                           => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                                                                                 => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                                                                                   => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                     => ( ! [X1: $i] :
                                                                                                                                                                                            ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                                                                            = X1 )
                                                                                                                                                                                       => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                              ( ! [X3: $i] :
                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                                                      ( ( in @ X4 @ X1 )
                                                                                                                                                                                                     => ( ( X2 @ X3 )
                                                                                                                                                                                                       => ( ( X2 @ X4 )
                                                                                                                                                                                                         => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                             => ( ~ ! [X3: $i] :
                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                     => ~ ( X2 @ X3 ) )
                                                                                                                                                                                               => ~ ! [X3: $i] :
                                                                                                                                                                                                      ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                     => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                       != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                         => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                ( ~ ! [X3: $i] :
                                                                                                                                                                                                      ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                     => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                       != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                                                                               => ~ ! [X3: $i] :
                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                     => ~ ( X2 @ X3 ) ) )
                                                                                                                                                                                           => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                 => ( ( X2 @ X3 )
                                                                                                                                                                                                   => ( ! [X4: $i] :
                                                                                                                                                                                                          ( ( in @ X4 @ X1 )
                                                                                                                                                                                                         => ( ( X2 @ X4 )
                                                                                                                                                                                                           => ( X4 = X3 ) ) )
                                                                                                                                                                                                     => ~ ! [X4: $i] :
                                                                                                                                                                                                            ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                           => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                             != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                                                                             => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                    ( ! [X3: $i] :
                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                                                            ( ( in @ X4 @ X1 )
                                                                                                                                                                                                           => ( ( X2 @ X3 )
                                                                                                                                                                                                             => ( ( X2 @ X4 )
                                                                                                                                                                                                               => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                   => ( ~ ! [X3: $i] :
                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                           => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                     => ~ ! [X3: $i] :
                                                                                                                                                                                                            ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                           => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                             != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                      ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                                                                        = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                     => ( X1 = X2 ) )
                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                        ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                       => ( X1 = X3 ) )
                                                                                                                                                                                                   => ( ! [X1: $i] :
                                                                                                                                                                                                          ( ( iskpair @ X1 )
                                                                                                                                                                                                         => ~ ! [X2: $i] :
                                                                                                                                                                                                                ( ( in @ X2
                                                                                                                                                                                                                  @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                    @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                                                                               => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                    @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                 != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                     => ( ! [X1: $i] :
                                                                                                                                                                                                            ( ~ ! [X2: $i] :
                                                                                                                                                                                                                  ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                 => ( X1
                                                                                                                                                                                                                   != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                           => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                              ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                              = X1 )
                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                               => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                  ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                    = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                 => ( X1 = X3 ) )
                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                    ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                      = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                   => ( X1 = X3 ) )
                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                      ( ( X1 = X2 )
                                                                                                                                                                                                                     => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                        = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                        ( ( X1 = X2 )
                                                                                                                                                                                                                       => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                          = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                          ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                            = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                         => ( ( X3 = X4 )
                                                                                                                                                                                                                           => ( X2 = X4 ) ) )
                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                            ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                              = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                                                                           => ( X1 = X2 ) )
                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                              ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                             => ( X2 = X4 ) )
                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                  = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                               => ( X2 = X4 ) )
                                                                                                                                                                                                                           => ( ! [X1: $i] :
                                                                                                                                                                                                                                  ( ( iskpair @ X1 )
                                                                                                                                                                                                                                 => ~ ! [X2: $i] :
                                                                                                                                                                                                                                        ( ( in @ X2
                                                                                                                                                                                                                                          @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                            @ ^ [X3: $i] :
                                                                                                                                                                                                                                                ( X1
                                                                                                                                                                                                                                                = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                                                                       => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                            @ ^ [X3: $i] :
                                                                                                                                                                                                                                                ( X1
                                                                                                                                                                                                                                                = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                                                                         != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                    ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                    = X2 )
                                                                                                                                                                                                                               => ( sP8
                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                       => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                          ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                         => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                            ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                           => ( in @ X4 @ X2 ) )
                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                 => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                    = X3 ) ) )
                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                   => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                      = X4 ) ) )
                                                                                                                                                                                                                                           => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                               => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                                                                                  = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h102,assumption,
    ! [X1: $i > $o] :
      ( ~ ! [X2: $i] :
            ~ ( X1 @ X2 )
     => ( ! [X2: $i,X3: $i] :
            ( ( X1 @ X2 )
           => ( ( X1 @ X3 )
             => ( X2 = X3 ) ) )
       => ~ ! [X2: $i] :
              ( ( X1 @ X2 )
             => ~ ! [X3: $i] :
                    ( ( X1 @ X3 )
                   => ( X2 = X3 ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h103,assumption,
    ~ ( ! [X1: $i > $o] :
          ( ~ ! [X2: $i] :
                ~ ! [X3: $i] :
                    ( ( X1 @ X3 )
                    = ( X3 = X2 ) )
         => ~ ! [X2: $i] :
                ( ( X1 @ X2 )
               => ~ ! [X3: $i] :
                      ( ( X1 @ X3 )
                     => ( X2 = X3 ) ) ) )
     => ( ! [X1: $i,X2: $i] :
            ( ( X1 = X2 )
           => ! [X3: $i,X4: $i] :
                ( ( X3 = X4 )
               => ( ( in @ X3 @ X1 )
                 => ( in @ X4 @ X2 ) ) ) )
       => ( ! [X1: $i,X2: $i] :
              ( ( X1 = X2 )
             => ! [X3: $i,X4: $i] :
                  ( ( X3 = X4 )
                 => ( ( in @ X3 @ X1 )
                    = ( in @ X4 @ X2 ) ) ) )
         => ( ! [X1: $i > $o] :
                ( ~ ! [X2: $i] :
                      ( ( X1 @ X2 )
                     => ~ ! [X3: $i] :
                            ( ( X1 @ X3 )
                           => ( X2 = X3 ) ) )
               => ! [X2: $i,X3: $i] :
                    ( ( X1 @ X2 )
                   => ( ( X1 @ X3 )
                     => ( X2 = X3 ) ) ) )
           => ( ! [X1: $i > $o,X2: $i > $o] :
                  ( ! [X3: $i,X4: $i] :
                      ( ( X3 = X4 )
                     => ( ( X1 @ X3 )
                        = ( X2 @ X4 ) ) )
                 => ( ( ~ ! [X3: $i] :
                            ( ( X1 @ X3 )
                           => ~ ! [X4: $i] :
                                  ( ( X1 @ X4 )
                                 => ( X3 = X4 ) ) ) )
                    = ( ~ ! [X3: $i] :
                            ( ( X2 @ X3 )
                           => ~ ! [X4: $i] :
                                  ( ( X2 @ X4 )
                                 => ( X3 = X4 ) ) ) ) ) )
             => ( ! [X1: $i,X2: $i] :
                    ( ( X1 = X2 )
                   => ! [X3: $i,X4: $i] :
                        ( ( X3 = X4 )
                       => ( ( setadjoin @ X1 @ X3 )
                          = ( setadjoin @ X2 @ X4 ) ) ) )
               => ( ! [X1: $i,X2: $i] :
                      ( ( X1 = X2 )
                     => ( ( powerset @ X1 )
                        = ( powerset @ X2 ) ) )
                 => ( ! [X1: $i,X2: $i] :
                        ( ( X1 = X2 )
                       => ( ( setunion @ X1 )
                          = ( setunion @ X2 ) ) )
                   => ( ! [X1: $i > $o] :
                          ( ~ ! [X2: $i] :
                                ( ( X1 @ X2 )
                               => ~ ! [X3: $i] :
                                      ( ( X1 @ X3 )
                                     => ( X2 = X3 ) ) )
                         => ! [X2: $i,X3: $i] :
                              ( ( X1 @ X2 )
                             => ( ( X1 @ X3 )
                               => ( X2 = X3 ) ) ) )
                     => ( ! [X1: $i > $o,X2: $i > $o] :
                            ( ! [X3: $i,X4: $i] :
                                ( ( X3 = X4 )
                               => ( ( X1 @ X3 )
                                  = ( X2 @ X4 ) ) )
                           => ( ~ ! [X3: $i] :
                                    ( ( X1 @ X3 )
                                   => ~ ! [X4: $i] :
                                          ( ( X1 @ X4 )
                                         => ( X3 = X4 ) ) )
                             => ( ~ ! [X3: $i] :
                                      ( ( X2 @ X3 )
                                     => ~ ! [X4: $i] :
                                            ( ( X2 @ X4 )
                                           => ( X3 = X4 ) ) )
                               => ( ( descr @ X1 )
                                  = ( descr @ X2 ) ) ) ) )
                       => ( ! [X1: $i,X2: $i] :
                              ( ( X1 = X2 )
                             => ! [X3: $i > $o,X4: $i > $o] :
                                  ( ! [X5: $i] :
                                      ( ( in @ X5 @ X1 )
                                     => ! [X6: $i] :
                                          ( ( in @ X6 @ X2 )
                                         => ( ( X5 = X6 )
                                           => ( ( X3 @ X5 )
                                              = ( X4 @ X6 ) ) ) ) )
                                 => ( ( dsetconstr @ X1 @ X3 )
                                    = ( dsetconstr @ X2 @ X4 ) ) ) )
                         => ( ! [X1: $i,X2: $i] :
                                ( ! [X3: $i] :
                                    ( ( in @ X3 @ X1 )
                                   => ( in @ X3 @ X2 ) )
                               => ( subset @ X1 @ X2 ) )
                           => ( ! [X1: $i,X2: $i] :
                                  ( ( X1 = X2 )
                                 => ( subset @ X2 @ X1 ) )
                             => ( ! [X1: $i,X2: $i] :
                                    ( ( X1 = X2 )
                                   => ( subset @ X1 @ X2 ) )
                               => ( ! [X1: $i,X2: $i] :
                                      ( ! [X3: $i] :
                                          ( ( in @ X3 @ X1 )
                                         => ( in @ X3 @ X2 ) )
                                     => ( subset @ X1 @ X2 ) )
                                 => ( ! [X1: $i] : ( subset @ emptyset @ X1 )
                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                          ( ( subset @ X1 @ X2 )
                                         => ( ( in @ X3 @ X1 )
                                           => ( in @ X3 @ X2 ) ) )
                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                            ( ( subset @ X1 @ X2 )
                                           => ( ~ ( in @ X3 @ X2 )
                                             => ~ ( in @ X3 @ X1 ) ) )
                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                              ( ( in @ X3 @ X1 )
                                             => ( ~ ( in @ X3 @ X2 )
                                               => ~ ( subset @ X1 @ X2 ) ) )
                                         => ( ! [X1: $i,X2: $i] :
                                                ( ~ ( subset @ X1 @ X2 )
                                               => ( X1 != X2 ) )
                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                  ( ( in @ X3 @ X1 )
                                                 => ( ~ ( in @ X3 @ X2 )
                                                   => ( X1 != X2 ) ) )
                                             => ( ! [X1: $i] : ( subset @ X1 @ X1 )
                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                      ( ( subset @ X1 @ X2 )
                                                     => ( ( subset @ X2 @ X3 )
                                                       => ( subset @ X1 @ X3 ) ) )
                                                 => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) )
                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                          ( ( subset @ X1 @ X3 )
                                                         => ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
                                                     => ( ! [X1: $i,X2: $i] :
                                                            ( ( subset @ X1 @ X2 )
                                                           => ( in @ X1 @ ( powerset @ X2 ) ) )
                                                       => ( ! [X1: $i,X2: $i] :
                                                              ( ( subset @ X1 @ X2 )
                                                             => ( ( subset @ X2 @ X1 )
                                                               => ( X1 = X2 ) ) )
                                                         => ( ! [X1: $i] :
                                                                ( ( subset @ X1 @ emptyset )
                                                               => ( X1 = emptyset ) )
                                                           => ( ! [X1: $i,X2: $i] :
                                                                  ( ( subset @ X2 @ X1 )
                                                                 => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                             => ( ! [X1: $i,X2: $i] :
                                                                    ( ( in @ X2 @ ( powerset @ X1 ) )
                                                                   => ( subset @ X2 @ X1 ) )
                                                               => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
                                                                 => ( ! [X1: $i,X2: $i] :
                                                                        ( ( subset @ X1 @ X2 )
                                                                       => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
                                                                   => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                                                                     => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                              ( ( in @ X3 @ X1 )
                                                                             => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                         => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                  ( ( in @ X3 @ X2 )
                                                                                 => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                                                                    ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                   => ( ( ( in @ X3 @ X1 )
                                                                                       => X4 )
                                                                                     => ( ( ( in @ X3 @ X2 )
                                                                                         => X4 )
                                                                                       => X4 ) ) )
                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                      ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                     => ( ~ ( in @ X3 @ X1 )
                                                                                       => ( in @ X3 @ X2 ) ) )
                                                                                 => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                                                                                   => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                            ( ( in @ X3 @ X1 )
                                                                                           => ( ( in @ X3 @ X2 )
                                                                                             => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                              ( ( subset @ X3 @ X1 )
                                                                                             => ( ( subset @ X3 @ X2 )
                                                                                               => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                               => ( in @ X3 @ X1 ) )
                                                                                           => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                    ( ( subset @ X1 @ X2 )
                                                                                                   => ( ( binintersect @ X1 @ X2 )
                                                                                                      = X1 ) )
                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                      ( ( ( binintersect @ X1 @ X2 )
                                                                                                        = X2 )
                                                                                                     => ( subset @ X2 @ X1 ) )
                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                        ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                       => ( in @ X3 @ X2 ) )
                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                          ( ! [X3: $i] :
                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                             => ~ ( in @ X3 @ X2 ) )
                                                                                                         => ( ( binintersect @ X1 @ X2 )
                                                                                                            = emptyset ) )
                                                                                                     => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                              ( ( subset @ X2 @ X1 )
                                                                                                             => ( ( binintersect @ X1 @ X2 )
                                                                                                                = X2 ) )
                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                ( ( ( binintersect @ X1 @ X2 )
                                                                                                                  = X1 )
                                                                                                               => ( subset @ X1 @ X2 ) )
                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                  ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                                                                                  = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                   => ( ~ ( in @ X3 @ X2 )
                                                                                                                     => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                      ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                     => ( in @ X3 @ X1 ) )
                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                        ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                       => ~ ( in @ X3 @ X2 ) )
                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                          ( ( subset @ X1 @ X2 )
                                                                                                                         => ( ( setminus @ X1 @ X2 )
                                                                                                                            = emptyset ) )
                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                            ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                           => ( ( in @ X3 @ X1 )
                                                                                                                             => ( in @ X3 @ X2 ) ) )
                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                              ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                             => ( ~ ( in @ X3 @ X2 )
                                                                                                                               => ~ ( in @ X3 @ X1 ) ) )
                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                ( ~ ( in @ X3 @ X1 )
                                                                                                                               => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                  ( ( in @ X3 @ X2 )
                                                                                                                                 => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                             => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                      ( ( ( setminus @ X1 @ X2 )
                                                                                                                                        = emptyset )
                                                                                                                                     => ( subset @ X1 @ X2 ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                        ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                                                                       => ! [X4: $o] :
                                                                                                                                            ( ( ( in @ X3 @ X1 )
                                                                                                                                             => ( ~ ( in @ X3 @ X2 )
                                                                                                                                               => X4 ) )
                                                                                                                                           => ( ( ~ ( in @ X3 @ X1 )
                                                                                                                                               => ( ( in @ X3 @ X2 )
                                                                                                                                                 => X4 ) )
                                                                                                                                             => X4 ) ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                         => ( ~ ( in @ X3 @ X2 )
                                                                                                                                           => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                            ( ~ ( in @ X3 @ X1 )
                                                                                                                                           => ( ( in @ X3 @ X2 )
                                                                                                                                             => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                             => ( ( in @ X3 @ X2 )
                                                                                                                                               => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                ( ~ ( in @ X3 @ X1 )
                                                                                                                                               => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                 => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                           => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                             => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                               => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                 => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                   => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                            ( ( in @ X2 @ X1 )
                                                                                                                                                           => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                              ( ( in @ X2 @ X1 )
                                                                                                                                                             => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                               => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                  ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                 => ( ( X3 != X1 )
                                                                                                                                                                   => ( X3 = X2 ) ) )
                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                                                       => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                                                         => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                                                           => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                                                                             => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                                                                               => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                                                                 => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                               => ~ ! [X4: $i] :
                                                                                                                                                                                      ( ( in @ X4 @ X1 )
                                                                                                                                                                                     => ! [X5: $i] :
                                                                                                                                                                                          ( ( in @ X5 @ X2 )
                                                                                                                                                                                         => ( X3
                                                                                                                                                                                           != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                                                                           => ( sP5
                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                    ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                                                                                   => ~ ! [X3: $i] :
                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                         => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                                                                               => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                                                                                 => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                   => ( ! [X1: $i] :
                                                                                                                                                                                          ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                                                                          = X1 )
                                                                                                                                                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                            ( ! [X3: $i] :
                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                                    ( ( in @ X4 @ X1 )
                                                                                                                                                                                                   => ( ( X2 @ X3 )
                                                                                                                                                                                                     => ( ( X2 @ X4 )
                                                                                                                                                                                                       => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                           => ( ~ ! [X3: $i] :
                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                   => ~ ( X2 @ X3 ) )
                                                                                                                                                                                             => ~ ! [X3: $i] :
                                                                                                                                                                                                    ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                   => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                     != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                       => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                              ( ~ ! [X3: $i] :
                                                                                                                                                                                                    ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                   => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                     != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                                                                             => ~ ! [X3: $i] :
                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                   => ~ ( X2 @ X3 ) ) )
                                                                                                                                                                                         => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                               => ( ( X2 @ X3 )
                                                                                                                                                                                                 => ( ! [X4: $i] :
                                                                                                                                                                                                        ( ( in @ X4 @ X1 )
                                                                                                                                                                                                       => ( ( X2 @ X4 )
                                                                                                                                                                                                         => ( X4 = X3 ) ) )
                                                                                                                                                                                                   => ~ ! [X4: $i] :
                                                                                                                                                                                                          ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                         => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                           != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                                                                           => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                  ( ! [X3: $i] :
                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                                                          ( ( in @ X4 @ X1 )
                                                                                                                                                                                                         => ( ( X2 @ X3 )
                                                                                                                                                                                                           => ( ( X2 @ X4 )
                                                                                                                                                                                                             => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                 => ( ~ ! [X3: $i] :
                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                         => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                   => ~ ! [X3: $i] :
                                                                                                                                                                                                          ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                         => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                           != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                    ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                                                                      = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                   => ( X1 = X2 ) )
                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                      ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                     => ( X1 = X3 ) )
                                                                                                                                                                                                 => ( ! [X1: $i] :
                                                                                                                                                                                                        ( ( iskpair @ X1 )
                                                                                                                                                                                                       => ~ ! [X2: $i] :
                                                                                                                                                                                                              ( ( in @ X2
                                                                                                                                                                                                                @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                  @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                                                                             => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                  @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                               != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                   => ( ! [X1: $i] :
                                                                                                                                                                                                          ( ~ ! [X2: $i] :
                                                                                                                                                                                                                ( ( in @ X2 @ X1 )
                                                                                                                                                                                                               => ( X1
                                                                                                                                                                                                                 != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                         => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                            ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                            = X1 )
                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                              ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                             => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                  = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                               => ( X1 = X3 ) )
                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                  ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                    = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                 => ( X1 = X3 ) )
                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                    ( ( X1 = X2 )
                                                                                                                                                                                                                   => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                      = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                      ( ( X1 = X2 )
                                                                                                                                                                                                                     => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                        = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                        ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                          = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                       => ( ( X3 = X4 )
                                                                                                                                                                                                                         => ( X2 = X4 ) ) )
                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                          ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                            = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                                                                         => ( X1 = X2 ) )
                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                            ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                              = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                           => ( X2 = X4 ) )
                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                              ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                             => ( X2 = X4 ) )
                                                                                                                                                                                                                         => ( ! [X1: $i] :
                                                                                                                                                                                                                                ( ( iskpair @ X1 )
                                                                                                                                                                                                                               => ~ ! [X2: $i] :
                                                                                                                                                                                                                                      ( ( in @ X2
                                                                                                                                                                                                                                        @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                          @ ^ [X3: $i] :
                                                                                                                                                                                                                                              ( X1
                                                                                                                                                                                                                                              = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                                                                     => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                          @ ^ [X3: $i] :
                                                                                                                                                                                                                                              ( X1
                                                                                                                                                                                                                                              = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                                                                       != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                  ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                  = X2 )
                                                                                                                                                                                                                             => ( sP8
                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                      ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                     => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                        ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                       => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                          ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                         => ( in @ X4 @ X2 ) )
                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                               => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                  = X3 ) ) )
                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                 => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                    = X4 ) ) )
                                                                                                                                                                                                                                         => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                              ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                             => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                                                                                = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h104,assumption,
    ! [X1: $i > $o] :
      ( ~ ! [X2: $i] :
            ~ ! [X3: $i] :
                ( ( X1 @ X3 )
                = ( X3 = X2 ) )
     => ~ ! [X2: $i] :
            ( ( X1 @ X2 )
           => ~ ! [X3: $i] :
                  ( ( X1 @ X3 )
                 => ( X2 = X3 ) ) ) ),
    introduced(assumption,[]) ).

thf(h105,assumption,
    ~ ( ! [X1: $i,X2: $i] :
          ( ( X1 = X2 )
         => ! [X3: $i,X4: $i] :
              ( ( X3 = X4 )
             => ( ( in @ X3 @ X1 )
               => ( in @ X4 @ X2 ) ) ) )
     => ( ! [X1: $i,X2: $i] :
            ( ( X1 = X2 )
           => ! [X3: $i,X4: $i] :
                ( ( X3 = X4 )
               => ( ( in @ X3 @ X1 )
                  = ( in @ X4 @ X2 ) ) ) )
       => ( ! [X1: $i > $o] :
              ( ~ ! [X2: $i] :
                    ( ( X1 @ X2 )
                   => ~ ! [X3: $i] :
                          ( ( X1 @ X3 )
                         => ( X2 = X3 ) ) )
             => ! [X2: $i,X3: $i] :
                  ( ( X1 @ X2 )
                 => ( ( X1 @ X3 )
                   => ( X2 = X3 ) ) ) )
         => ( ! [X1: $i > $o,X2: $i > $o] :
                ( ! [X3: $i,X4: $i] :
                    ( ( X3 = X4 )
                   => ( ( X1 @ X3 )
                      = ( X2 @ X4 ) ) )
               => ( ( ~ ! [X3: $i] :
                          ( ( X1 @ X3 )
                         => ~ ! [X4: $i] :
                                ( ( X1 @ X4 )
                               => ( X3 = X4 ) ) ) )
                  = ( ~ ! [X3: $i] :
                          ( ( X2 @ X3 )
                         => ~ ! [X4: $i] :
                                ( ( X2 @ X4 )
                               => ( X3 = X4 ) ) ) ) ) )
           => ( ! [X1: $i,X2: $i] :
                  ( ( X1 = X2 )
                 => ! [X3: $i,X4: $i] :
                      ( ( X3 = X4 )
                     => ( ( setadjoin @ X1 @ X3 )
                        = ( setadjoin @ X2 @ X4 ) ) ) )
             => ( ! [X1: $i,X2: $i] :
                    ( ( X1 = X2 )
                   => ( ( powerset @ X1 )
                      = ( powerset @ X2 ) ) )
               => ( ! [X1: $i,X2: $i] :
                      ( ( X1 = X2 )
                     => ( ( setunion @ X1 )
                        = ( setunion @ X2 ) ) )
                 => ( ! [X1: $i > $o] :
                        ( ~ ! [X2: $i] :
                              ( ( X1 @ X2 )
                             => ~ ! [X3: $i] :
                                    ( ( X1 @ X3 )
                                   => ( X2 = X3 ) ) )
                       => ! [X2: $i,X3: $i] :
                            ( ( X1 @ X2 )
                           => ( ( X1 @ X3 )
                             => ( X2 = X3 ) ) ) )
                   => ( ! [X1: $i > $o,X2: $i > $o] :
                          ( ! [X3: $i,X4: $i] :
                              ( ( X3 = X4 )
                             => ( ( X1 @ X3 )
                                = ( X2 @ X4 ) ) )
                         => ( ~ ! [X3: $i] :
                                  ( ( X1 @ X3 )
                                 => ~ ! [X4: $i] :
                                        ( ( X1 @ X4 )
                                       => ( X3 = X4 ) ) )
                           => ( ~ ! [X3: $i] :
                                    ( ( X2 @ X3 )
                                   => ~ ! [X4: $i] :
                                          ( ( X2 @ X4 )
                                         => ( X3 = X4 ) ) )
                             => ( ( descr @ X1 )
                                = ( descr @ X2 ) ) ) ) )
                     => ( ! [X1: $i,X2: $i] :
                            ( ( X1 = X2 )
                           => ! [X3: $i > $o,X4: $i > $o] :
                                ( ! [X5: $i] :
                                    ( ( in @ X5 @ X1 )
                                   => ! [X6: $i] :
                                        ( ( in @ X6 @ X2 )
                                       => ( ( X5 = X6 )
                                         => ( ( X3 @ X5 )
                                            = ( X4 @ X6 ) ) ) ) )
                               => ( ( dsetconstr @ X1 @ X3 )
                                  = ( dsetconstr @ X2 @ X4 ) ) ) )
                       => ( ! [X1: $i,X2: $i] :
                              ( ! [X3: $i] :
                                  ( ( in @ X3 @ X1 )
                                 => ( in @ X3 @ X2 ) )
                             => ( subset @ X1 @ X2 ) )
                         => ( ! [X1: $i,X2: $i] :
                                ( ( X1 = X2 )
                               => ( subset @ X2 @ X1 ) )
                           => ( ! [X1: $i,X2: $i] :
                                  ( ( X1 = X2 )
                                 => ( subset @ X1 @ X2 ) )
                             => ( ! [X1: $i,X2: $i] :
                                    ( ! [X3: $i] :
                                        ( ( in @ X3 @ X1 )
                                       => ( in @ X3 @ X2 ) )
                                   => ( subset @ X1 @ X2 ) )
                               => ( ! [X1: $i] : ( subset @ emptyset @ X1 )
                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                        ( ( subset @ X1 @ X2 )
                                       => ( ( in @ X3 @ X1 )
                                         => ( in @ X3 @ X2 ) ) )
                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                          ( ( subset @ X1 @ X2 )
                                         => ( ~ ( in @ X3 @ X2 )
                                           => ~ ( in @ X3 @ X1 ) ) )
                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                            ( ( in @ X3 @ X1 )
                                           => ( ~ ( in @ X3 @ X2 )
                                             => ~ ( subset @ X1 @ X2 ) ) )
                                       => ( ! [X1: $i,X2: $i] :
                                              ( ~ ( subset @ X1 @ X2 )
                                             => ( X1 != X2 ) )
                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                ( ( in @ X3 @ X1 )
                                               => ( ~ ( in @ X3 @ X2 )
                                                 => ( X1 != X2 ) ) )
                                           => ( ! [X1: $i] : ( subset @ X1 @ X1 )
                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                    ( ( subset @ X1 @ X2 )
                                                   => ( ( subset @ X2 @ X3 )
                                                     => ( subset @ X1 @ X3 ) ) )
                                               => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) )
                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                        ( ( subset @ X1 @ X3 )
                                                       => ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
                                                   => ( ! [X1: $i,X2: $i] :
                                                          ( ( subset @ X1 @ X2 )
                                                         => ( in @ X1 @ ( powerset @ X2 ) ) )
                                                     => ( ! [X1: $i,X2: $i] :
                                                            ( ( subset @ X1 @ X2 )
                                                           => ( ( subset @ X2 @ X1 )
                                                             => ( X1 = X2 ) ) )
                                                       => ( ! [X1: $i] :
                                                              ( ( subset @ X1 @ emptyset )
                                                             => ( X1 = emptyset ) )
                                                         => ( ! [X1: $i,X2: $i] :
                                                                ( ( subset @ X2 @ X1 )
                                                               => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                           => ( ! [X1: $i,X2: $i] :
                                                                  ( ( in @ X2 @ ( powerset @ X1 ) )
                                                                 => ( subset @ X2 @ X1 ) )
                                                             => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
                                                               => ( ! [X1: $i,X2: $i] :
                                                                      ( ( subset @ X1 @ X2 )
                                                                     => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
                                                                 => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                                                                   => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                            ( ( in @ X3 @ X1 )
                                                                           => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                       => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                ( ( in @ X3 @ X2 )
                                                                               => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                                                                  ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                 => ( ( ( in @ X3 @ X1 )
                                                                                     => X4 )
                                                                                   => ( ( ( in @ X3 @ X2 )
                                                                                       => X4 )
                                                                                     => X4 ) ) )
                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                    ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                   => ( ~ ( in @ X3 @ X1 )
                                                                                     => ( in @ X3 @ X2 ) ) )
                                                                               => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                                                                                 => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                          ( ( in @ X3 @ X1 )
                                                                                         => ( ( in @ X3 @ X2 )
                                                                                           => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                            ( ( subset @ X3 @ X1 )
                                                                                           => ( ( subset @ X3 @ X2 )
                                                                                             => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                              ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                             => ( in @ X3 @ X1 ) )
                                                                                         => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                  ( ( subset @ X1 @ X2 )
                                                                                                 => ( ( binintersect @ X1 @ X2 )
                                                                                                    = X1 ) )
                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                    ( ( ( binintersect @ X1 @ X2 )
                                                                                                      = X2 )
                                                                                                   => ( subset @ X2 @ X1 ) )
                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                      ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                     => ( in @ X3 @ X2 ) )
                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                        ( ! [X3: $i] :
                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                           => ~ ( in @ X3 @ X2 ) )
                                                                                                       => ( ( binintersect @ X1 @ X2 )
                                                                                                          = emptyset ) )
                                                                                                   => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                            ( ( subset @ X2 @ X1 )
                                                                                                           => ( ( binintersect @ X1 @ X2 )
                                                                                                              = X2 ) )
                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                              ( ( ( binintersect @ X1 @ X2 )
                                                                                                                = X1 )
                                                                                                             => ( subset @ X1 @ X2 ) )
                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                                                                                = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                 => ( ~ ( in @ X3 @ X2 )
                                                                                                                   => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                    ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                   => ( in @ X3 @ X1 ) )
                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                      ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                     => ~ ( in @ X3 @ X2 ) )
                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                        ( ( subset @ X1 @ X2 )
                                                                                                                       => ( ( setminus @ X1 @ X2 )
                                                                                                                          = emptyset ) )
                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                          ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                         => ( ( in @ X3 @ X1 )
                                                                                                                           => ( in @ X3 @ X2 ) ) )
                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                            ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                           => ( ~ ( in @ X3 @ X2 )
                                                                                                                             => ~ ( in @ X3 @ X1 ) ) )
                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                              ( ~ ( in @ X3 @ X1 )
                                                                                                                             => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                ( ( in @ X3 @ X2 )
                                                                                                                               => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                           => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                    ( ( ( setminus @ X1 @ X2 )
                                                                                                                                      = emptyset )
                                                                                                                                   => ( subset @ X1 @ X2 ) )
                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                      ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                                                                     => ! [X4: $o] :
                                                                                                                                          ( ( ( in @ X3 @ X1 )
                                                                                                                                           => ( ~ ( in @ X3 @ X2 )
                                                                                                                                             => X4 ) )
                                                                                                                                         => ( ( ~ ( in @ X3 @ X1 )
                                                                                                                                             => ( ( in @ X3 @ X2 )
                                                                                                                                               => X4 ) )
                                                                                                                                           => X4 ) ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                       => ( ~ ( in @ X3 @ X2 )
                                                                                                                                         => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                          ( ~ ( in @ X3 @ X1 )
                                                                                                                                         => ( ( in @ X3 @ X2 )
                                                                                                                                           => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                           => ( ( in @ X3 @ X2 )
                                                                                                                                             => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                              ( ~ ( in @ X3 @ X1 )
                                                                                                                                             => ( ~ ( in @ X3 @ X2 )
                                                                                                                                               => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                         => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                           => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                             => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                               => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                 => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                          ( ( in @ X2 @ X1 )
                                                                                                                                                         => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                            ( ( in @ X2 @ X1 )
                                                                                                                                                           => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                             => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                               => ( ( X3 != X1 )
                                                                                                                                                                 => ( X3 = X2 ) ) )
                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                                                     => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                                                       => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                                                         => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                                                           => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                                                                             => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                                                                               => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                              ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                             => ~ ! [X4: $i] :
                                                                                                                                                                                    ( ( in @ X4 @ X1 )
                                                                                                                                                                                   => ! [X5: $i] :
                                                                                                                                                                                        ( ( in @ X5 @ X2 )
                                                                                                                                                                                       => ( X3
                                                                                                                                                                                         != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                                                                         => ( sP5
                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                  ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                                                                                 => ~ ! [X3: $i] :
                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                       => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                                                                             => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                                                                               => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                 => ( ! [X1: $i] :
                                                                                                                                                                                        ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                                                                        = X1 )
                                                                                                                                                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                          ( ! [X3: $i] :
                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                                  ( ( in @ X4 @ X1 )
                                                                                                                                                                                                 => ( ( X2 @ X3 )
                                                                                                                                                                                                   => ( ( X2 @ X4 )
                                                                                                                                                                                                     => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                         => ( ~ ! [X3: $i] :
                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                 => ~ ( X2 @ X3 ) )
                                                                                                                                                                                           => ~ ! [X3: $i] :
                                                                                                                                                                                                  ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                 => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                   != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                            ( ~ ! [X3: $i] :
                                                                                                                                                                                                  ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                 => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                   != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                                                                           => ~ ! [X3: $i] :
                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                 => ~ ( X2 @ X3 ) ) )
                                                                                                                                                                                       => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                             => ( ( X2 @ X3 )
                                                                                                                                                                                               => ( ! [X4: $i] :
                                                                                                                                                                                                      ( ( in @ X4 @ X1 )
                                                                                                                                                                                                     => ( ( X2 @ X4 )
                                                                                                                                                                                                       => ( X4 = X3 ) ) )
                                                                                                                                                                                                 => ~ ! [X4: $i] :
                                                                                                                                                                                                        ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                       => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                         != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                                                                         => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                ( ! [X3: $i] :
                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                                                        ( ( in @ X4 @ X1 )
                                                                                                                                                                                                       => ( ( X2 @ X3 )
                                                                                                                                                                                                         => ( ( X2 @ X4 )
                                                                                                                                                                                                           => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                               => ( ~ ! [X3: $i] :
                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                       => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                 => ~ ! [X3: $i] :
                                                                                                                                                                                                        ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                       => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                         != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                  ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                                                                    = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                 => ( X1 = X2 ) )
                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                    ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                   => ( X1 = X3 ) )
                                                                                                                                                                                               => ( ! [X1: $i] :
                                                                                                                                                                                                      ( ( iskpair @ X1 )
                                                                                                                                                                                                     => ~ ! [X2: $i] :
                                                                                                                                                                                                            ( ( in @ X2
                                                                                                                                                                                                              @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                                                                           => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                             != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                 => ( ! [X1: $i] :
                                                                                                                                                                                                        ( ~ ! [X2: $i] :
                                                                                                                                                                                                              ( ( in @ X2 @ X1 )
                                                                                                                                                                                                             => ( X1
                                                                                                                                                                                                               != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                       => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                          ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                          = X1 )
                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                            ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                           => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                              ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                             => ( X1 = X3 ) )
                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                  = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                               => ( X1 = X3 ) )
                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                  ( ( X1 = X2 )
                                                                                                                                                                                                                 => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                    = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                    ( ( X1 = X2 )
                                                                                                                                                                                                                   => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                      = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                      ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                        = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                     => ( ( X3 = X4 )
                                                                                                                                                                                                                       => ( X2 = X4 ) ) )
                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                        ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                          = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                                                                       => ( X1 = X2 ) )
                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                          ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                            = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                         => ( X2 = X4 ) )
                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                            ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                              = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                           => ( X2 = X4 ) )
                                                                                                                                                                                                                       => ( ! [X1: $i] :
                                                                                                                                                                                                                              ( ( iskpair @ X1 )
                                                                                                                                                                                                                             => ~ ! [X2: $i] :
                                                                                                                                                                                                                                    ( ( in @ X2
                                                                                                                                                                                                                                      @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                        @ ^ [X3: $i] :
                                                                                                                                                                                                                                            ( X1
                                                                                                                                                                                                                                            = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                                                                   => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                        @ ^ [X3: $i] :
                                                                                                                                                                                                                                            ( X1
                                                                                                                                                                                                                                            = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                                                                     != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                = X2 )
                                                                                                                                                                                                                           => ( sP8
                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                    ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                   => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                      ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                     => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                        ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                       => ( in @ X4 @ X2 ) )
                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                             => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                = X3 ) ) )
                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                               => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                  = X4 ) ) )
                                                                                                                                                                                                                                       => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                            ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                           => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                                                                              = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h106,assumption,
    ! [X1: $i,X2: $i] :
      ( ( X1 = X2 )
     => ! [X3: $i,X4: $i] :
          ( ( X3 = X4 )
         => ( ( in @ X3 @ X1 )
           => ( in @ X4 @ X2 ) ) ) ),
    introduced(assumption,[]) ).

thf(h107,assumption,
    ~ ( ! [X1: $i,X2: $i] :
          ( ( X1 = X2 )
         => ! [X3: $i,X4: $i] :
              ( ( X3 = X4 )
             => ( ( in @ X3 @ X1 )
                = ( in @ X4 @ X2 ) ) ) )
     => ( ! [X1: $i > $o] :
            ( ~ ! [X2: $i] :
                  ( ( X1 @ X2 )
                 => ~ ! [X3: $i] :
                        ( ( X1 @ X3 )
                       => ( X2 = X3 ) ) )
           => ! [X2: $i,X3: $i] :
                ( ( X1 @ X2 )
               => ( ( X1 @ X3 )
                 => ( X2 = X3 ) ) ) )
       => ( ! [X1: $i > $o,X2: $i > $o] :
              ( ! [X3: $i,X4: $i] :
                  ( ( X3 = X4 )
                 => ( ( X1 @ X3 )
                    = ( X2 @ X4 ) ) )
             => ( ( ~ ! [X3: $i] :
                        ( ( X1 @ X3 )
                       => ~ ! [X4: $i] :
                              ( ( X1 @ X4 )
                             => ( X3 = X4 ) ) ) )
                = ( ~ ! [X3: $i] :
                        ( ( X2 @ X3 )
                       => ~ ! [X4: $i] :
                              ( ( X2 @ X4 )
                             => ( X3 = X4 ) ) ) ) ) )
         => ( ! [X1: $i,X2: $i] :
                ( ( X1 = X2 )
               => ! [X3: $i,X4: $i] :
                    ( ( X3 = X4 )
                   => ( ( setadjoin @ X1 @ X3 )
                      = ( setadjoin @ X2 @ X4 ) ) ) )
           => ( ! [X1: $i,X2: $i] :
                  ( ( X1 = X2 )
                 => ( ( powerset @ X1 )
                    = ( powerset @ X2 ) ) )
             => ( ! [X1: $i,X2: $i] :
                    ( ( X1 = X2 )
                   => ( ( setunion @ X1 )
                      = ( setunion @ X2 ) ) )
               => ( ! [X1: $i > $o] :
                      ( ~ ! [X2: $i] :
                            ( ( X1 @ X2 )
                           => ~ ! [X3: $i] :
                                  ( ( X1 @ X3 )
                                 => ( X2 = X3 ) ) )
                     => ! [X2: $i,X3: $i] :
                          ( ( X1 @ X2 )
                         => ( ( X1 @ X3 )
                           => ( X2 = X3 ) ) ) )
                 => ( ! [X1: $i > $o,X2: $i > $o] :
                        ( ! [X3: $i,X4: $i] :
                            ( ( X3 = X4 )
                           => ( ( X1 @ X3 )
                              = ( X2 @ X4 ) ) )
                       => ( ~ ! [X3: $i] :
                                ( ( X1 @ X3 )
                               => ~ ! [X4: $i] :
                                      ( ( X1 @ X4 )
                                     => ( X3 = X4 ) ) )
                         => ( ~ ! [X3: $i] :
                                  ( ( X2 @ X3 )
                                 => ~ ! [X4: $i] :
                                        ( ( X2 @ X4 )
                                       => ( X3 = X4 ) ) )
                           => ( ( descr @ X1 )
                              = ( descr @ X2 ) ) ) ) )
                   => ( ! [X1: $i,X2: $i] :
                          ( ( X1 = X2 )
                         => ! [X3: $i > $o,X4: $i > $o] :
                              ( ! [X5: $i] :
                                  ( ( in @ X5 @ X1 )
                                 => ! [X6: $i] :
                                      ( ( in @ X6 @ X2 )
                                     => ( ( X5 = X6 )
                                       => ( ( X3 @ X5 )
                                          = ( X4 @ X6 ) ) ) ) )
                             => ( ( dsetconstr @ X1 @ X3 )
                                = ( dsetconstr @ X2 @ X4 ) ) ) )
                     => ( ! [X1: $i,X2: $i] :
                            ( ! [X3: $i] :
                                ( ( in @ X3 @ X1 )
                               => ( in @ X3 @ X2 ) )
                           => ( subset @ X1 @ X2 ) )
                       => ( ! [X1: $i,X2: $i] :
                              ( ( X1 = X2 )
                             => ( subset @ X2 @ X1 ) )
                         => ( ! [X1: $i,X2: $i] :
                                ( ( X1 = X2 )
                               => ( subset @ X1 @ X2 ) )
                           => ( ! [X1: $i,X2: $i] :
                                  ( ! [X3: $i] :
                                      ( ( in @ X3 @ X1 )
                                     => ( in @ X3 @ X2 ) )
                                 => ( subset @ X1 @ X2 ) )
                             => ( ! [X1: $i] : ( subset @ emptyset @ X1 )
                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                      ( ( subset @ X1 @ X2 )
                                     => ( ( in @ X3 @ X1 )
                                       => ( in @ X3 @ X2 ) ) )
                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                        ( ( subset @ X1 @ X2 )
                                       => ( ~ ( in @ X3 @ X2 )
                                         => ~ ( in @ X3 @ X1 ) ) )
                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                          ( ( in @ X3 @ X1 )
                                         => ( ~ ( in @ X3 @ X2 )
                                           => ~ ( subset @ X1 @ X2 ) ) )
                                     => ( ! [X1: $i,X2: $i] :
                                            ( ~ ( subset @ X1 @ X2 )
                                           => ( X1 != X2 ) )
                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                              ( ( in @ X3 @ X1 )
                                             => ( ~ ( in @ X3 @ X2 )
                                               => ( X1 != X2 ) ) )
                                         => ( ! [X1: $i] : ( subset @ X1 @ X1 )
                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                  ( ( subset @ X1 @ X2 )
                                                 => ( ( subset @ X2 @ X3 )
                                                   => ( subset @ X1 @ X3 ) ) )
                                             => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) )
                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                      ( ( subset @ X1 @ X3 )
                                                     => ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
                                                 => ( ! [X1: $i,X2: $i] :
                                                        ( ( subset @ X1 @ X2 )
                                                       => ( in @ X1 @ ( powerset @ X2 ) ) )
                                                   => ( ! [X1: $i,X2: $i] :
                                                          ( ( subset @ X1 @ X2 )
                                                         => ( ( subset @ X2 @ X1 )
                                                           => ( X1 = X2 ) ) )
                                                     => ( ! [X1: $i] :
                                                            ( ( subset @ X1 @ emptyset )
                                                           => ( X1 = emptyset ) )
                                                       => ( ! [X1: $i,X2: $i] :
                                                              ( ( subset @ X2 @ X1 )
                                                             => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                         => ( ! [X1: $i,X2: $i] :
                                                                ( ( in @ X2 @ ( powerset @ X1 ) )
                                                               => ( subset @ X2 @ X1 ) )
                                                           => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
                                                             => ( ! [X1: $i,X2: $i] :
                                                                    ( ( subset @ X1 @ X2 )
                                                                   => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
                                                               => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                                                                 => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                          ( ( in @ X3 @ X1 )
                                                                         => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                     => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                              ( ( in @ X3 @ X2 )
                                                                             => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                                                                ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                               => ( ( ( in @ X3 @ X1 )
                                                                                   => X4 )
                                                                                 => ( ( ( in @ X3 @ X2 )
                                                                                     => X4 )
                                                                                   => X4 ) ) )
                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                  ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                 => ( ~ ( in @ X3 @ X1 )
                                                                                   => ( in @ X3 @ X2 ) ) )
                                                                             => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                                                                               => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                        ( ( in @ X3 @ X1 )
                                                                                       => ( ( in @ X3 @ X2 )
                                                                                         => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                          ( ( subset @ X3 @ X1 )
                                                                                         => ( ( subset @ X3 @ X2 )
                                                                                           => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                            ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                           => ( in @ X3 @ X1 ) )
                                                                                       => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                ( ( subset @ X1 @ X2 )
                                                                                               => ( ( binintersect @ X1 @ X2 )
                                                                                                  = X1 ) )
                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                  ( ( ( binintersect @ X1 @ X2 )
                                                                                                    = X2 )
                                                                                                 => ( subset @ X2 @ X1 ) )
                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                    ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                   => ( in @ X3 @ X2 ) )
                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                      ( ! [X3: $i] :
                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                         => ~ ( in @ X3 @ X2 ) )
                                                                                                     => ( ( binintersect @ X1 @ X2 )
                                                                                                        = emptyset ) )
                                                                                                 => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                          ( ( subset @ X2 @ X1 )
                                                                                                         => ( ( binintersect @ X1 @ X2 )
                                                                                                            = X2 ) )
                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                            ( ( ( binintersect @ X1 @ X2 )
                                                                                                              = X1 )
                                                                                                           => ( subset @ X1 @ X2 ) )
                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                              ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                                                                              = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                               => ( ~ ( in @ X3 @ X2 )
                                                                                                                 => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                  ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                 => ( in @ X3 @ X1 ) )
                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                    ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                   => ~ ( in @ X3 @ X2 ) )
                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                      ( ( subset @ X1 @ X2 )
                                                                                                                     => ( ( setminus @ X1 @ X2 )
                                                                                                                        = emptyset ) )
                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                        ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                       => ( ( in @ X3 @ X1 )
                                                                                                                         => ( in @ X3 @ X2 ) ) )
                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                          ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                         => ( ~ ( in @ X3 @ X2 )
                                                                                                                           => ~ ( in @ X3 @ X1 ) ) )
                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                            ( ~ ( in @ X3 @ X1 )
                                                                                                                           => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                              ( ( in @ X3 @ X2 )
                                                                                                                             => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                         => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                  ( ( ( setminus @ X1 @ X2 )
                                                                                                                                    = emptyset )
                                                                                                                                 => ( subset @ X1 @ X2 ) )
                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                    ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                                                                   => ! [X4: $o] :
                                                                                                                                        ( ( ( in @ X3 @ X1 )
                                                                                                                                         => ( ~ ( in @ X3 @ X2 )
                                                                                                                                           => X4 ) )
                                                                                                                                       => ( ( ~ ( in @ X3 @ X1 )
                                                                                                                                           => ( ( in @ X3 @ X2 )
                                                                                                                                             => X4 ) )
                                                                                                                                         => X4 ) ) )
                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                     => ( ~ ( in @ X3 @ X2 )
                                                                                                                                       => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                        ( ~ ( in @ X3 @ X1 )
                                                                                                                                       => ( ( in @ X3 @ X2 )
                                                                                                                                         => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                         => ( ( in @ X3 @ X2 )
                                                                                                                                           => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                            ( ~ ( in @ X3 @ X1 )
                                                                                                                                           => ( ~ ( in @ X3 @ X2 )
                                                                                                                                             => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                         => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                           => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                             => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                               => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                        ( ( in @ X2 @ X1 )
                                                                                                                                                       => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                          ( ( in @ X2 @ X1 )
                                                                                                                                                         => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                           => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                              ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                             => ( ( X3 != X1 )
                                                                                                                                                               => ( X3 = X2 ) ) )
                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                                                   => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                                                     => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                                                       => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                                                         => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                                                           => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                                                                             => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                            ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                           => ~ ! [X4: $i] :
                                                                                                                                                                                  ( ( in @ X4 @ X1 )
                                                                                                                                                                                 => ! [X5: $i] :
                                                                                                                                                                                      ( ( in @ X5 @ X2 )
                                                                                                                                                                                     => ( X3
                                                                                                                                                                                       != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                                                                       => ( sP5
                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                                                                               => ~ ! [X3: $i] :
                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                     => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                                                                           => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                                                                             => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                               => ( ! [X1: $i] :
                                                                                                                                                                                      ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                                                                      = X1 )
                                                                                                                                                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                        ( ! [X3: $i] :
                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                                                ( ( in @ X4 @ X1 )
                                                                                                                                                                                               => ( ( X2 @ X3 )
                                                                                                                                                                                                 => ( ( X2 @ X4 )
                                                                                                                                                                                                   => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                       => ( ~ ! [X3: $i] :
                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                               => ~ ( X2 @ X3 ) )
                                                                                                                                                                                         => ~ ! [X3: $i] :
                                                                                                                                                                                                ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                               => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                 != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                          ( ~ ! [X3: $i] :
                                                                                                                                                                                                ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                               => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                 != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                                                                         => ~ ! [X3: $i] :
                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                               => ~ ( X2 @ X3 ) ) )
                                                                                                                                                                                     => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                           => ( ( X2 @ X3 )
                                                                                                                                                                                             => ( ! [X4: $i] :
                                                                                                                                                                                                    ( ( in @ X4 @ X1 )
                                                                                                                                                                                                   => ( ( X2 @ X4 )
                                                                                                                                                                                                     => ( X4 = X3 ) ) )
                                                                                                                                                                                               => ~ ! [X4: $i] :
                                                                                                                                                                                                      ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                     => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                       != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                                                                       => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                              ( ! [X3: $i] :
                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                                                      ( ( in @ X4 @ X1 )
                                                                                                                                                                                                     => ( ( X2 @ X3 )
                                                                                                                                                                                                       => ( ( X2 @ X4 )
                                                                                                                                                                                                         => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                             => ( ~ ! [X3: $i] :
                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                     => ~ ( X2 @ X3 ) )
                                                                                                                                                                                               => ~ ! [X3: $i] :
                                                                                                                                                                                                      ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                     => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                       != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                                                                  = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                               => ( X1 = X2 ) )
                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                  ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                 => ( X1 = X3 ) )
                                                                                                                                                                                             => ( ! [X1: $i] :
                                                                                                                                                                                                    ( ( iskpair @ X1 )
                                                                                                                                                                                                   => ~ ! [X2: $i] :
                                                                                                                                                                                                          ( ( in @ X2
                                                                                                                                                                                                            @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                              @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                                                                         => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                              @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                           != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                               => ( ! [X1: $i] :
                                                                                                                                                                                                      ( ~ ! [X2: $i] :
                                                                                                                                                                                                            ( ( in @ X2 @ X1 )
                                                                                                                                                                                                           => ( X1
                                                                                                                                                                                                             != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                     => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                        ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                        = X1 )
                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                         => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                            ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                              = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                           => ( X1 = X3 ) )
                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                              ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                             => ( X1 = X3 ) )
                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                ( ( X1 = X2 )
                                                                                                                                                                                                               => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                  = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                  ( ( X1 = X2 )
                                                                                                                                                                                                                 => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                    = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                    ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                      = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                   => ( ( X3 = X4 )
                                                                                                                                                                                                                     => ( X2 = X4 ) ) )
                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                      ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                        = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                                                                     => ( X1 = X2 ) )
                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                        ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                          = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                       => ( X2 = X4 ) )
                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                          ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                            = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                         => ( X2 = X4 ) )
                                                                                                                                                                                                                     => ( ! [X1: $i] :
                                                                                                                                                                                                                            ( ( iskpair @ X1 )
                                                                                                                                                                                                                           => ~ ! [X2: $i] :
                                                                                                                                                                                                                                  ( ( in @ X2
                                                                                                                                                                                                                                    @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                      @ ^ [X3: $i] :
                                                                                                                                                                                                                                          ( X1
                                                                                                                                                                                                                                          = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                                                                 => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                      @ ^ [X3: $i] :
                                                                                                                                                                                                                                          ( X1
                                                                                                                                                                                                                                          = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                                                                   != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                              ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                              = X2 )
                                                                                                                                                                                                                         => ( sP8
                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                  ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                 => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                    ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                   => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                      ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                     => ( in @ X4 @ X2 ) )
                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                           => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                              = X3 ) ) )
                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                             => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                = X4 ) ) )
                                                                                                                                                                                                                                     => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                         => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                                                                            = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h108,assumption,
    ! [X1: $i,X2: $i] :
      ( ( X1 = X2 )
     => ! [X3: $i,X4: $i] :
          ( ( X3 = X4 )
         => ( ( in @ X3 @ X1 )
            = ( in @ X4 @ X2 ) ) ) ),
    introduced(assumption,[]) ).

thf(h109,assumption,
    ~ ( ! [X1: $i > $o] :
          ( ~ ! [X2: $i] :
                ( ( X1 @ X2 )
               => ~ ! [X3: $i] :
                      ( ( X1 @ X3 )
                     => ( X2 = X3 ) ) )
         => ! [X2: $i,X3: $i] :
              ( ( X1 @ X2 )
             => ( ( X1 @ X3 )
               => ( X2 = X3 ) ) ) )
     => ( ! [X1: $i > $o,X2: $i > $o] :
            ( ! [X3: $i,X4: $i] :
                ( ( X3 = X4 )
               => ( ( X1 @ X3 )
                  = ( X2 @ X4 ) ) )
           => ( ( ~ ! [X3: $i] :
                      ( ( X1 @ X3 )
                     => ~ ! [X4: $i] :
                            ( ( X1 @ X4 )
                           => ( X3 = X4 ) ) ) )
              = ( ~ ! [X3: $i] :
                      ( ( X2 @ X3 )
                     => ~ ! [X4: $i] :
                            ( ( X2 @ X4 )
                           => ( X3 = X4 ) ) ) ) ) )
       => ( ! [X1: $i,X2: $i] :
              ( ( X1 = X2 )
             => ! [X3: $i,X4: $i] :
                  ( ( X3 = X4 )
                 => ( ( setadjoin @ X1 @ X3 )
                    = ( setadjoin @ X2 @ X4 ) ) ) )
         => ( ! [X1: $i,X2: $i] :
                ( ( X1 = X2 )
               => ( ( powerset @ X1 )
                  = ( powerset @ X2 ) ) )
           => ( ! [X1: $i,X2: $i] :
                  ( ( X1 = X2 )
                 => ( ( setunion @ X1 )
                    = ( setunion @ X2 ) ) )
             => ( ! [X1: $i > $o] :
                    ( ~ ! [X2: $i] :
                          ( ( X1 @ X2 )
                         => ~ ! [X3: $i] :
                                ( ( X1 @ X3 )
                               => ( X2 = X3 ) ) )
                   => ! [X2: $i,X3: $i] :
                        ( ( X1 @ X2 )
                       => ( ( X1 @ X3 )
                         => ( X2 = X3 ) ) ) )
               => ( ! [X1: $i > $o,X2: $i > $o] :
                      ( ! [X3: $i,X4: $i] :
                          ( ( X3 = X4 )
                         => ( ( X1 @ X3 )
                            = ( X2 @ X4 ) ) )
                     => ( ~ ! [X3: $i] :
                              ( ( X1 @ X3 )
                             => ~ ! [X4: $i] :
                                    ( ( X1 @ X4 )
                                   => ( X3 = X4 ) ) )
                       => ( ~ ! [X3: $i] :
                                ( ( X2 @ X3 )
                               => ~ ! [X4: $i] :
                                      ( ( X2 @ X4 )
                                     => ( X3 = X4 ) ) )
                         => ( ( descr @ X1 )
                            = ( descr @ X2 ) ) ) ) )
                 => ( ! [X1: $i,X2: $i] :
                        ( ( X1 = X2 )
                       => ! [X3: $i > $o,X4: $i > $o] :
                            ( ! [X5: $i] :
                                ( ( in @ X5 @ X1 )
                               => ! [X6: $i] :
                                    ( ( in @ X6 @ X2 )
                                   => ( ( X5 = X6 )
                                     => ( ( X3 @ X5 )
                                        = ( X4 @ X6 ) ) ) ) )
                           => ( ( dsetconstr @ X1 @ X3 )
                              = ( dsetconstr @ X2 @ X4 ) ) ) )
                   => ( ! [X1: $i,X2: $i] :
                          ( ! [X3: $i] :
                              ( ( in @ X3 @ X1 )
                             => ( in @ X3 @ X2 ) )
                         => ( subset @ X1 @ X2 ) )
                     => ( ! [X1: $i,X2: $i] :
                            ( ( X1 = X2 )
                           => ( subset @ X2 @ X1 ) )
                       => ( ! [X1: $i,X2: $i] :
                              ( ( X1 = X2 )
                             => ( subset @ X1 @ X2 ) )
                         => ( ! [X1: $i,X2: $i] :
                                ( ! [X3: $i] :
                                    ( ( in @ X3 @ X1 )
                                   => ( in @ X3 @ X2 ) )
                               => ( subset @ X1 @ X2 ) )
                           => ( ! [X1: $i] : ( subset @ emptyset @ X1 )
                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                    ( ( subset @ X1 @ X2 )
                                   => ( ( in @ X3 @ X1 )
                                     => ( in @ X3 @ X2 ) ) )
                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                      ( ( subset @ X1 @ X2 )
                                     => ( ~ ( in @ X3 @ X2 )
                                       => ~ ( in @ X3 @ X1 ) ) )
                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                        ( ( in @ X3 @ X1 )
                                       => ( ~ ( in @ X3 @ X2 )
                                         => ~ ( subset @ X1 @ X2 ) ) )
                                   => ( ! [X1: $i,X2: $i] :
                                          ( ~ ( subset @ X1 @ X2 )
                                         => ( X1 != X2 ) )
                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                            ( ( in @ X3 @ X1 )
                                           => ( ~ ( in @ X3 @ X2 )
                                             => ( X1 != X2 ) ) )
                                       => ( ! [X1: $i] : ( subset @ X1 @ X1 )
                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                ( ( subset @ X1 @ X2 )
                                               => ( ( subset @ X2 @ X3 )
                                                 => ( subset @ X1 @ X3 ) ) )
                                           => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) )
                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                    ( ( subset @ X1 @ X3 )
                                                   => ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
                                               => ( ! [X1: $i,X2: $i] :
                                                      ( ( subset @ X1 @ X2 )
                                                     => ( in @ X1 @ ( powerset @ X2 ) ) )
                                                 => ( ! [X1: $i,X2: $i] :
                                                        ( ( subset @ X1 @ X2 )
                                                       => ( ( subset @ X2 @ X1 )
                                                         => ( X1 = X2 ) ) )
                                                   => ( ! [X1: $i] :
                                                          ( ( subset @ X1 @ emptyset )
                                                         => ( X1 = emptyset ) )
                                                     => ( ! [X1: $i,X2: $i] :
                                                            ( ( subset @ X2 @ X1 )
                                                           => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                       => ( ! [X1: $i,X2: $i] :
                                                              ( ( in @ X2 @ ( powerset @ X1 ) )
                                                             => ( subset @ X2 @ X1 ) )
                                                         => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
                                                           => ( ! [X1: $i,X2: $i] :
                                                                  ( ( subset @ X1 @ X2 )
                                                                 => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
                                                             => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                                                               => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                        ( ( in @ X3 @ X1 )
                                                                       => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                   => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                            ( ( in @ X3 @ X2 )
                                                                           => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                                                              ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                             => ( ( ( in @ X3 @ X1 )
                                                                                 => X4 )
                                                                               => ( ( ( in @ X3 @ X2 )
                                                                                   => X4 )
                                                                                 => X4 ) ) )
                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                               => ( ~ ( in @ X3 @ X1 )
                                                                                 => ( in @ X3 @ X2 ) ) )
                                                                           => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                                                                             => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                      ( ( in @ X3 @ X1 )
                                                                                     => ( ( in @ X3 @ X2 )
                                                                                       => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                        ( ( subset @ X3 @ X1 )
                                                                                       => ( ( subset @ X3 @ X2 )
                                                                                         => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                          ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                         => ( in @ X3 @ X1 ) )
                                                                                     => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                              ( ( subset @ X1 @ X2 )
                                                                                             => ( ( binintersect @ X1 @ X2 )
                                                                                                = X1 ) )
                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                ( ( ( binintersect @ X1 @ X2 )
                                                                                                  = X2 )
                                                                                               => ( subset @ X2 @ X1 ) )
                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                  ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                 => ( in @ X3 @ X2 ) )
                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                    ( ! [X3: $i] :
                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                       => ~ ( in @ X3 @ X2 ) )
                                                                                                   => ( ( binintersect @ X1 @ X2 )
                                                                                                      = emptyset ) )
                                                                                               => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                        ( ( subset @ X2 @ X1 )
                                                                                                       => ( ( binintersect @ X1 @ X2 )
                                                                                                          = X2 ) )
                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                          ( ( ( binintersect @ X1 @ X2 )
                                                                                                            = X1 )
                                                                                                         => ( subset @ X1 @ X2 ) )
                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                            ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                                                                            = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                             => ( ~ ( in @ X3 @ X2 )
                                                                                                               => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                               => ( in @ X3 @ X1 ) )
                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                  ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                 => ~ ( in @ X3 @ X2 ) )
                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                    ( ( subset @ X1 @ X2 )
                                                                                                                   => ( ( setminus @ X1 @ X2 )
                                                                                                                      = emptyset ) )
                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                      ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                     => ( ( in @ X3 @ X1 )
                                                                                                                       => ( in @ X3 @ X2 ) ) )
                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                        ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                       => ( ~ ( in @ X3 @ X2 )
                                                                                                                         => ~ ( in @ X3 @ X1 ) ) )
                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                          ( ~ ( in @ X3 @ X1 )
                                                                                                                         => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                            ( ( in @ X3 @ X2 )
                                                                                                                           => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                       => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                ( ( ( setminus @ X1 @ X2 )
                                                                                                                                  = emptyset )
                                                                                                                               => ( subset @ X1 @ X2 ) )
                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                  ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                                                                 => ! [X4: $o] :
                                                                                                                                      ( ( ( in @ X3 @ X1 )
                                                                                                                                       => ( ~ ( in @ X3 @ X2 )
                                                                                                                                         => X4 ) )
                                                                                                                                     => ( ( ~ ( in @ X3 @ X1 )
                                                                                                                                         => ( ( in @ X3 @ X2 )
                                                                                                                                           => X4 ) )
                                                                                                                                       => X4 ) ) )
                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                   => ( ~ ( in @ X3 @ X2 )
                                                                                                                                     => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                      ( ~ ( in @ X3 @ X1 )
                                                                                                                                     => ( ( in @ X3 @ X2 )
                                                                                                                                       => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                       => ( ( in @ X3 @ X2 )
                                                                                                                                         => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                          ( ~ ( in @ X3 @ X1 )
                                                                                                                                         => ( ~ ( in @ X3 @ X2 )
                                                                                                                                           => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                         => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                           => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                             => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                      ( ( in @ X2 @ X1 )
                                                                                                                                                     => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                        ( ( in @ X2 @ X1 )
                                                                                                                                                       => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                         => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                            ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                           => ( ( X3 != X1 )
                                                                                                                                                             => ( X3 = X2 ) ) )
                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                                                 => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                                                   => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                                                     => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                                                       => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                                                         => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                                                           => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                         => ~ ! [X4: $i] :
                                                                                                                                                                                ( ( in @ X4 @ X1 )
                                                                                                                                                                               => ! [X5: $i] :
                                                                                                                                                                                    ( ( in @ X5 @ X2 )
                                                                                                                                                                                   => ( X3
                                                                                                                                                                                     != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                                                                     => ( sP5
                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                              ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                                                                             => ~ ! [X3: $i] :
                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                   => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                                                                         => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                                                                           => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                             => ( ! [X1: $i] :
                                                                                                                                                                                    ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                                                                    = X1 )
                                                                                                                                                                               => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                      ( ! [X3: $i] :
                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                                              ( ( in @ X4 @ X1 )
                                                                                                                                                                                             => ( ( X2 @ X3 )
                                                                                                                                                                                               => ( ( X2 @ X4 )
                                                                                                                                                                                                 => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                     => ( ~ ! [X3: $i] :
                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                             => ~ ( X2 @ X3 ) )
                                                                                                                                                                                       => ~ ! [X3: $i] :
                                                                                                                                                                                              ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                             => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                               != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                        ( ~ ! [X3: $i] :
                                                                                                                                                                                              ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                             => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                               != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                                                                       => ~ ! [X3: $i] :
                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                             => ~ ( X2 @ X3 ) ) )
                                                                                                                                                                                   => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                         => ( ( X2 @ X3 )
                                                                                                                                                                                           => ( ! [X4: $i] :
                                                                                                                                                                                                  ( ( in @ X4 @ X1 )
                                                                                                                                                                                                 => ( ( X2 @ X4 )
                                                                                                                                                                                                   => ( X4 = X3 ) ) )
                                                                                                                                                                                             => ~ ! [X4: $i] :
                                                                                                                                                                                                    ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                   => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                     != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                            ( ! [X3: $i] :
                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                                    ( ( in @ X4 @ X1 )
                                                                                                                                                                                                   => ( ( X2 @ X3 )
                                                                                                                                                                                                     => ( ( X2 @ X4 )
                                                                                                                                                                                                       => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                           => ( ~ ! [X3: $i] :
                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                   => ~ ( X2 @ X3 ) )
                                                                                                                                                                                             => ~ ! [X3: $i] :
                                                                                                                                                                                                    ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                   => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                     != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                              ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                                                                = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                             => ( X1 = X2 ) )
                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                               => ( X1 = X3 ) )
                                                                                                                                                                                           => ( ! [X1: $i] :
                                                                                                                                                                                                  ( ( iskpair @ X1 )
                                                                                                                                                                                                 => ~ ! [X2: $i] :
                                                                                                                                                                                                        ( ( in @ X2
                                                                                                                                                                                                          @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                            @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                                                                       => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                            @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                         != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                             => ( ! [X1: $i] :
                                                                                                                                                                                                    ( ~ ! [X2: $i] :
                                                                                                                                                                                                          ( ( in @ X2 @ X1 )
                                                                                                                                                                                                         => ( X1
                                                                                                                                                                                                           != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                   => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                      ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                      = X1 )
                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                       => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                          ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                            = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                         => ( X1 = X3 ) )
                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                            ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                              = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                           => ( X1 = X3 ) )
                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                              ( ( X1 = X2 )
                                                                                                                                                                                                             => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                ( ( X1 = X2 )
                                                                                                                                                                                                               => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                  = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                  ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                    = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                 => ( ( X3 = X4 )
                                                                                                                                                                                                                   => ( X2 = X4 ) ) )
                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                    ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                      = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                                                                   => ( X1 = X2 ) )
                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                      ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                        = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                     => ( X2 = X4 ) )
                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                        ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                          = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                       => ( X2 = X4 ) )
                                                                                                                                                                                                                   => ( ! [X1: $i] :
                                                                                                                                                                                                                          ( ( iskpair @ X1 )
                                                                                                                                                                                                                         => ~ ! [X2: $i] :
                                                                                                                                                                                                                                ( ( in @ X2
                                                                                                                                                                                                                                  @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                    @ ^ [X3: $i] :
                                                                                                                                                                                                                                        ( X1
                                                                                                                                                                                                                                        = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                                                               => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                    @ ^ [X3: $i] :
                                                                                                                                                                                                                                        ( X1
                                                                                                                                                                                                                                        = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                                                                 != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                            ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                            = X2 )
                                                                                                                                                                                                                       => ( sP8
                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                               => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                  ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                 => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                    ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                   => ( in @ X4 @ X2 ) )
                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                         => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                            = X3 ) ) )
                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                           => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                              = X4 ) ) )
                                                                                                                                                                                                                                   => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                       => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                                                                          = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h110,assumption,
    ! [X1: $i > $o] :
      ( ~ ! [X2: $i] :
            ( ( X1 @ X2 )
           => ~ ! [X3: $i] :
                  ( ( X1 @ X3 )
                 => ( X2 = X3 ) ) )
     => ! [X2: $i,X3: $i] :
          ( ( X1 @ X2 )
         => ( ( X1 @ X3 )
           => ( X2 = X3 ) ) ) ),
    introduced(assumption,[]) ).

thf(h111,assumption,
    ~ ( ! [X1: $i > $o,X2: $i > $o] :
          ( ! [X3: $i,X4: $i] :
              ( ( X3 = X4 )
             => ( ( X1 @ X3 )
                = ( X2 @ X4 ) ) )
         => ( ( ~ ! [X3: $i] :
                    ( ( X1 @ X3 )
                   => ~ ! [X4: $i] :
                          ( ( X1 @ X4 )
                         => ( X3 = X4 ) ) ) )
            = ( ~ ! [X3: $i] :
                    ( ( X2 @ X3 )
                   => ~ ! [X4: $i] :
                          ( ( X2 @ X4 )
                         => ( X3 = X4 ) ) ) ) ) )
     => ( ! [X1: $i,X2: $i] :
            ( ( X1 = X2 )
           => ! [X3: $i,X4: $i] :
                ( ( X3 = X4 )
               => ( ( setadjoin @ X1 @ X3 )
                  = ( setadjoin @ X2 @ X4 ) ) ) )
       => ( ! [X1: $i,X2: $i] :
              ( ( X1 = X2 )
             => ( ( powerset @ X1 )
                = ( powerset @ X2 ) ) )
         => ( ! [X1: $i,X2: $i] :
                ( ( X1 = X2 )
               => ( ( setunion @ X1 )
                  = ( setunion @ X2 ) ) )
           => ( ! [X1: $i > $o] :
                  ( ~ ! [X2: $i] :
                        ( ( X1 @ X2 )
                       => ~ ! [X3: $i] :
                              ( ( X1 @ X3 )
                             => ( X2 = X3 ) ) )
                 => ! [X2: $i,X3: $i] :
                      ( ( X1 @ X2 )
                     => ( ( X1 @ X3 )
                       => ( X2 = X3 ) ) ) )
             => ( ! [X1: $i > $o,X2: $i > $o] :
                    ( ! [X3: $i,X4: $i] :
                        ( ( X3 = X4 )
                       => ( ( X1 @ X3 )
                          = ( X2 @ X4 ) ) )
                   => ( ~ ! [X3: $i] :
                            ( ( X1 @ X3 )
                           => ~ ! [X4: $i] :
                                  ( ( X1 @ X4 )
                                 => ( X3 = X4 ) ) )
                     => ( ~ ! [X3: $i] :
                              ( ( X2 @ X3 )
                             => ~ ! [X4: $i] :
                                    ( ( X2 @ X4 )
                                   => ( X3 = X4 ) ) )
                       => ( ( descr @ X1 )
                          = ( descr @ X2 ) ) ) ) )
               => ( ! [X1: $i,X2: $i] :
                      ( ( X1 = X2 )
                     => ! [X3: $i > $o,X4: $i > $o] :
                          ( ! [X5: $i] :
                              ( ( in @ X5 @ X1 )
                             => ! [X6: $i] :
                                  ( ( in @ X6 @ X2 )
                                 => ( ( X5 = X6 )
                                   => ( ( X3 @ X5 )
                                      = ( X4 @ X6 ) ) ) ) )
                         => ( ( dsetconstr @ X1 @ X3 )
                            = ( dsetconstr @ X2 @ X4 ) ) ) )
                 => ( ! [X1: $i,X2: $i] :
                        ( ! [X3: $i] :
                            ( ( in @ X3 @ X1 )
                           => ( in @ X3 @ X2 ) )
                       => ( subset @ X1 @ X2 ) )
                   => ( ! [X1: $i,X2: $i] :
                          ( ( X1 = X2 )
                         => ( subset @ X2 @ X1 ) )
                     => ( ! [X1: $i,X2: $i] :
                            ( ( X1 = X2 )
                           => ( subset @ X1 @ X2 ) )
                       => ( ! [X1: $i,X2: $i] :
                              ( ! [X3: $i] :
                                  ( ( in @ X3 @ X1 )
                                 => ( in @ X3 @ X2 ) )
                             => ( subset @ X1 @ X2 ) )
                         => ( ! [X1: $i] : ( subset @ emptyset @ X1 )
                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                  ( ( subset @ X1 @ X2 )
                                 => ( ( in @ X3 @ X1 )
                                   => ( in @ X3 @ X2 ) ) )
                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                    ( ( subset @ X1 @ X2 )
                                   => ( ~ ( in @ X3 @ X2 )
                                     => ~ ( in @ X3 @ X1 ) ) )
                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                      ( ( in @ X3 @ X1 )
                                     => ( ~ ( in @ X3 @ X2 )
                                       => ~ ( subset @ X1 @ X2 ) ) )
                                 => ( ! [X1: $i,X2: $i] :
                                        ( ~ ( subset @ X1 @ X2 )
                                       => ( X1 != X2 ) )
                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                          ( ( in @ X3 @ X1 )
                                         => ( ~ ( in @ X3 @ X2 )
                                           => ( X1 != X2 ) ) )
                                     => ( ! [X1: $i] : ( subset @ X1 @ X1 )
                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                              ( ( subset @ X1 @ X2 )
                                             => ( ( subset @ X2 @ X3 )
                                               => ( subset @ X1 @ X3 ) ) )
                                         => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) )
                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                  ( ( subset @ X1 @ X3 )
                                                 => ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
                                             => ( ! [X1: $i,X2: $i] :
                                                    ( ( subset @ X1 @ X2 )
                                                   => ( in @ X1 @ ( powerset @ X2 ) ) )
                                               => ( ! [X1: $i,X2: $i] :
                                                      ( ( subset @ X1 @ X2 )
                                                     => ( ( subset @ X2 @ X1 )
                                                       => ( X1 = X2 ) ) )
                                                 => ( ! [X1: $i] :
                                                        ( ( subset @ X1 @ emptyset )
                                                       => ( X1 = emptyset ) )
                                                   => ( ! [X1: $i,X2: $i] :
                                                          ( ( subset @ X2 @ X1 )
                                                         => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                     => ( ! [X1: $i,X2: $i] :
                                                            ( ( in @ X2 @ ( powerset @ X1 ) )
                                                           => ( subset @ X2 @ X1 ) )
                                                       => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
                                                         => ( ! [X1: $i,X2: $i] :
                                                                ( ( subset @ X1 @ X2 )
                                                               => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
                                                           => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                                                             => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                      ( ( in @ X3 @ X1 )
                                                                     => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                 => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                          ( ( in @ X3 @ X2 )
                                                                         => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                                                            ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                           => ( ( ( in @ X3 @ X1 )
                                                                               => X4 )
                                                                             => ( ( ( in @ X3 @ X2 )
                                                                                 => X4 )
                                                                               => X4 ) ) )
                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                              ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                             => ( ~ ( in @ X3 @ X1 )
                                                                               => ( in @ X3 @ X2 ) ) )
                                                                         => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                                                                           => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                    ( ( in @ X3 @ X1 )
                                                                                   => ( ( in @ X3 @ X2 )
                                                                                     => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                      ( ( subset @ X3 @ X1 )
                                                                                     => ( ( subset @ X3 @ X2 )
                                                                                       => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                        ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                       => ( in @ X3 @ X1 ) )
                                                                                   => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                            ( ( subset @ X1 @ X2 )
                                                                                           => ( ( binintersect @ X1 @ X2 )
                                                                                              = X1 ) )
                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                              ( ( ( binintersect @ X1 @ X2 )
                                                                                                = X2 )
                                                                                             => ( subset @ X2 @ X1 ) )
                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                               => ( in @ X3 @ X2 ) )
                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                  ( ! [X3: $i] :
                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                     => ~ ( in @ X3 @ X2 ) )
                                                                                                 => ( ( binintersect @ X1 @ X2 )
                                                                                                    = emptyset ) )
                                                                                             => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                      ( ( subset @ X2 @ X1 )
                                                                                                     => ( ( binintersect @ X1 @ X2 )
                                                                                                        = X2 ) )
                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                        ( ( ( binintersect @ X1 @ X2 )
                                                                                                          = X1 )
                                                                                                       => ( subset @ X1 @ X2 ) )
                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                          ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                                                                          = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                           => ( ~ ( in @ X3 @ X2 )
                                                                                                             => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                              ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                             => ( in @ X3 @ X1 ) )
                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                               => ~ ( in @ X3 @ X2 ) )
                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                  ( ( subset @ X1 @ X2 )
                                                                                                                 => ( ( setminus @ X1 @ X2 )
                                                                                                                    = emptyset ) )
                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                    ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                   => ( ( in @ X3 @ X1 )
                                                                                                                     => ( in @ X3 @ X2 ) ) )
                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                      ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                     => ( ~ ( in @ X3 @ X2 )
                                                                                                                       => ~ ( in @ X3 @ X1 ) ) )
                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                        ( ~ ( in @ X3 @ X1 )
                                                                                                                       => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                          ( ( in @ X3 @ X2 )
                                                                                                                         => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                     => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                              ( ( ( setminus @ X1 @ X2 )
                                                                                                                                = emptyset )
                                                                                                                             => ( subset @ X1 @ X2 ) )
                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                                                               => ! [X4: $o] :
                                                                                                                                    ( ( ( in @ X3 @ X1 )
                                                                                                                                     => ( ~ ( in @ X3 @ X2 )
                                                                                                                                       => X4 ) )
                                                                                                                                   => ( ( ~ ( in @ X3 @ X1 )
                                                                                                                                       => ( ( in @ X3 @ X2 )
                                                                                                                                         => X4 ) )
                                                                                                                                     => X4 ) ) )
                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                 => ( ~ ( in @ X3 @ X2 )
                                                                                                                                   => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                    ( ~ ( in @ X3 @ X1 )
                                                                                                                                   => ( ( in @ X3 @ X2 )
                                                                                                                                     => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                     => ( ( in @ X3 @ X2 )
                                                                                                                                       => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                        ( ~ ( in @ X3 @ X1 )
                                                                                                                                       => ( ~ ( in @ X3 @ X2 )
                                                                                                                                         => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                         => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                           => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                    ( ( in @ X2 @ X1 )
                                                                                                                                                   => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                      ( ( in @ X2 @ X1 )
                                                                                                                                                     => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                       => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                          ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                         => ( ( X3 != X1 )
                                                                                                                                                           => ( X3 = X2 ) ) )
                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                                                               => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                                                 => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                                                   => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                                                     => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                                                       => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                                                         => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                       => ~ ! [X4: $i] :
                                                                                                                                                                              ( ( in @ X4 @ X1 )
                                                                                                                                                                             => ! [X5: $i] :
                                                                                                                                                                                  ( ( in @ X5 @ X2 )
                                                                                                                                                                                 => ( X3
                                                                                                                                                                                   != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                                                                   => ( sP5
                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                            ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                                                                           => ~ ! [X3: $i] :
                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                 => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                                                                       => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                                                                         => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                           => ( ! [X1: $i] :
                                                                                                                                                                                  ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                                                                  = X1 )
                                                                                                                                                                             => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                    ( ! [X3: $i] :
                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                                            ( ( in @ X4 @ X1 )
                                                                                                                                                                                           => ( ( X2 @ X3 )
                                                                                                                                                                                             => ( ( X2 @ X4 )
                                                                                                                                                                                               => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                   => ( ~ ! [X3: $i] :
                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                           => ~ ( X2 @ X3 ) )
                                                                                                                                                                                     => ~ ! [X3: $i] :
                                                                                                                                                                                            ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                           => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                             != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                               => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                      ( ~ ! [X3: $i] :
                                                                                                                                                                                            ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                           => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                             != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                                                                     => ~ ! [X3: $i] :
                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                           => ~ ( X2 @ X3 ) ) )
                                                                                                                                                                                 => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                       => ( ( X2 @ X3 )
                                                                                                                                                                                         => ( ! [X4: $i] :
                                                                                                                                                                                                ( ( in @ X4 @ X1 )
                                                                                                                                                                                               => ( ( X2 @ X4 )
                                                                                                                                                                                                 => ( X4 = X3 ) ) )
                                                                                                                                                                                           => ~ ! [X4: $i] :
                                                                                                                                                                                                  ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                 => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                   != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                          ( ! [X3: $i] :
                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                                  ( ( in @ X4 @ X1 )
                                                                                                                                                                                                 => ( ( X2 @ X3 )
                                                                                                                                                                                                   => ( ( X2 @ X4 )
                                                                                                                                                                                                     => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                         => ( ~ ! [X3: $i] :
                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                 => ~ ( X2 @ X3 ) )
                                                                                                                                                                                           => ~ ! [X3: $i] :
                                                                                                                                                                                                  ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                 => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                   != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                            ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                                                              = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                           => ( X1 = X2 ) )
                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                              ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                             => ( X1 = X3 ) )
                                                                                                                                                                                         => ( ! [X1: $i] :
                                                                                                                                                                                                ( ( iskpair @ X1 )
                                                                                                                                                                                               => ~ ! [X2: $i] :
                                                                                                                                                                                                      ( ( in @ X2
                                                                                                                                                                                                        @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                          @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                                                                     => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                          @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                       != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                           => ( ! [X1: $i] :
                                                                                                                                                                                                  ( ~ ! [X2: $i] :
                                                                                                                                                                                                        ( ( in @ X2 @ X1 )
                                                                                                                                                                                                       => ( X1
                                                                                                                                                                                                         != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                 => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                    ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                    = X1 )
                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                      ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                     => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                        ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                          = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                       => ( X1 = X3 ) )
                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                          ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                            = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                         => ( X1 = X3 ) )
                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                            ( ( X1 = X2 )
                                                                                                                                                                                                           => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                              = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                              ( ( X1 = X2 )
                                                                                                                                                                                                             => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                  = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                               => ( ( X3 = X4 )
                                                                                                                                                                                                                 => ( X2 = X4 ) ) )
                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                  ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                    = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                                                                 => ( X1 = X2 ) )
                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                    ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                      = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                   => ( X2 = X4 ) )
                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                      ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                        = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                     => ( X2 = X4 ) )
                                                                                                                                                                                                                 => ( ! [X1: $i] :
                                                                                                                                                                                                                        ( ( iskpair @ X1 )
                                                                                                                                                                                                                       => ~ ! [X2: $i] :
                                                                                                                                                                                                                              ( ( in @ X2
                                                                                                                                                                                                                                @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                  @ ^ [X3: $i] :
                                                                                                                                                                                                                                      ( X1
                                                                                                                                                                                                                                      = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                                                             => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                  @ ^ [X3: $i] :
                                                                                                                                                                                                                                      ( X1
                                                                                                                                                                                                                                      = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                                                               != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                          ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                          = X2 )
                                                                                                                                                                                                                     => ( sP8
                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                              ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                             => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                               => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                  ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                 => ( in @ X4 @ X2 ) )
                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                       => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                          = X3 ) ) )
                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                         => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                            = X4 ) ) )
                                                                                                                                                                                                                                 => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                      ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                     => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                                                                        = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h112,assumption,
    ! [X1: $i > $o,X2: $i > $o] :
      ( ! [X3: $i,X4: $i] :
          ( ( X3 = X4 )
         => ( ( X1 @ X3 )
            = ( X2 @ X4 ) ) )
     => ( ( ~ ! [X3: $i] :
                ( ( X1 @ X3 )
               => ~ ! [X4: $i] :
                      ( ( X1 @ X4 )
                     => ( X3 = X4 ) ) ) )
        = ( ~ ! [X3: $i] :
                ( ( X2 @ X3 )
               => ~ ! [X4: $i] :
                      ( ( X2 @ X4 )
                     => ( X3 = X4 ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h113,assumption,
    ~ ( ! [X1: $i,X2: $i] :
          ( ( X1 = X2 )
         => ! [X3: $i,X4: $i] :
              ( ( X3 = X4 )
             => ( ( setadjoin @ X1 @ X3 )
                = ( setadjoin @ X2 @ X4 ) ) ) )
     => ( ! [X1: $i,X2: $i] :
            ( ( X1 = X2 )
           => ( ( powerset @ X1 )
              = ( powerset @ X2 ) ) )
       => ( ! [X1: $i,X2: $i] :
              ( ( X1 = X2 )
             => ( ( setunion @ X1 )
                = ( setunion @ X2 ) ) )
         => ( ! [X1: $i > $o] :
                ( ~ ! [X2: $i] :
                      ( ( X1 @ X2 )
                     => ~ ! [X3: $i] :
                            ( ( X1 @ X3 )
                           => ( X2 = X3 ) ) )
               => ! [X2: $i,X3: $i] :
                    ( ( X1 @ X2 )
                   => ( ( X1 @ X3 )
                     => ( X2 = X3 ) ) ) )
           => ( ! [X1: $i > $o,X2: $i > $o] :
                  ( ! [X3: $i,X4: $i] :
                      ( ( X3 = X4 )
                     => ( ( X1 @ X3 )
                        = ( X2 @ X4 ) ) )
                 => ( ~ ! [X3: $i] :
                          ( ( X1 @ X3 )
                         => ~ ! [X4: $i] :
                                ( ( X1 @ X4 )
                               => ( X3 = X4 ) ) )
                   => ( ~ ! [X3: $i] :
                            ( ( X2 @ X3 )
                           => ~ ! [X4: $i] :
                                  ( ( X2 @ X4 )
                                 => ( X3 = X4 ) ) )
                     => ( ( descr @ X1 )
                        = ( descr @ X2 ) ) ) ) )
             => ( ! [X1: $i,X2: $i] :
                    ( ( X1 = X2 )
                   => ! [X3: $i > $o,X4: $i > $o] :
                        ( ! [X5: $i] :
                            ( ( in @ X5 @ X1 )
                           => ! [X6: $i] :
                                ( ( in @ X6 @ X2 )
                               => ( ( X5 = X6 )
                                 => ( ( X3 @ X5 )
                                    = ( X4 @ X6 ) ) ) ) )
                       => ( ( dsetconstr @ X1 @ X3 )
                          = ( dsetconstr @ X2 @ X4 ) ) ) )
               => ( ! [X1: $i,X2: $i] :
                      ( ! [X3: $i] :
                          ( ( in @ X3 @ X1 )
                         => ( in @ X3 @ X2 ) )
                     => ( subset @ X1 @ X2 ) )
                 => ( ! [X1: $i,X2: $i] :
                        ( ( X1 = X2 )
                       => ( subset @ X2 @ X1 ) )
                   => ( ! [X1: $i,X2: $i] :
                          ( ( X1 = X2 )
                         => ( subset @ X1 @ X2 ) )
                     => ( ! [X1: $i,X2: $i] :
                            ( ! [X3: $i] :
                                ( ( in @ X3 @ X1 )
                               => ( in @ X3 @ X2 ) )
                           => ( subset @ X1 @ X2 ) )
                       => ( ! [X1: $i] : ( subset @ emptyset @ X1 )
                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                ( ( subset @ X1 @ X2 )
                               => ( ( in @ X3 @ X1 )
                                 => ( in @ X3 @ X2 ) ) )
                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                  ( ( subset @ X1 @ X2 )
                                 => ( ~ ( in @ X3 @ X2 )
                                   => ~ ( in @ X3 @ X1 ) ) )
                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                    ( ( in @ X3 @ X1 )
                                   => ( ~ ( in @ X3 @ X2 )
                                     => ~ ( subset @ X1 @ X2 ) ) )
                               => ( ! [X1: $i,X2: $i] :
                                      ( ~ ( subset @ X1 @ X2 )
                                     => ( X1 != X2 ) )
                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                        ( ( in @ X3 @ X1 )
                                       => ( ~ ( in @ X3 @ X2 )
                                         => ( X1 != X2 ) ) )
                                   => ( ! [X1: $i] : ( subset @ X1 @ X1 )
                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                            ( ( subset @ X1 @ X2 )
                                           => ( ( subset @ X2 @ X3 )
                                             => ( subset @ X1 @ X3 ) ) )
                                       => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) )
                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                ( ( subset @ X1 @ X3 )
                                               => ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
                                           => ( ! [X1: $i,X2: $i] :
                                                  ( ( subset @ X1 @ X2 )
                                                 => ( in @ X1 @ ( powerset @ X2 ) ) )
                                             => ( ! [X1: $i,X2: $i] :
                                                    ( ( subset @ X1 @ X2 )
                                                   => ( ( subset @ X2 @ X1 )
                                                     => ( X1 = X2 ) ) )
                                               => ( ! [X1: $i] :
                                                      ( ( subset @ X1 @ emptyset )
                                                     => ( X1 = emptyset ) )
                                                 => ( ! [X1: $i,X2: $i] :
                                                        ( ( subset @ X2 @ X1 )
                                                       => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                   => ( ! [X1: $i,X2: $i] :
                                                          ( ( in @ X2 @ ( powerset @ X1 ) )
                                                         => ( subset @ X2 @ X1 ) )
                                                     => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
                                                       => ( ! [X1: $i,X2: $i] :
                                                              ( ( subset @ X1 @ X2 )
                                                             => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
                                                         => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                                                           => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                    ( ( in @ X3 @ X1 )
                                                                   => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                               => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                        ( ( in @ X3 @ X2 )
                                                                       => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                                                          ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                         => ( ( ( in @ X3 @ X1 )
                                                                             => X4 )
                                                                           => ( ( ( in @ X3 @ X2 )
                                                                               => X4 )
                                                                             => X4 ) ) )
                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                            ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                           => ( ~ ( in @ X3 @ X1 )
                                                                             => ( in @ X3 @ X2 ) ) )
                                                                       => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                                                                         => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                  ( ( in @ X3 @ X1 )
                                                                                 => ( ( in @ X3 @ X2 )
                                                                                   => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                    ( ( subset @ X3 @ X1 )
                                                                                   => ( ( subset @ X3 @ X2 )
                                                                                     => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                      ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                     => ( in @ X3 @ X1 ) )
                                                                                 => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                          ( ( subset @ X1 @ X2 )
                                                                                         => ( ( binintersect @ X1 @ X2 )
                                                                                            = X1 ) )
                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                            ( ( ( binintersect @ X1 @ X2 )
                                                                                              = X2 )
                                                                                           => ( subset @ X2 @ X1 ) )
                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                              ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                             => ( in @ X3 @ X2 ) )
                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                ( ! [X3: $i] :
                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                   => ~ ( in @ X3 @ X2 ) )
                                                                                               => ( ( binintersect @ X1 @ X2 )
                                                                                                  = emptyset ) )
                                                                                           => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                    ( ( subset @ X2 @ X1 )
                                                                                                   => ( ( binintersect @ X1 @ X2 )
                                                                                                      = X2 ) )
                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                      ( ( ( binintersect @ X1 @ X2 )
                                                                                                        = X1 )
                                                                                                     => ( subset @ X1 @ X2 ) )
                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                        ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                                                                        = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                         => ( ~ ( in @ X3 @ X2 )
                                                                                                           => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                            ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                           => ( in @ X3 @ X1 ) )
                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                              ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                             => ~ ( in @ X3 @ X2 ) )
                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                ( ( subset @ X1 @ X2 )
                                                                                                               => ( ( setminus @ X1 @ X2 )
                                                                                                                  = emptyset ) )
                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                  ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                 => ( ( in @ X3 @ X1 )
                                                                                                                   => ( in @ X3 @ X2 ) ) )
                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                    ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                   => ( ~ ( in @ X3 @ X2 )
                                                                                                                     => ~ ( in @ X3 @ X1 ) ) )
                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                      ( ~ ( in @ X3 @ X1 )
                                                                                                                     => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                        ( ( in @ X3 @ X2 )
                                                                                                                       => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                   => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                            ( ( ( setminus @ X1 @ X2 )
                                                                                                                              = emptyset )
                                                                                                                           => ( subset @ X1 @ X2 ) )
                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                              ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                                                             => ! [X4: $o] :
                                                                                                                                  ( ( ( in @ X3 @ X1 )
                                                                                                                                   => ( ~ ( in @ X3 @ X2 )
                                                                                                                                     => X4 ) )
                                                                                                                                 => ( ( ~ ( in @ X3 @ X1 )
                                                                                                                                     => ( ( in @ X3 @ X2 )
                                                                                                                                       => X4 ) )
                                                                                                                                   => X4 ) ) )
                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                               => ( ~ ( in @ X3 @ X2 )
                                                                                                                                 => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                  ( ~ ( in @ X3 @ X1 )
                                                                                                                                 => ( ( in @ X3 @ X2 )
                                                                                                                                   => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                   => ( ( in @ X3 @ X2 )
                                                                                                                                     => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                      ( ~ ( in @ X3 @ X1 )
                                                                                                                                     => ( ~ ( in @ X3 @ X2 )
                                                                                                                                       => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                         => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                  ( ( in @ X2 @ X1 )
                                                                                                                                                 => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                    ( ( in @ X2 @ X1 )
                                                                                                                                                   => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                     => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                        ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                       => ( ( X3 != X1 )
                                                                                                                                                         => ( X3 = X2 ) ) )
                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                                                             => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                                                               => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                                                 => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                                                   => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                                                     => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                                                       => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                      ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                     => ~ ! [X4: $i] :
                                                                                                                                                                            ( ( in @ X4 @ X1 )
                                                                                                                                                                           => ! [X5: $i] :
                                                                                                                                                                                ( ( in @ X5 @ X2 )
                                                                                                                                                                               => ( X3
                                                                                                                                                                                 != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                                                                 => ( sP5
                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                          ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                                                                         => ~ ! [X3: $i] :
                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                               => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                                                                     => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                                                                       => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                         => ( ! [X1: $i] :
                                                                                                                                                                                ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                                                                = X1 )
                                                                                                                                                                           => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                  ( ! [X3: $i] :
                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                                          ( ( in @ X4 @ X1 )
                                                                                                                                                                                         => ( ( X2 @ X3 )
                                                                                                                                                                                           => ( ( X2 @ X4 )
                                                                                                                                                                                             => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                 => ( ~ ! [X3: $i] :
                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                         => ~ ( X2 @ X3 ) )
                                                                                                                                                                                   => ~ ! [X3: $i] :
                                                                                                                                                                                          ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                         => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                           != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                             => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                    ( ~ ! [X3: $i] :
                                                                                                                                                                                          ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                         => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                           != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                                                                   => ~ ! [X3: $i] :
                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                         => ~ ( X2 @ X3 ) ) )
                                                                                                                                                                               => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                     => ( ( X2 @ X3 )
                                                                                                                                                                                       => ( ! [X4: $i] :
                                                                                                                                                                                              ( ( in @ X4 @ X1 )
                                                                                                                                                                                             => ( ( X2 @ X4 )
                                                                                                                                                                                               => ( X4 = X3 ) ) )
                                                                                                                                                                                         => ~ ! [X4: $i] :
                                                                                                                                                                                                ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                               => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                 != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                        ( ! [X3: $i] :
                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                                                ( ( in @ X4 @ X1 )
                                                                                                                                                                                               => ( ( X2 @ X3 )
                                                                                                                                                                                                 => ( ( X2 @ X4 )
                                                                                                                                                                                                   => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                       => ( ~ ! [X3: $i] :
                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                               => ~ ( X2 @ X3 ) )
                                                                                                                                                                                         => ~ ! [X3: $i] :
                                                                                                                                                                                                ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                               => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                 != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                          ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                                                            = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                         => ( X1 = X2 ) )
                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                            ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                           => ( X1 = X3 ) )
                                                                                                                                                                                       => ( ! [X1: $i] :
                                                                                                                                                                                              ( ( iskpair @ X1 )
                                                                                                                                                                                             => ~ ! [X2: $i] :
                                                                                                                                                                                                    ( ( in @ X2
                                                                                                                                                                                                      @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                        @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                                                                   => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                        @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                     != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                         => ( ! [X1: $i] :
                                                                                                                                                                                                ( ~ ! [X2: $i] :
                                                                                                                                                                                                      ( ( in @ X2 @ X1 )
                                                                                                                                                                                                     => ( X1
                                                                                                                                                                                                       != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                               => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                  ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                  = X1 )
                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                    ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                   => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                      ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                        = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                     => ( X1 = X3 ) )
                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                        ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                          = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                       => ( X1 = X3 ) )
                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                          ( ( X1 = X2 )
                                                                                                                                                                                                         => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                            = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                            ( ( X1 = X2 )
                                                                                                                                                                                                           => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                              = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                              ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                             => ( ( X3 = X4 )
                                                                                                                                                                                                               => ( X2 = X4 ) ) )
                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                  = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                                                               => ( X1 = X2 ) )
                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                  ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                    = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                 => ( X2 = X4 ) )
                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                    ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                      = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                   => ( X2 = X4 ) )
                                                                                                                                                                                                               => ( ! [X1: $i] :
                                                                                                                                                                                                                      ( ( iskpair @ X1 )
                                                                                                                                                                                                                     => ~ ! [X2: $i] :
                                                                                                                                                                                                                            ( ( in @ X2
                                                                                                                                                                                                                              @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                @ ^ [X3: $i] :
                                                                                                                                                                                                                                    ( X1
                                                                                                                                                                                                                                    = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                                                           => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                @ ^ [X3: $i] :
                                                                                                                                                                                                                                    ( X1
                                                                                                                                                                                                                                    = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                                                             != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                        ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                        = X2 )
                                                                                                                                                                                                                   => ( sP8
                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                            ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                           => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                              ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                             => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                               => ( in @ X4 @ X2 ) )
                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                     => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                        = X3 ) ) )
                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                       => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                          = X4 ) ) )
                                                                                                                                                                                                                               => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                    ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                   => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                                                                      = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h114,assumption,
    ! [X1: $i,X2: $i] :
      ( ( X1 = X2 )
     => ! [X3: $i,X4: $i] :
          ( ( X3 = X4 )
         => ( ( setadjoin @ X1 @ X3 )
            = ( setadjoin @ X2 @ X4 ) ) ) ),
    introduced(assumption,[]) ).

thf(h115,assumption,
    ~ ( ! [X1: $i,X2: $i] :
          ( ( X1 = X2 )
         => ( ( powerset @ X1 )
            = ( powerset @ X2 ) ) )
     => ( ! [X1: $i,X2: $i] :
            ( ( X1 = X2 )
           => ( ( setunion @ X1 )
              = ( setunion @ X2 ) ) )
       => ( ! [X1: $i > $o] :
              ( ~ ! [X2: $i] :
                    ( ( X1 @ X2 )
                   => ~ ! [X3: $i] :
                          ( ( X1 @ X3 )
                         => ( X2 = X3 ) ) )
             => ! [X2: $i,X3: $i] :
                  ( ( X1 @ X2 )
                 => ( ( X1 @ X3 )
                   => ( X2 = X3 ) ) ) )
         => ( ! [X1: $i > $o,X2: $i > $o] :
                ( ! [X3: $i,X4: $i] :
                    ( ( X3 = X4 )
                   => ( ( X1 @ X3 )
                      = ( X2 @ X4 ) ) )
               => ( ~ ! [X3: $i] :
                        ( ( X1 @ X3 )
                       => ~ ! [X4: $i] :
                              ( ( X1 @ X4 )
                             => ( X3 = X4 ) ) )
                 => ( ~ ! [X3: $i] :
                          ( ( X2 @ X3 )
                         => ~ ! [X4: $i] :
                                ( ( X2 @ X4 )
                               => ( X3 = X4 ) ) )
                   => ( ( descr @ X1 )
                      = ( descr @ X2 ) ) ) ) )
           => ( ! [X1: $i,X2: $i] :
                  ( ( X1 = X2 )
                 => ! [X3: $i > $o,X4: $i > $o] :
                      ( ! [X5: $i] :
                          ( ( in @ X5 @ X1 )
                         => ! [X6: $i] :
                              ( ( in @ X6 @ X2 )
                             => ( ( X5 = X6 )
                               => ( ( X3 @ X5 )
                                  = ( X4 @ X6 ) ) ) ) )
                     => ( ( dsetconstr @ X1 @ X3 )
                        = ( dsetconstr @ X2 @ X4 ) ) ) )
             => ( ! [X1: $i,X2: $i] :
                    ( ! [X3: $i] :
                        ( ( in @ X3 @ X1 )
                       => ( in @ X3 @ X2 ) )
                   => ( subset @ X1 @ X2 ) )
               => ( ! [X1: $i,X2: $i] :
                      ( ( X1 = X2 )
                     => ( subset @ X2 @ X1 ) )
                 => ( ! [X1: $i,X2: $i] :
                        ( ( X1 = X2 )
                       => ( subset @ X1 @ X2 ) )
                   => ( ! [X1: $i,X2: $i] :
                          ( ! [X3: $i] :
                              ( ( in @ X3 @ X1 )
                             => ( in @ X3 @ X2 ) )
                         => ( subset @ X1 @ X2 ) )
                     => ( ! [X1: $i] : ( subset @ emptyset @ X1 )
                       => ( ! [X1: $i,X2: $i,X3: $i] :
                              ( ( subset @ X1 @ X2 )
                             => ( ( in @ X3 @ X1 )
                               => ( in @ X3 @ X2 ) ) )
                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                ( ( subset @ X1 @ X2 )
                               => ( ~ ( in @ X3 @ X2 )
                                 => ~ ( in @ X3 @ X1 ) ) )
                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                  ( ( in @ X3 @ X1 )
                                 => ( ~ ( in @ X3 @ X2 )
                                   => ~ ( subset @ X1 @ X2 ) ) )
                             => ( ! [X1: $i,X2: $i] :
                                    ( ~ ( subset @ X1 @ X2 )
                                   => ( X1 != X2 ) )
                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                      ( ( in @ X3 @ X1 )
                                     => ( ~ ( in @ X3 @ X2 )
                                       => ( X1 != X2 ) ) )
                                 => ( ! [X1: $i] : ( subset @ X1 @ X1 )
                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                          ( ( subset @ X1 @ X2 )
                                         => ( ( subset @ X2 @ X3 )
                                           => ( subset @ X1 @ X3 ) ) )
                                     => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) )
                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                              ( ( subset @ X1 @ X3 )
                                             => ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
                                         => ( ! [X1: $i,X2: $i] :
                                                ( ( subset @ X1 @ X2 )
                                               => ( in @ X1 @ ( powerset @ X2 ) ) )
                                           => ( ! [X1: $i,X2: $i] :
                                                  ( ( subset @ X1 @ X2 )
                                                 => ( ( subset @ X2 @ X1 )
                                                   => ( X1 = X2 ) ) )
                                             => ( ! [X1: $i] :
                                                    ( ( subset @ X1 @ emptyset )
                                                   => ( X1 = emptyset ) )
                                               => ( ! [X1: $i,X2: $i] :
                                                      ( ( subset @ X2 @ X1 )
                                                     => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                 => ( ! [X1: $i,X2: $i] :
                                                        ( ( in @ X2 @ ( powerset @ X1 ) )
                                                       => ( subset @ X2 @ X1 ) )
                                                   => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
                                                     => ( ! [X1: $i,X2: $i] :
                                                            ( ( subset @ X1 @ X2 )
                                                           => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
                                                       => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                                                         => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                  ( ( in @ X3 @ X1 )
                                                                 => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                             => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                      ( ( in @ X3 @ X2 )
                                                                     => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                                                        ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                       => ( ( ( in @ X3 @ X1 )
                                                                           => X4 )
                                                                         => ( ( ( in @ X3 @ X2 )
                                                                             => X4 )
                                                                           => X4 ) ) )
                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                          ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                         => ( ~ ( in @ X3 @ X1 )
                                                                           => ( in @ X3 @ X2 ) ) )
                                                                     => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                                                                       => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                ( ( in @ X3 @ X1 )
                                                                               => ( ( in @ X3 @ X2 )
                                                                                 => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                  ( ( subset @ X3 @ X1 )
                                                                                 => ( ( subset @ X3 @ X2 )
                                                                                   => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                    ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                   => ( in @ X3 @ X1 ) )
                                                                               => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                        ( ( subset @ X1 @ X2 )
                                                                                       => ( ( binintersect @ X1 @ X2 )
                                                                                          = X1 ) )
                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                          ( ( ( binintersect @ X1 @ X2 )
                                                                                            = X2 )
                                                                                         => ( subset @ X2 @ X1 ) )
                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                            ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                           => ( in @ X3 @ X2 ) )
                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                              ( ! [X3: $i] :
                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                 => ~ ( in @ X3 @ X2 ) )
                                                                                             => ( ( binintersect @ X1 @ X2 )
                                                                                                = emptyset ) )
                                                                                         => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                  ( ( subset @ X2 @ X1 )
                                                                                                 => ( ( binintersect @ X1 @ X2 )
                                                                                                    = X2 ) )
                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                    ( ( ( binintersect @ X1 @ X2 )
                                                                                                      = X1 )
                                                                                                   => ( subset @ X1 @ X2 ) )
                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                      ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                                                                      = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                       => ( ~ ( in @ X3 @ X2 )
                                                                                                         => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                          ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                         => ( in @ X3 @ X1 ) )
                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                            ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                           => ~ ( in @ X3 @ X2 ) )
                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                              ( ( subset @ X1 @ X2 )
                                                                                                             => ( ( setminus @ X1 @ X2 )
                                                                                                                = emptyset ) )
                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                               => ( ( in @ X3 @ X1 )
                                                                                                                 => ( in @ X3 @ X2 ) ) )
                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                  ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                 => ( ~ ( in @ X3 @ X2 )
                                                                                                                   => ~ ( in @ X3 @ X1 ) ) )
                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                    ( ~ ( in @ X3 @ X1 )
                                                                                                                   => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                      ( ( in @ X3 @ X2 )
                                                                                                                     => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                 => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                          ( ( ( setminus @ X1 @ X2 )
                                                                                                                            = emptyset )
                                                                                                                         => ( subset @ X1 @ X2 ) )
                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                            ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                                                           => ! [X4: $o] :
                                                                                                                                ( ( ( in @ X3 @ X1 )
                                                                                                                                 => ( ~ ( in @ X3 @ X2 )
                                                                                                                                   => X4 ) )
                                                                                                                               => ( ( ~ ( in @ X3 @ X1 )
                                                                                                                                   => ( ( in @ X3 @ X2 )
                                                                                                                                     => X4 ) )
                                                                                                                                 => X4 ) ) )
                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                             => ( ~ ( in @ X3 @ X2 )
                                                                                                                               => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                ( ~ ( in @ X3 @ X1 )
                                                                                                                               => ( ( in @ X3 @ X2 )
                                                                                                                                 => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                 => ( ( in @ X3 @ X2 )
                                                                                                                                   => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                    ( ~ ( in @ X3 @ X1 )
                                                                                                                                   => ( ~ ( in @ X3 @ X2 )
                                                                                                                                     => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                               => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                ( ( in @ X2 @ X1 )
                                                                                                                                               => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                  ( ( in @ X2 @ X1 )
                                                                                                                                                 => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                   => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                      ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                     => ( ( X3 != X1 )
                                                                                                                                                       => ( X3 = X2 ) ) )
                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                                           => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                                                             => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                                                               => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                                                 => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                                                   => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                                                     => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                    ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                   => ~ ! [X4: $i] :
                                                                                                                                                                          ( ( in @ X4 @ X1 )
                                                                                                                                                                         => ! [X5: $i] :
                                                                                                                                                                              ( ( in @ X5 @ X2 )
                                                                                                                                                                             => ( X3
                                                                                                                                                                               != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                                                               => ( sP5
                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                        ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                                                                       => ~ ! [X3: $i] :
                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                             => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                                                                   => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                                                                     => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                       => ( ! [X1: $i] :
                                                                                                                                                                              ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                                                              = X1 )
                                                                                                                                                                         => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                ( ! [X3: $i] :
                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                                        ( ( in @ X4 @ X1 )
                                                                                                                                                                                       => ( ( X2 @ X3 )
                                                                                                                                                                                         => ( ( X2 @ X4 )
                                                                                                                                                                                           => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                               => ( ~ ! [X3: $i] :
                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                       => ~ ( X2 @ X3 ) )
                                                                                                                                                                                 => ~ ! [X3: $i] :
                                                                                                                                                                                        ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                       => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                         != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                           => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                  ( ~ ! [X3: $i] :
                                                                                                                                                                                        ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                       => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                         != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                                                                 => ~ ! [X3: $i] :
                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                       => ~ ( X2 @ X3 ) ) )
                                                                                                                                                                             => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                   => ( ( X2 @ X3 )
                                                                                                                                                                                     => ( ! [X4: $i] :
                                                                                                                                                                                            ( ( in @ X4 @ X1 )
                                                                                                                                                                                           => ( ( X2 @ X4 )
                                                                                                                                                                                             => ( X4 = X3 ) ) )
                                                                                                                                                                                       => ~ ! [X4: $i] :
                                                                                                                                                                                              ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                             => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                               != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                                                               => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                      ( ! [X3: $i] :
                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                                              ( ( in @ X4 @ X1 )
                                                                                                                                                                                             => ( ( X2 @ X3 )
                                                                                                                                                                                               => ( ( X2 @ X4 )
                                                                                                                                                                                                 => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                     => ( ~ ! [X3: $i] :
                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                             => ~ ( X2 @ X3 ) )
                                                                                                                                                                                       => ~ ! [X3: $i] :
                                                                                                                                                                                              ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                             => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                               != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                        ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                                                          = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                       => ( X1 = X2 ) )
                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                          ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                         => ( X1 = X3 ) )
                                                                                                                                                                                     => ( ! [X1: $i] :
                                                                                                                                                                                            ( ( iskpair @ X1 )
                                                                                                                                                                                           => ~ ! [X2: $i] :
                                                                                                                                                                                                  ( ( in @ X2
                                                                                                                                                                                                    @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                      @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                                                                 => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                      @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                   != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                       => ( ! [X1: $i] :
                                                                                                                                                                                              ( ~ ! [X2: $i] :
                                                                                                                                                                                                    ( ( in @ X2 @ X1 )
                                                                                                                                                                                                   => ( X1
                                                                                                                                                                                                     != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                             => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                = X1 )
                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                  ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                 => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                    ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                      = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                   => ( X1 = X3 ) )
                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                      ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                        = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                     => ( X1 = X3 ) )
                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                        ( ( X1 = X2 )
                                                                                                                                                                                                       => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                          = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                          ( ( X1 = X2 )
                                                                                                                                                                                                         => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                            = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                            ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                              = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                           => ( ( X3 = X4 )
                                                                                                                                                                                                             => ( X2 = X4 ) ) )
                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                              ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                                                             => ( X1 = X2 ) )
                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                  = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                               => ( X2 = X4 ) )
                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                  ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                    = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                 => ( X2 = X4 ) )
                                                                                                                                                                                                             => ( ! [X1: $i] :
                                                                                                                                                                                                                    ( ( iskpair @ X1 )
                                                                                                                                                                                                                   => ~ ! [X2: $i] :
                                                                                                                                                                                                                          ( ( in @ X2
                                                                                                                                                                                                                            @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                              @ ^ [X3: $i] :
                                                                                                                                                                                                                                  ( X1
                                                                                                                                                                                                                                  = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                                                         => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                              @ ^ [X3: $i] :
                                                                                                                                                                                                                                  ( X1
                                                                                                                                                                                                                                  = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                                                           != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                      ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                      = X2 )
                                                                                                                                                                                                                 => ( sP8
                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                         => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                            ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                           => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                              ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                             => ( in @ X4 @ X2 ) )
                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                   => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                      = X3 ) ) )
                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                     => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                        = X4 ) ) )
                                                                                                                                                                                                                             => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                  ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                 => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                                                                    = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h116,assumption,
    ! [X1: $i,X2: $i] :
      ( ( X1 = X2 )
     => ( ( powerset @ X1 )
        = ( powerset @ X2 ) ) ),
    introduced(assumption,[]) ).

thf(h117,assumption,
    ~ ( ! [X1: $i,X2: $i] :
          ( ( X1 = X2 )
         => ( ( setunion @ X1 )
            = ( setunion @ X2 ) ) )
     => ( ! [X1: $i > $o] :
            ( ~ ! [X2: $i] :
                  ( ( X1 @ X2 )
                 => ~ ! [X3: $i] :
                        ( ( X1 @ X3 )
                       => ( X2 = X3 ) ) )
           => ! [X2: $i,X3: $i] :
                ( ( X1 @ X2 )
               => ( ( X1 @ X3 )
                 => ( X2 = X3 ) ) ) )
       => ( ! [X1: $i > $o,X2: $i > $o] :
              ( ! [X3: $i,X4: $i] :
                  ( ( X3 = X4 )
                 => ( ( X1 @ X3 )
                    = ( X2 @ X4 ) ) )
             => ( ~ ! [X3: $i] :
                      ( ( X1 @ X3 )
                     => ~ ! [X4: $i] :
                            ( ( X1 @ X4 )
                           => ( X3 = X4 ) ) )
               => ( ~ ! [X3: $i] :
                        ( ( X2 @ X3 )
                       => ~ ! [X4: $i] :
                              ( ( X2 @ X4 )
                             => ( X3 = X4 ) ) )
                 => ( ( descr @ X1 )
                    = ( descr @ X2 ) ) ) ) )
         => ( ! [X1: $i,X2: $i] :
                ( ( X1 = X2 )
               => ! [X3: $i > $o,X4: $i > $o] :
                    ( ! [X5: $i] :
                        ( ( in @ X5 @ X1 )
                       => ! [X6: $i] :
                            ( ( in @ X6 @ X2 )
                           => ( ( X5 = X6 )
                             => ( ( X3 @ X5 )
                                = ( X4 @ X6 ) ) ) ) )
                   => ( ( dsetconstr @ X1 @ X3 )
                      = ( dsetconstr @ X2 @ X4 ) ) ) )
           => ( ! [X1: $i,X2: $i] :
                  ( ! [X3: $i] :
                      ( ( in @ X3 @ X1 )
                     => ( in @ X3 @ X2 ) )
                 => ( subset @ X1 @ X2 ) )
             => ( ! [X1: $i,X2: $i] :
                    ( ( X1 = X2 )
                   => ( subset @ X2 @ X1 ) )
               => ( ! [X1: $i,X2: $i] :
                      ( ( X1 = X2 )
                     => ( subset @ X1 @ X2 ) )
                 => ( ! [X1: $i,X2: $i] :
                        ( ! [X3: $i] :
                            ( ( in @ X3 @ X1 )
                           => ( in @ X3 @ X2 ) )
                       => ( subset @ X1 @ X2 ) )
                   => ( ! [X1: $i] : ( subset @ emptyset @ X1 )
                     => ( ! [X1: $i,X2: $i,X3: $i] :
                            ( ( subset @ X1 @ X2 )
                           => ( ( in @ X3 @ X1 )
                             => ( in @ X3 @ X2 ) ) )
                       => ( ! [X1: $i,X2: $i,X3: $i] :
                              ( ( subset @ X1 @ X2 )
                             => ( ~ ( in @ X3 @ X2 )
                               => ~ ( in @ X3 @ X1 ) ) )
                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                ( ( in @ X3 @ X1 )
                               => ( ~ ( in @ X3 @ X2 )
                                 => ~ ( subset @ X1 @ X2 ) ) )
                           => ( ! [X1: $i,X2: $i] :
                                  ( ~ ( subset @ X1 @ X2 )
                                 => ( X1 != X2 ) )
                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                    ( ( in @ X3 @ X1 )
                                   => ( ~ ( in @ X3 @ X2 )
                                     => ( X1 != X2 ) ) )
                               => ( ! [X1: $i] : ( subset @ X1 @ X1 )
                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                        ( ( subset @ X1 @ X2 )
                                       => ( ( subset @ X2 @ X3 )
                                         => ( subset @ X1 @ X3 ) ) )
                                   => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) )
                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                            ( ( subset @ X1 @ X3 )
                                           => ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
                                       => ( ! [X1: $i,X2: $i] :
                                              ( ( subset @ X1 @ X2 )
                                             => ( in @ X1 @ ( powerset @ X2 ) ) )
                                         => ( ! [X1: $i,X2: $i] :
                                                ( ( subset @ X1 @ X2 )
                                               => ( ( subset @ X2 @ X1 )
                                                 => ( X1 = X2 ) ) )
                                           => ( ! [X1: $i] :
                                                  ( ( subset @ X1 @ emptyset )
                                                 => ( X1 = emptyset ) )
                                             => ( ! [X1: $i,X2: $i] :
                                                    ( ( subset @ X2 @ X1 )
                                                   => ( in @ X2 @ ( powerset @ X1 ) ) )
                                               => ( ! [X1: $i,X2: $i] :
                                                      ( ( in @ X2 @ ( powerset @ X1 ) )
                                                     => ( subset @ X2 @ X1 ) )
                                                 => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
                                                   => ( ! [X1: $i,X2: $i] :
                                                          ( ( subset @ X1 @ X2 )
                                                         => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
                                                     => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                                                       => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                ( ( in @ X3 @ X1 )
                                                               => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                           => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                    ( ( in @ X3 @ X2 )
                                                                   => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                                                      ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                     => ( ( ( in @ X3 @ X1 )
                                                                         => X4 )
                                                                       => ( ( ( in @ X3 @ X2 )
                                                                           => X4 )
                                                                         => X4 ) ) )
                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                        ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                       => ( ~ ( in @ X3 @ X1 )
                                                                         => ( in @ X3 @ X2 ) ) )
                                                                   => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                                                                     => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                              ( ( in @ X3 @ X1 )
                                                                             => ( ( in @ X3 @ X2 )
                                                                               => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                ( ( subset @ X3 @ X1 )
                                                                               => ( ( subset @ X3 @ X2 )
                                                                                 => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                  ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                 => ( in @ X3 @ X1 ) )
                                                                             => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                      ( ( subset @ X1 @ X2 )
                                                                                     => ( ( binintersect @ X1 @ X2 )
                                                                                        = X1 ) )
                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                        ( ( ( binintersect @ X1 @ X2 )
                                                                                          = X2 )
                                                                                       => ( subset @ X2 @ X1 ) )
                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                          ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                         => ( in @ X3 @ X2 ) )
                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                            ( ! [X3: $i] :
                                                                                                ( ( in @ X3 @ X1 )
                                                                                               => ~ ( in @ X3 @ X2 ) )
                                                                                           => ( ( binintersect @ X1 @ X2 )
                                                                                              = emptyset ) )
                                                                                       => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                ( ( subset @ X2 @ X1 )
                                                                                               => ( ( binintersect @ X1 @ X2 )
                                                                                                  = X2 ) )
                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                  ( ( ( binintersect @ X1 @ X2 )
                                                                                                    = X1 )
                                                                                                 => ( subset @ X1 @ X2 ) )
                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                    ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                                                                    = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                     => ( ~ ( in @ X3 @ X2 )
                                                                                                       => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                        ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                       => ( in @ X3 @ X1 ) )
                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                          ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                         => ~ ( in @ X3 @ X2 ) )
                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                            ( ( subset @ X1 @ X2 )
                                                                                                           => ( ( setminus @ X1 @ X2 )
                                                                                                              = emptyset ) )
                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                              ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                             => ( ( in @ X3 @ X1 )
                                                                                                               => ( in @ X3 @ X2 ) ) )
                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                               => ( ~ ( in @ X3 @ X2 )
                                                                                                                 => ~ ( in @ X3 @ X1 ) ) )
                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                  ( ~ ( in @ X3 @ X1 )
                                                                                                                 => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                    ( ( in @ X3 @ X2 )
                                                                                                                   => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                               => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                        ( ( ( setminus @ X1 @ X2 )
                                                                                                                          = emptyset )
                                                                                                                       => ( subset @ X1 @ X2 ) )
                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                          ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                                                         => ! [X4: $o] :
                                                                                                                              ( ( ( in @ X3 @ X1 )
                                                                                                                               => ( ~ ( in @ X3 @ X2 )
                                                                                                                                 => X4 ) )
                                                                                                                             => ( ( ~ ( in @ X3 @ X1 )
                                                                                                                                 => ( ( in @ X3 @ X2 )
                                                                                                                                   => X4 ) )
                                                                                                                               => X4 ) ) )
                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                           => ( ~ ( in @ X3 @ X2 )
                                                                                                                             => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                              ( ~ ( in @ X3 @ X1 )
                                                                                                                             => ( ( in @ X3 @ X2 )
                                                                                                                               => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                               => ( ( in @ X3 @ X2 )
                                                                                                                                 => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                  ( ~ ( in @ X3 @ X1 )
                                                                                                                                 => ( ~ ( in @ X3 @ X2 )
                                                                                                                                   => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                             => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                               => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                              ( ( in @ X2 @ X1 )
                                                                                                                                             => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                ( ( in @ X2 @ X1 )
                                                                                                                                               => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                 => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                    ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                   => ( ( X3 != X1 )
                                                                                                                                                     => ( X3 = X2 ) ) )
                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                                         => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                                           => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                                                             => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                                                               => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                                                 => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                                                   => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                  ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                 => ~ ! [X4: $i] :
                                                                                                                                                                        ( ( in @ X4 @ X1 )
                                                                                                                                                                       => ! [X5: $i] :
                                                                                                                                                                            ( ( in @ X5 @ X2 )
                                                                                                                                                                           => ( X3
                                                                                                                                                                             != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                                                             => ( sP5
                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                      ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                                                                     => ~ ! [X3: $i] :
                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                           => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                                                                 => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                                                                   => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                     => ( ! [X1: $i] :
                                                                                                                                                                            ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                                                            = X1 )
                                                                                                                                                                       => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                              ( ! [X3: $i] :
                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                                      ( ( in @ X4 @ X1 )
                                                                                                                                                                                     => ( ( X2 @ X3 )
                                                                                                                                                                                       => ( ( X2 @ X4 )
                                                                                                                                                                                         => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                             => ( ~ ! [X3: $i] :
                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                     => ~ ( X2 @ X3 ) )
                                                                                                                                                                               => ~ ! [X3: $i] :
                                                                                                                                                                                      ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                     => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                       != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                         => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                ( ~ ! [X3: $i] :
                                                                                                                                                                                      ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                     => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                       != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                                                               => ~ ! [X3: $i] :
                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                     => ~ ( X2 @ X3 ) ) )
                                                                                                                                                                           => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                 => ( ( X2 @ X3 )
                                                                                                                                                                                   => ( ! [X4: $i] :
                                                                                                                                                                                          ( ( in @ X4 @ X1 )
                                                                                                                                                                                         => ( ( X2 @ X4 )
                                                                                                                                                                                           => ( X4 = X3 ) ) )
                                                                                                                                                                                     => ~ ! [X4: $i] :
                                                                                                                                                                                            ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                           => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                             != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                                                             => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                    ( ! [X3: $i] :
                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                                            ( ( in @ X4 @ X1 )
                                                                                                                                                                                           => ( ( X2 @ X3 )
                                                                                                                                                                                             => ( ( X2 @ X4 )
                                                                                                                                                                                               => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                   => ( ~ ! [X3: $i] :
                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                           => ~ ( X2 @ X3 ) )
                                                                                                                                                                                     => ~ ! [X3: $i] :
                                                                                                                                                                                            ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                           => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                             != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                      ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                                                        = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                     => ( X1 = X2 ) )
                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                        ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                       => ( X1 = X3 ) )
                                                                                                                                                                                   => ( ! [X1: $i] :
                                                                                                                                                                                          ( ( iskpair @ X1 )
                                                                                                                                                                                         => ~ ! [X2: $i] :
                                                                                                                                                                                                ( ( in @ X2
                                                                                                                                                                                                  @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                    @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                                                               => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                    @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                 != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                     => ( ! [X1: $i] :
                                                                                                                                                                                            ( ~ ! [X2: $i] :
                                                                                                                                                                                                  ( ( in @ X2 @ X1 )
                                                                                                                                                                                                 => ( X1
                                                                                                                                                                                                   != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                           => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                              ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                              = X1 )
                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                               => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                  ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                    = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                 => ( X1 = X3 ) )
                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                    ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                      = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                   => ( X1 = X3 ) )
                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                      ( ( X1 = X2 )
                                                                                                                                                                                                     => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                        = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                        ( ( X1 = X2 )
                                                                                                                                                                                                       => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                          = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                          ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                            = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                         => ( ( X3 = X4 )
                                                                                                                                                                                                           => ( X2 = X4 ) ) )
                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                            ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                              = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                                                           => ( X1 = X2 ) )
                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                              ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                             => ( X2 = X4 ) )
                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                  = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                               => ( X2 = X4 ) )
                                                                                                                                                                                                           => ( ! [X1: $i] :
                                                                                                                                                                                                                  ( ( iskpair @ X1 )
                                                                                                                                                                                                                 => ~ ! [X2: $i] :
                                                                                                                                                                                                                        ( ( in @ X2
                                                                                                                                                                                                                          @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                            @ ^ [X3: $i] :
                                                                                                                                                                                                                                ( X1
                                                                                                                                                                                                                                = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                                                       => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                            @ ^ [X3: $i] :
                                                                                                                                                                                                                                ( X1
                                                                                                                                                                                                                                = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                                                         != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                    ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                    = X2 )
                                                                                                                                                                                                               => ( sP8
                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                       => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                          ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                         => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                            ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                           => ( in @ X4 @ X2 ) )
                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                 => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                    = X3 ) ) )
                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                   => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                      = X4 ) ) )
                                                                                                                                                                                                                           => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                               => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                                                                  = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h118,assumption,
    ! [X1: $i,X2: $i] :
      ( ( X1 = X2 )
     => ( ( setunion @ X1 )
        = ( setunion @ X2 ) ) ),
    introduced(assumption,[]) ).

thf(h119,assumption,
    ~ ( ! [X1: $i > $o] :
          ( ~ ! [X2: $i] :
                ( ( X1 @ X2 )
               => ~ ! [X3: $i] :
                      ( ( X1 @ X3 )
                     => ( X2 = X3 ) ) )
         => ! [X2: $i,X3: $i] :
              ( ( X1 @ X2 )
             => ( ( X1 @ X3 )
               => ( X2 = X3 ) ) ) )
     => ( ! [X1: $i > $o,X2: $i > $o] :
            ( ! [X3: $i,X4: $i] :
                ( ( X3 = X4 )
               => ( ( X1 @ X3 )
                  = ( X2 @ X4 ) ) )
           => ( ~ ! [X3: $i] :
                    ( ( X1 @ X3 )
                   => ~ ! [X4: $i] :
                          ( ( X1 @ X4 )
                         => ( X3 = X4 ) ) )
             => ( ~ ! [X3: $i] :
                      ( ( X2 @ X3 )
                     => ~ ! [X4: $i] :
                            ( ( X2 @ X4 )
                           => ( X3 = X4 ) ) )
               => ( ( descr @ X1 )
                  = ( descr @ X2 ) ) ) ) )
       => ( ! [X1: $i,X2: $i] :
              ( ( X1 = X2 )
             => ! [X3: $i > $o,X4: $i > $o] :
                  ( ! [X5: $i] :
                      ( ( in @ X5 @ X1 )
                     => ! [X6: $i] :
                          ( ( in @ X6 @ X2 )
                         => ( ( X5 = X6 )
                           => ( ( X3 @ X5 )
                              = ( X4 @ X6 ) ) ) ) )
                 => ( ( dsetconstr @ X1 @ X3 )
                    = ( dsetconstr @ X2 @ X4 ) ) ) )
         => ( ! [X1: $i,X2: $i] :
                ( ! [X3: $i] :
                    ( ( in @ X3 @ X1 )
                   => ( in @ X3 @ X2 ) )
               => ( subset @ X1 @ X2 ) )
           => ( ! [X1: $i,X2: $i] :
                  ( ( X1 = X2 )
                 => ( subset @ X2 @ X1 ) )
             => ( ! [X1: $i,X2: $i] :
                    ( ( X1 = X2 )
                   => ( subset @ X1 @ X2 ) )
               => ( ! [X1: $i,X2: $i] :
                      ( ! [X3: $i] :
                          ( ( in @ X3 @ X1 )
                         => ( in @ X3 @ X2 ) )
                     => ( subset @ X1 @ X2 ) )
                 => ( ! [X1: $i] : ( subset @ emptyset @ X1 )
                   => ( ! [X1: $i,X2: $i,X3: $i] :
                          ( ( subset @ X1 @ X2 )
                         => ( ( in @ X3 @ X1 )
                           => ( in @ X3 @ X2 ) ) )
                     => ( ! [X1: $i,X2: $i,X3: $i] :
                            ( ( subset @ X1 @ X2 )
                           => ( ~ ( in @ X3 @ X2 )
                             => ~ ( in @ X3 @ X1 ) ) )
                       => ( ! [X1: $i,X2: $i,X3: $i] :
                              ( ( in @ X3 @ X1 )
                             => ( ~ ( in @ X3 @ X2 )
                               => ~ ( subset @ X1 @ X2 ) ) )
                         => ( ! [X1: $i,X2: $i] :
                                ( ~ ( subset @ X1 @ X2 )
                               => ( X1 != X2 ) )
                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                  ( ( in @ X3 @ X1 )
                                 => ( ~ ( in @ X3 @ X2 )
                                   => ( X1 != X2 ) ) )
                             => ( ! [X1: $i] : ( subset @ X1 @ X1 )
                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                      ( ( subset @ X1 @ X2 )
                                     => ( ( subset @ X2 @ X3 )
                                       => ( subset @ X1 @ X3 ) ) )
                                 => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) )
                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                          ( ( subset @ X1 @ X3 )
                                         => ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
                                     => ( ! [X1: $i,X2: $i] :
                                            ( ( subset @ X1 @ X2 )
                                           => ( in @ X1 @ ( powerset @ X2 ) ) )
                                       => ( ! [X1: $i,X2: $i] :
                                              ( ( subset @ X1 @ X2 )
                                             => ( ( subset @ X2 @ X1 )
                                               => ( X1 = X2 ) ) )
                                         => ( ! [X1: $i] :
                                                ( ( subset @ X1 @ emptyset )
                                               => ( X1 = emptyset ) )
                                           => ( ! [X1: $i,X2: $i] :
                                                  ( ( subset @ X2 @ X1 )
                                                 => ( in @ X2 @ ( powerset @ X1 ) ) )
                                             => ( ! [X1: $i,X2: $i] :
                                                    ( ( in @ X2 @ ( powerset @ X1 ) )
                                                   => ( subset @ X2 @ X1 ) )
                                               => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
                                                 => ( ! [X1: $i,X2: $i] :
                                                        ( ( subset @ X1 @ X2 )
                                                       => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
                                                   => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                                                     => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                              ( ( in @ X3 @ X1 )
                                                             => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                         => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                  ( ( in @ X3 @ X2 )
                                                                 => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                                                    ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                   => ( ( ( in @ X3 @ X1 )
                                                                       => X4 )
                                                                     => ( ( ( in @ X3 @ X2 )
                                                                         => X4 )
                                                                       => X4 ) ) )
                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                      ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                     => ( ~ ( in @ X3 @ X1 )
                                                                       => ( in @ X3 @ X2 ) ) )
                                                                 => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                                                                   => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                            ( ( in @ X3 @ X1 )
                                                                           => ( ( in @ X3 @ X2 )
                                                                             => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                              ( ( subset @ X3 @ X1 )
                                                                             => ( ( subset @ X3 @ X2 )
                                                                               => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                               => ( in @ X3 @ X1 ) )
                                                                           => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                    ( ( subset @ X1 @ X2 )
                                                                                   => ( ( binintersect @ X1 @ X2 )
                                                                                      = X1 ) )
                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                      ( ( ( binintersect @ X1 @ X2 )
                                                                                        = X2 )
                                                                                     => ( subset @ X2 @ X1 ) )
                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                        ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                       => ( in @ X3 @ X2 ) )
                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                          ( ! [X3: $i] :
                                                                                              ( ( in @ X3 @ X1 )
                                                                                             => ~ ( in @ X3 @ X2 ) )
                                                                                         => ( ( binintersect @ X1 @ X2 )
                                                                                            = emptyset ) )
                                                                                     => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                              ( ( subset @ X2 @ X1 )
                                                                                             => ( ( binintersect @ X1 @ X2 )
                                                                                                = X2 ) )
                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                ( ( ( binintersect @ X1 @ X2 )
                                                                                                  = X1 )
                                                                                               => ( subset @ X1 @ X2 ) )
                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                  ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                                                                  = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                   => ( ~ ( in @ X3 @ X2 )
                                                                                                     => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                      ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                     => ( in @ X3 @ X1 ) )
                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                        ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                       => ~ ( in @ X3 @ X2 ) )
                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                          ( ( subset @ X1 @ X2 )
                                                                                                         => ( ( setminus @ X1 @ X2 )
                                                                                                            = emptyset ) )
                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                            ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                           => ( ( in @ X3 @ X1 )
                                                                                                             => ( in @ X3 @ X2 ) ) )
                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                              ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                             => ( ~ ( in @ X3 @ X2 )
                                                                                                               => ~ ( in @ X3 @ X1 ) ) )
                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                ( ~ ( in @ X3 @ X1 )
                                                                                                               => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                  ( ( in @ X3 @ X2 )
                                                                                                                 => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                             => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                      ( ( ( setminus @ X1 @ X2 )
                                                                                                                        = emptyset )
                                                                                                                     => ( subset @ X1 @ X2 ) )
                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                        ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                                                       => ! [X4: $o] :
                                                                                                                            ( ( ( in @ X3 @ X1 )
                                                                                                                             => ( ~ ( in @ X3 @ X2 )
                                                                                                                               => X4 ) )
                                                                                                                           => ( ( ~ ( in @ X3 @ X1 )
                                                                                                                               => ( ( in @ X3 @ X2 )
                                                                                                                                 => X4 ) )
                                                                                                                             => X4 ) ) )
                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                         => ( ~ ( in @ X3 @ X2 )
                                                                                                                           => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                            ( ~ ( in @ X3 @ X1 )
                                                                                                                           => ( ( in @ X3 @ X2 )
                                                                                                                             => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                             => ( ( in @ X3 @ X2 )
                                                                                                                               => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                ( ~ ( in @ X3 @ X1 )
                                                                                                                               => ( ~ ( in @ X3 @ X2 )
                                                                                                                                 => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                           => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                             => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                               => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                            ( ( in @ X2 @ X1 )
                                                                                                                                           => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                              ( ( in @ X2 @ X1 )
                                                                                                                                             => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                               => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                  ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                 => ( ( X3 != X1 )
                                                                                                                                                   => ( X3 = X2 ) ) )
                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                                       => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                                         => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                                           => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                                                             => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                                                               => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                                                 => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                               => ~ ! [X4: $i] :
                                                                                                                                                                      ( ( in @ X4 @ X1 )
                                                                                                                                                                     => ! [X5: $i] :
                                                                                                                                                                          ( ( in @ X5 @ X2 )
                                                                                                                                                                         => ( X3
                                                                                                                                                                           != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                                                           => ( sP5
                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                    ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                                                                   => ~ ! [X3: $i] :
                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                         => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                                                               => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                                                                 => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                   => ( ! [X1: $i] :
                                                                                                                                                                          ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                                                          = X1 )
                                                                                                                                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                            ( ! [X3: $i] :
                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                    ( ( in @ X4 @ X1 )
                                                                                                                                                                                   => ( ( X2 @ X3 )
                                                                                                                                                                                     => ( ( X2 @ X4 )
                                                                                                                                                                                       => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                           => ( ~ ! [X3: $i] :
                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                   => ~ ( X2 @ X3 ) )
                                                                                                                                                                             => ~ ! [X3: $i] :
                                                                                                                                                                                    ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                   => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                     != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                       => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                              ( ~ ! [X3: $i] :
                                                                                                                                                                                    ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                   => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                     != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                                                             => ~ ! [X3: $i] :
                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                   => ~ ( X2 @ X3 ) ) )
                                                                                                                                                                         => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                               => ( ( X2 @ X3 )
                                                                                                                                                                                 => ( ! [X4: $i] :
                                                                                                                                                                                        ( ( in @ X4 @ X1 )
                                                                                                                                                                                       => ( ( X2 @ X4 )
                                                                                                                                                                                         => ( X4 = X3 ) ) )
                                                                                                                                                                                   => ~ ! [X4: $i] :
                                                                                                                                                                                          ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                         => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                           != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                                                           => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                  ( ! [X3: $i] :
                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                                          ( ( in @ X4 @ X1 )
                                                                                                                                                                                         => ( ( X2 @ X3 )
                                                                                                                                                                                           => ( ( X2 @ X4 )
                                                                                                                                                                                             => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                 => ( ~ ! [X3: $i] :
                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                         => ~ ( X2 @ X3 ) )
                                                                                                                                                                                   => ~ ! [X3: $i] :
                                                                                                                                                                                          ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                         => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                           != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                    ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                                                      = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                   => ( X1 = X2 ) )
                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                      ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                     => ( X1 = X3 ) )
                                                                                                                                                                                 => ( ! [X1: $i] :
                                                                                                                                                                                        ( ( iskpair @ X1 )
                                                                                                                                                                                       => ~ ! [X2: $i] :
                                                                                                                                                                                              ( ( in @ X2
                                                                                                                                                                                                @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                  @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                                                             => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                  @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                                                               != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                   => ( ! [X1: $i] :
                                                                                                                                                                                          ( ~ ! [X2: $i] :
                                                                                                                                                                                                ( ( in @ X2 @ X1 )
                                                                                                                                                                                               => ( X1
                                                                                                                                                                                                 != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                         => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                            ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                            = X1 )
                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                              ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                             => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                  = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                               => ( X1 = X3 ) )
                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                  ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                    = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                 => ( X1 = X3 ) )
                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                    ( ( X1 = X2 )
                                                                                                                                                                                                   => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                      = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                      ( ( X1 = X2 )
                                                                                                                                                                                                     => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                        = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                        ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                          = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                       => ( ( X3 = X4 )
                                                                                                                                                                                                         => ( X2 = X4 ) ) )
                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                          ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                            = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                                                         => ( X1 = X2 ) )
                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                            ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                              = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                           => ( X2 = X4 ) )
                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                              ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                             => ( X2 = X4 ) )
                                                                                                                                                                                                         => ( ! [X1: $i] :
                                                                                                                                                                                                                ( ( iskpair @ X1 )
                                                                                                                                                                                                               => ~ ! [X2: $i] :
                                                                                                                                                                                                                      ( ( in @ X2
                                                                                                                                                                                                                        @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                          @ ^ [X3: $i] :
                                                                                                                                                                                                                              ( X1
                                                                                                                                                                                                                              = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                                                     => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                          @ ^ [X3: $i] :
                                                                                                                                                                                                                              ( X1
                                                                                                                                                                                                                              = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                                                       != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                  ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                  = X2 )
                                                                                                                                                                                                             => ( sP8
                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                      ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                     => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                        ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                       => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                          ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                         => ( in @ X4 @ X2 ) )
                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                               => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                  = X3 ) ) )
                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                 => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                    = X4 ) ) )
                                                                                                                                                                                                                         => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                              ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                             => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                                                                = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h120,assumption,
    ~ ( ! [X1: $i > $o,X2: $i > $o] :
          ( ! [X3: $i,X4: $i] :
              ( ( X3 = X4 )
             => ( ( X1 @ X3 )
                = ( X2 @ X4 ) ) )
         => ( ~ ! [X3: $i] :
                  ( ( X1 @ X3 )
                 => ~ ! [X4: $i] :
                        ( ( X1 @ X4 )
                       => ( X3 = X4 ) ) )
           => ( ~ ! [X3: $i] :
                    ( ( X2 @ X3 )
                   => ~ ! [X4: $i] :
                          ( ( X2 @ X4 )
                         => ( X3 = X4 ) ) )
             => ( ( descr @ X1 )
                = ( descr @ X2 ) ) ) ) )
     => ( ! [X1: $i,X2: $i] :
            ( ( X1 = X2 )
           => ! [X3: $i > $o,X4: $i > $o] :
                ( ! [X5: $i] :
                    ( ( in @ X5 @ X1 )
                   => ! [X6: $i] :
                        ( ( in @ X6 @ X2 )
                       => ( ( X5 = X6 )
                         => ( ( X3 @ X5 )
                            = ( X4 @ X6 ) ) ) ) )
               => ( ( dsetconstr @ X1 @ X3 )
                  = ( dsetconstr @ X2 @ X4 ) ) ) )
       => ( ! [X1: $i,X2: $i] :
              ( ! [X3: $i] :
                  ( ( in @ X3 @ X1 )
                 => ( in @ X3 @ X2 ) )
             => ( subset @ X1 @ X2 ) )
         => ( ! [X1: $i,X2: $i] :
                ( ( X1 = X2 )
               => ( subset @ X2 @ X1 ) )
           => ( ! [X1: $i,X2: $i] :
                  ( ( X1 = X2 )
                 => ( subset @ X1 @ X2 ) )
             => ( ! [X1: $i,X2: $i] :
                    ( ! [X3: $i] :
                        ( ( in @ X3 @ X1 )
                       => ( in @ X3 @ X2 ) )
                   => ( subset @ X1 @ X2 ) )
               => ( ! [X1: $i] : ( subset @ emptyset @ X1 )
                 => ( ! [X1: $i,X2: $i,X3: $i] :
                        ( ( subset @ X1 @ X2 )
                       => ( ( in @ X3 @ X1 )
                         => ( in @ X3 @ X2 ) ) )
                   => ( ! [X1: $i,X2: $i,X3: $i] :
                          ( ( subset @ X1 @ X2 )
                         => ( ~ ( in @ X3 @ X2 )
                           => ~ ( in @ X3 @ X1 ) ) )
                     => ( ! [X1: $i,X2: $i,X3: $i] :
                            ( ( in @ X3 @ X1 )
                           => ( ~ ( in @ X3 @ X2 )
                             => ~ ( subset @ X1 @ X2 ) ) )
                       => ( ! [X1: $i,X2: $i] :
                              ( ~ ( subset @ X1 @ X2 )
                             => ( X1 != X2 ) )
                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                ( ( in @ X3 @ X1 )
                               => ( ~ ( in @ X3 @ X2 )
                                 => ( X1 != X2 ) ) )
                           => ( ! [X1: $i] : ( subset @ X1 @ X1 )
                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                    ( ( subset @ X1 @ X2 )
                                   => ( ( subset @ X2 @ X3 )
                                     => ( subset @ X1 @ X3 ) ) )
                               => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) )
                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                        ( ( subset @ X1 @ X3 )
                                       => ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
                                   => ( ! [X1: $i,X2: $i] :
                                          ( ( subset @ X1 @ X2 )
                                         => ( in @ X1 @ ( powerset @ X2 ) ) )
                                     => ( ! [X1: $i,X2: $i] :
                                            ( ( subset @ X1 @ X2 )
                                           => ( ( subset @ X2 @ X1 )
                                             => ( X1 = X2 ) ) )
                                       => ( ! [X1: $i] :
                                              ( ( subset @ X1 @ emptyset )
                                             => ( X1 = emptyset ) )
                                         => ( ! [X1: $i,X2: $i] :
                                                ( ( subset @ X2 @ X1 )
                                               => ( in @ X2 @ ( powerset @ X1 ) ) )
                                           => ( ! [X1: $i,X2: $i] :
                                                  ( ( in @ X2 @ ( powerset @ X1 ) )
                                                 => ( subset @ X2 @ X1 ) )
                                             => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
                                               => ( ! [X1: $i,X2: $i] :
                                                      ( ( subset @ X1 @ X2 )
                                                     => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
                                                 => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                                                   => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                            ( ( in @ X3 @ X1 )
                                                           => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                       => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                ( ( in @ X3 @ X2 )
                                                               => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                                                  ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                 => ( ( ( in @ X3 @ X1 )
                                                                     => X4 )
                                                                   => ( ( ( in @ X3 @ X2 )
                                                                       => X4 )
                                                                     => X4 ) ) )
                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                    ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                   => ( ~ ( in @ X3 @ X1 )
                                                                     => ( in @ X3 @ X2 ) ) )
                                                               => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                                                                 => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                          ( ( in @ X3 @ X1 )
                                                                         => ( ( in @ X3 @ X2 )
                                                                           => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                            ( ( subset @ X3 @ X1 )
                                                                           => ( ( subset @ X3 @ X2 )
                                                                             => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                              ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                             => ( in @ X3 @ X1 ) )
                                                                         => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                  ( ( subset @ X1 @ X2 )
                                                                                 => ( ( binintersect @ X1 @ X2 )
                                                                                    = X1 ) )
                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                    ( ( ( binintersect @ X1 @ X2 )
                                                                                      = X2 )
                                                                                   => ( subset @ X2 @ X1 ) )
                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                      ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                     => ( in @ X3 @ X2 ) )
                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                        ( ! [X3: $i] :
                                                                                            ( ( in @ X3 @ X1 )
                                                                                           => ~ ( in @ X3 @ X2 ) )
                                                                                       => ( ( binintersect @ X1 @ X2 )
                                                                                          = emptyset ) )
                                                                                   => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                            ( ( subset @ X2 @ X1 )
                                                                                           => ( ( binintersect @ X1 @ X2 )
                                                                                              = X2 ) )
                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                              ( ( ( binintersect @ X1 @ X2 )
                                                                                                = X1 )
                                                                                             => ( subset @ X1 @ X2 ) )
                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                                                                = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                 => ( ~ ( in @ X3 @ X2 )
                                                                                                   => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                    ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                   => ( in @ X3 @ X1 ) )
                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                      ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                     => ~ ( in @ X3 @ X2 ) )
                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                        ( ( subset @ X1 @ X2 )
                                                                                                       => ( ( setminus @ X1 @ X2 )
                                                                                                          = emptyset ) )
                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                          ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                         => ( ( in @ X3 @ X1 )
                                                                                                           => ( in @ X3 @ X2 ) ) )
                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                            ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                           => ( ~ ( in @ X3 @ X2 )
                                                                                                             => ~ ( in @ X3 @ X1 ) ) )
                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                              ( ~ ( in @ X3 @ X1 )
                                                                                                             => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                ( ( in @ X3 @ X2 )
                                                                                                               => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                           => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                    ( ( ( setminus @ X1 @ X2 )
                                                                                                                      = emptyset )
                                                                                                                   => ( subset @ X1 @ X2 ) )
                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                      ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                                                     => ! [X4: $o] :
                                                                                                                          ( ( ( in @ X3 @ X1 )
                                                                                                                           => ( ~ ( in @ X3 @ X2 )
                                                                                                                             => X4 ) )
                                                                                                                         => ( ( ~ ( in @ X3 @ X1 )
                                                                                                                             => ( ( in @ X3 @ X2 )
                                                                                                                               => X4 ) )
                                                                                                                           => X4 ) ) )
                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                       => ( ~ ( in @ X3 @ X2 )
                                                                                                                         => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                          ( ~ ( in @ X3 @ X1 )
                                                                                                                         => ( ( in @ X3 @ X2 )
                                                                                                                           => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                           => ( ( in @ X3 @ X2 )
                                                                                                                             => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                              ( ~ ( in @ X3 @ X1 )
                                                                                                                             => ( ~ ( in @ X3 @ X2 )
                                                                                                                               => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                         => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                           => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                             => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                               => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                          ( ( in @ X2 @ X1 )
                                                                                                                                         => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                            ( ( in @ X2 @ X1 )
                                                                                                                                           => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                             => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                               => ( ( X3 != X1 )
                                                                                                                                                 => ( X3 = X2 ) ) )
                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                                     => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                                       => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                                         => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                                           => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                                                             => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                                                               => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                              ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                             => ~ ! [X4: $i] :
                                                                                                                                                                    ( ( in @ X4 @ X1 )
                                                                                                                                                                   => ! [X5: $i] :
                                                                                                                                                                        ( ( in @ X5 @ X2 )
                                                                                                                                                                       => ( X3
                                                                                                                                                                         != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                                                         => ( sP5
                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                  ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                                                                 => ~ ! [X3: $i] :
                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                       => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                                                             => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                                                               => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                 => ( ! [X1: $i] :
                                                                                                                                                                        ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                                                        = X1 )
                                                                                                                                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                          ( ! [X3: $i] :
                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                  ( ( in @ X4 @ X1 )
                                                                                                                                                                                 => ( ( X2 @ X3 )
                                                                                                                                                                                   => ( ( X2 @ X4 )
                                                                                                                                                                                     => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                         => ( ~ ! [X3: $i] :
                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                 => ~ ( X2 @ X3 ) )
                                                                                                                                                                           => ~ ! [X3: $i] :
                                                                                                                                                                                  ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                 => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                   != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                            ( ~ ! [X3: $i] :
                                                                                                                                                                                  ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                 => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                   != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                                                           => ~ ! [X3: $i] :
                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                 => ~ ( X2 @ X3 ) ) )
                                                                                                                                                                       => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                             => ( ( X2 @ X3 )
                                                                                                                                                                               => ( ! [X4: $i] :
                                                                                                                                                                                      ( ( in @ X4 @ X1 )
                                                                                                                                                                                     => ( ( X2 @ X4 )
                                                                                                                                                                                       => ( X4 = X3 ) ) )
                                                                                                                                                                                 => ~ ! [X4: $i] :
                                                                                                                                                                                        ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                       => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                         != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                                                         => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                ( ! [X3: $i] :
                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                                        ( ( in @ X4 @ X1 )
                                                                                                                                                                                       => ( ( X2 @ X3 )
                                                                                                                                                                                         => ( ( X2 @ X4 )
                                                                                                                                                                                           => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                               => ( ~ ! [X3: $i] :
                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                       => ~ ( X2 @ X3 ) )
                                                                                                                                                                                 => ~ ! [X3: $i] :
                                                                                                                                                                                        ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                       => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                         != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                  ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                                                    = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                 => ( X1 = X2 ) )
                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                    ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                   => ( X1 = X3 ) )
                                                                                                                                                                               => ( ! [X1: $i] :
                                                                                                                                                                                      ( ( iskpair @ X1 )
                                                                                                                                                                                     => ~ ! [X2: $i] :
                                                                                                                                                                                            ( ( in @ X2
                                                                                                                                                                                              @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                                                           => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                                                             != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                 => ( ! [X1: $i] :
                                                                                                                                                                                        ( ~ ! [X2: $i] :
                                                                                                                                                                                              ( ( in @ X2 @ X1 )
                                                                                                                                                                                             => ( X1
                                                                                                                                                                                               != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                       => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                          ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                          = X1 )
                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                            ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                           => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                              ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                             => ( X1 = X3 ) )
                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                  = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                               => ( X1 = X3 ) )
                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                  ( ( X1 = X2 )
                                                                                                                                                                                                 => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                    = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                    ( ( X1 = X2 )
                                                                                                                                                                                                   => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                      = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                      ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                        = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                     => ( ( X3 = X4 )
                                                                                                                                                                                                       => ( X2 = X4 ) ) )
                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                        ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                          = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                                                       => ( X1 = X2 ) )
                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                          ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                            = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                         => ( X2 = X4 ) )
                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                            ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                              = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                           => ( X2 = X4 ) )
                                                                                                                                                                                                       => ( ! [X1: $i] :
                                                                                                                                                                                                              ( ( iskpair @ X1 )
                                                                                                                                                                                                             => ~ ! [X2: $i] :
                                                                                                                                                                                                                    ( ( in @ X2
                                                                                                                                                                                                                      @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                        @ ^ [X3: $i] :
                                                                                                                                                                                                                            ( X1
                                                                                                                                                                                                                            = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                                                   => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                        @ ^ [X3: $i] :
                                                                                                                                                                                                                            ( X1
                                                                                                                                                                                                                            = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                                                     != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                = X2 )
                                                                                                                                                                                                           => ( sP8
                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                    ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                   => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                      ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                     => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                        ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                       => ( in @ X4 @ X2 ) )
                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                             => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                = X3 ) ) )
                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                               => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                  = X4 ) ) )
                                                                                                                                                                                                                       => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                            ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                           => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                                                              = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h121,assumption,
    ! [X1: $i > $o,X2: $i > $o] :
      ( ! [X3: $i,X4: $i] :
          ( ( X3 = X4 )
         => ( ( X1 @ X3 )
            = ( X2 @ X4 ) ) )
     => ( ~ ! [X3: $i] :
              ( ( X1 @ X3 )
             => ~ ! [X4: $i] :
                    ( ( X1 @ X4 )
                   => ( X3 = X4 ) ) )
       => ( ~ ! [X3: $i] :
                ( ( X2 @ X3 )
               => ~ ! [X4: $i] :
                      ( ( X2 @ X4 )
                     => ( X3 = X4 ) ) )
         => ( ( descr @ X1 )
            = ( descr @ X2 ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h122,assumption,
    ~ ( ! [X1: $i,X2: $i] :
          ( ( X1 = X2 )
         => ! [X3: $i > $o,X4: $i > $o] :
              ( ! [X5: $i] :
                  ( ( in @ X5 @ X1 )
                 => ! [X6: $i] :
                      ( ( in @ X6 @ X2 )
                     => ( ( X5 = X6 )
                       => ( ( X3 @ X5 )
                          = ( X4 @ X6 ) ) ) ) )
             => ( ( dsetconstr @ X1 @ X3 )
                = ( dsetconstr @ X2 @ X4 ) ) ) )
     => ( ! [X1: $i,X2: $i] :
            ( ! [X3: $i] :
                ( ( in @ X3 @ X1 )
               => ( in @ X3 @ X2 ) )
           => ( subset @ X1 @ X2 ) )
       => ( ! [X1: $i,X2: $i] :
              ( ( X1 = X2 )
             => ( subset @ X2 @ X1 ) )
         => ( ! [X1: $i,X2: $i] :
                ( ( X1 = X2 )
               => ( subset @ X1 @ X2 ) )
           => ( ! [X1: $i,X2: $i] :
                  ( ! [X3: $i] :
                      ( ( in @ X3 @ X1 )
                     => ( in @ X3 @ X2 ) )
                 => ( subset @ X1 @ X2 ) )
             => ( ! [X1: $i] : ( subset @ emptyset @ X1 )
               => ( ! [X1: $i,X2: $i,X3: $i] :
                      ( ( subset @ X1 @ X2 )
                     => ( ( in @ X3 @ X1 )
                       => ( in @ X3 @ X2 ) ) )
                 => ( ! [X1: $i,X2: $i,X3: $i] :
                        ( ( subset @ X1 @ X2 )
                       => ( ~ ( in @ X3 @ X2 )
                         => ~ ( in @ X3 @ X1 ) ) )
                   => ( ! [X1: $i,X2: $i,X3: $i] :
                          ( ( in @ X3 @ X1 )
                         => ( ~ ( in @ X3 @ X2 )
                           => ~ ( subset @ X1 @ X2 ) ) )
                     => ( ! [X1: $i,X2: $i] :
                            ( ~ ( subset @ X1 @ X2 )
                           => ( X1 != X2 ) )
                       => ( ! [X1: $i,X2: $i,X3: $i] :
                              ( ( in @ X3 @ X1 )
                             => ( ~ ( in @ X3 @ X2 )
                               => ( X1 != X2 ) ) )
                         => ( ! [X1: $i] : ( subset @ X1 @ X1 )
                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                  ( ( subset @ X1 @ X2 )
                                 => ( ( subset @ X2 @ X3 )
                                   => ( subset @ X1 @ X3 ) ) )
                             => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) )
                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                      ( ( subset @ X1 @ X3 )
                                     => ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
                                 => ( ! [X1: $i,X2: $i] :
                                        ( ( subset @ X1 @ X2 )
                                       => ( in @ X1 @ ( powerset @ X2 ) ) )
                                   => ( ! [X1: $i,X2: $i] :
                                          ( ( subset @ X1 @ X2 )
                                         => ( ( subset @ X2 @ X1 )
                                           => ( X1 = X2 ) ) )
                                     => ( ! [X1: $i] :
                                            ( ( subset @ X1 @ emptyset )
                                           => ( X1 = emptyset ) )
                                       => ( ! [X1: $i,X2: $i] :
                                              ( ( subset @ X2 @ X1 )
                                             => ( in @ X2 @ ( powerset @ X1 ) ) )
                                         => ( ! [X1: $i,X2: $i] :
                                                ( ( in @ X2 @ ( powerset @ X1 ) )
                                               => ( subset @ X2 @ X1 ) )
                                           => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
                                             => ( ! [X1: $i,X2: $i] :
                                                    ( ( subset @ X1 @ X2 )
                                                   => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
                                               => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                                                 => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                          ( ( in @ X3 @ X1 )
                                                         => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                     => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                              ( ( in @ X3 @ X2 )
                                                             => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                                                ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                               => ( ( ( in @ X3 @ X1 )
                                                                   => X4 )
                                                                 => ( ( ( in @ X3 @ X2 )
                                                                     => X4 )
                                                                   => X4 ) ) )
                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                  ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                 => ( ~ ( in @ X3 @ X1 )
                                                                   => ( in @ X3 @ X2 ) ) )
                                                             => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                                                               => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                        ( ( in @ X3 @ X1 )
                                                                       => ( ( in @ X3 @ X2 )
                                                                         => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                          ( ( subset @ X3 @ X1 )
                                                                         => ( ( subset @ X3 @ X2 )
                                                                           => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                            ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                           => ( in @ X3 @ X1 ) )
                                                                       => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                ( ( subset @ X1 @ X2 )
                                                                               => ( ( binintersect @ X1 @ X2 )
                                                                                  = X1 ) )
                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                  ( ( ( binintersect @ X1 @ X2 )
                                                                                    = X2 )
                                                                                 => ( subset @ X2 @ X1 ) )
                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                    ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                   => ( in @ X3 @ X2 ) )
                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                      ( ! [X3: $i] :
                                                                                          ( ( in @ X3 @ X1 )
                                                                                         => ~ ( in @ X3 @ X2 ) )
                                                                                     => ( ( binintersect @ X1 @ X2 )
                                                                                        = emptyset ) )
                                                                                 => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                          ( ( subset @ X2 @ X1 )
                                                                                         => ( ( binintersect @ X1 @ X2 )
                                                                                            = X2 ) )
                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                            ( ( ( binintersect @ X1 @ X2 )
                                                                                              = X1 )
                                                                                           => ( subset @ X1 @ X2 ) )
                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                              ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                                                              = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                ( ( in @ X3 @ X1 )
                                                                                               => ( ~ ( in @ X3 @ X2 )
                                                                                                 => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                  ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                 => ( in @ X3 @ X1 ) )
                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                    ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                   => ~ ( in @ X3 @ X2 ) )
                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                      ( ( subset @ X1 @ X2 )
                                                                                                     => ( ( setminus @ X1 @ X2 )
                                                                                                        = emptyset ) )
                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                        ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                       => ( ( in @ X3 @ X1 )
                                                                                                         => ( in @ X3 @ X2 ) ) )
                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                          ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                         => ( ~ ( in @ X3 @ X2 )
                                                                                                           => ~ ( in @ X3 @ X1 ) ) )
                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                            ( ~ ( in @ X3 @ X1 )
                                                                                                           => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                              ( ( in @ X3 @ X2 )
                                                                                                             => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                         => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                  ( ( ( setminus @ X1 @ X2 )
                                                                                                                    = emptyset )
                                                                                                                 => ( subset @ X1 @ X2 ) )
                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                    ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                                                   => ! [X4: $o] :
                                                                                                                        ( ( ( in @ X3 @ X1 )
                                                                                                                         => ( ~ ( in @ X3 @ X2 )
                                                                                                                           => X4 ) )
                                                                                                                       => ( ( ~ ( in @ X3 @ X1 )
                                                                                                                           => ( ( in @ X3 @ X2 )
                                                                                                                             => X4 ) )
                                                                                                                         => X4 ) ) )
                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                     => ( ~ ( in @ X3 @ X2 )
                                                                                                                       => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                        ( ~ ( in @ X3 @ X1 )
                                                                                                                       => ( ( in @ X3 @ X2 )
                                                                                                                         => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                         => ( ( in @ X3 @ X2 )
                                                                                                                           => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                            ( ~ ( in @ X3 @ X1 )
                                                                                                                           => ( ~ ( in @ X3 @ X2 )
                                                                                                                             => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                       => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                         => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                           => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                             => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                               => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                        ( ( in @ X2 @ X1 )
                                                                                                                                       => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                          ( ( in @ X2 @ X1 )
                                                                                                                                         => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                           => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                              ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                             => ( ( X3 != X1 )
                                                                                                                                               => ( X3 = X2 ) ) )
                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                                   => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                                     => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                                       => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                                         => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                                           => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                                                             => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                            ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                           => ~ ! [X4: $i] :
                                                                                                                                                                  ( ( in @ X4 @ X1 )
                                                                                                                                                                 => ! [X5: $i] :
                                                                                                                                                                      ( ( in @ X5 @ X2 )
                                                                                                                                                                     => ( X3
                                                                                                                                                                       != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                                                       => ( sP5
                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                                                               => ~ ! [X3: $i] :
                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                     => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                                                           => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                                                             => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                               => ( ! [X1: $i] :
                                                                                                                                                                      ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                                                      = X1 )
                                                                                                                                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                        ( ! [X3: $i] :
                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                                ( ( in @ X4 @ X1 )
                                                                                                                                                                               => ( ( X2 @ X3 )
                                                                                                                                                                                 => ( ( X2 @ X4 )
                                                                                                                                                                                   => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                       => ( ~ ! [X3: $i] :
                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                               => ~ ( X2 @ X3 ) )
                                                                                                                                                                         => ~ ! [X3: $i] :
                                                                                                                                                                                ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                               => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                 != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                          ( ~ ! [X3: $i] :
                                                                                                                                                                                ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                               => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                 != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                                                         => ~ ! [X3: $i] :
                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                               => ~ ( X2 @ X3 ) ) )
                                                                                                                                                                     => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                           => ( ( X2 @ X3 )
                                                                                                                                                                             => ( ! [X4: $i] :
                                                                                                                                                                                    ( ( in @ X4 @ X1 )
                                                                                                                                                                                   => ( ( X2 @ X4 )
                                                                                                                                                                                     => ( X4 = X3 ) ) )
                                                                                                                                                                               => ~ ! [X4: $i] :
                                                                                                                                                                                      ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                     => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                       != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                                                       => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                              ( ! [X3: $i] :
                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                                      ( ( in @ X4 @ X1 )
                                                                                                                                                                                     => ( ( X2 @ X3 )
                                                                                                                                                                                       => ( ( X2 @ X4 )
                                                                                                                                                                                         => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                             => ( ~ ! [X3: $i] :
                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                     => ~ ( X2 @ X3 ) )
                                                                                                                                                                               => ~ ! [X3: $i] :
                                                                                                                                                                                      ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                     => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                       != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                                                  = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                               => ( X1 = X2 ) )
                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                  ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                 => ( X1 = X3 ) )
                                                                                                                                                                             => ( ! [X1: $i] :
                                                                                                                                                                                    ( ( iskpair @ X1 )
                                                                                                                                                                                   => ~ ! [X2: $i] :
                                                                                                                                                                                          ( ( in @ X2
                                                                                                                                                                                            @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                              @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                                                         => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                              @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                                                           != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                               => ( ! [X1: $i] :
                                                                                                                                                                                      ( ~ ! [X2: $i] :
                                                                                                                                                                                            ( ( in @ X2 @ X1 )
                                                                                                                                                                                           => ( X1
                                                                                                                                                                                             != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                     => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                        ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                        = X1 )
                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                         => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                            ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                              = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                           => ( X1 = X3 ) )
                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                              ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                             => ( X1 = X3 ) )
                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                ( ( X1 = X2 )
                                                                                                                                                                                               => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                  = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                  ( ( X1 = X2 )
                                                                                                                                                                                                 => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                    = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                    ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                      = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                   => ( ( X3 = X4 )
                                                                                                                                                                                                     => ( X2 = X4 ) ) )
                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                      ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                        = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                                                     => ( X1 = X2 ) )
                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                        ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                          = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                       => ( X2 = X4 ) )
                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                          ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                            = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                         => ( X2 = X4 ) )
                                                                                                                                                                                                     => ( ! [X1: $i] :
                                                                                                                                                                                                            ( ( iskpair @ X1 )
                                                                                                                                                                                                           => ~ ! [X2: $i] :
                                                                                                                                                                                                                  ( ( in @ X2
                                                                                                                                                                                                                    @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                      @ ^ [X3: $i] :
                                                                                                                                                                                                                          ( X1
                                                                                                                                                                                                                          = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                                                 => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                      @ ^ [X3: $i] :
                                                                                                                                                                                                                          ( X1
                                                                                                                                                                                                                          = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                                                   != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                              ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                              = X2 )
                                                                                                                                                                                                         => ( sP8
                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                  ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                 => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                    ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                   => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                      ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                     => ( in @ X4 @ X2 ) )
                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                           => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                              = X3 ) ) )
                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                             => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                = X4 ) ) )
                                                                                                                                                                                                                     => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                         => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                                                            = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h123,assumption,
    ! [X1: $i,X2: $i] :
      ( ( X1 = X2 )
     => ! [X3: $i > $o,X4: $i > $o] :
          ( ! [X5: $i] :
              ( ( in @ X5 @ X1 )
             => ! [X6: $i] :
                  ( ( in @ X6 @ X2 )
                 => ( ( X5 = X6 )
                   => ( ( X3 @ X5 )
                      = ( X4 @ X6 ) ) ) ) )
         => ( ( dsetconstr @ X1 @ X3 )
            = ( dsetconstr @ X2 @ X4 ) ) ) ),
    introduced(assumption,[]) ).

thf(h124,assumption,
    ~ ( ! [X1: $i,X2: $i] :
          ( ! [X3: $i] :
              ( ( in @ X3 @ X1 )
             => ( in @ X3 @ X2 ) )
         => ( subset @ X1 @ X2 ) )
     => ( ! [X1: $i,X2: $i] :
            ( ( X1 = X2 )
           => ( subset @ X2 @ X1 ) )
       => ( ! [X1: $i,X2: $i] :
              ( ( X1 = X2 )
             => ( subset @ X1 @ X2 ) )
         => ( ! [X1: $i,X2: $i] :
                ( ! [X3: $i] :
                    ( ( in @ X3 @ X1 )
                   => ( in @ X3 @ X2 ) )
               => ( subset @ X1 @ X2 ) )
           => ( ! [X1: $i] : ( subset @ emptyset @ X1 )
             => ( ! [X1: $i,X2: $i,X3: $i] :
                    ( ( subset @ X1 @ X2 )
                   => ( ( in @ X3 @ X1 )
                     => ( in @ X3 @ X2 ) ) )
               => ( ! [X1: $i,X2: $i,X3: $i] :
                      ( ( subset @ X1 @ X2 )
                     => ( ~ ( in @ X3 @ X2 )
                       => ~ ( in @ X3 @ X1 ) ) )
                 => ( ! [X1: $i,X2: $i,X3: $i] :
                        ( ( in @ X3 @ X1 )
                       => ( ~ ( in @ X3 @ X2 )
                         => ~ ( subset @ X1 @ X2 ) ) )
                   => ( ! [X1: $i,X2: $i] :
                          ( ~ ( subset @ X1 @ X2 )
                         => ( X1 != X2 ) )
                     => ( ! [X1: $i,X2: $i,X3: $i] :
                            ( ( in @ X3 @ X1 )
                           => ( ~ ( in @ X3 @ X2 )
                             => ( X1 != X2 ) ) )
                       => ( ! [X1: $i] : ( subset @ X1 @ X1 )
                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                ( ( subset @ X1 @ X2 )
                               => ( ( subset @ X2 @ X3 )
                                 => ( subset @ X1 @ X3 ) ) )
                           => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) )
                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                    ( ( subset @ X1 @ X3 )
                                   => ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
                               => ( ! [X1: $i,X2: $i] :
                                      ( ( subset @ X1 @ X2 )
                                     => ( in @ X1 @ ( powerset @ X2 ) ) )
                                 => ( ! [X1: $i,X2: $i] :
                                        ( ( subset @ X1 @ X2 )
                                       => ( ( subset @ X2 @ X1 )
                                         => ( X1 = X2 ) ) )
                                   => ( ! [X1: $i] :
                                          ( ( subset @ X1 @ emptyset )
                                         => ( X1 = emptyset ) )
                                     => ( ! [X1: $i,X2: $i] :
                                            ( ( subset @ X2 @ X1 )
                                           => ( in @ X2 @ ( powerset @ X1 ) ) )
                                       => ( ! [X1: $i,X2: $i] :
                                              ( ( in @ X2 @ ( powerset @ X1 ) )
                                             => ( subset @ X2 @ X1 ) )
                                         => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
                                           => ( ! [X1: $i,X2: $i] :
                                                  ( ( subset @ X1 @ X2 )
                                                 => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
                                             => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                                               => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                        ( ( in @ X3 @ X1 )
                                                       => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                   => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                            ( ( in @ X3 @ X2 )
                                                           => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                                              ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                             => ( ( ( in @ X3 @ X1 )
                                                                 => X4 )
                                                               => ( ( ( in @ X3 @ X2 )
                                                                   => X4 )
                                                                 => X4 ) ) )
                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                               => ( ~ ( in @ X3 @ X1 )
                                                                 => ( in @ X3 @ X2 ) ) )
                                                           => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                                                             => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                      ( ( in @ X3 @ X1 )
                                                                     => ( ( in @ X3 @ X2 )
                                                                       => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                        ( ( subset @ X3 @ X1 )
                                                                       => ( ( subset @ X3 @ X2 )
                                                                         => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                          ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                         => ( in @ X3 @ X1 ) )
                                                                     => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                                                       => ( ! [X1: $i,X2: $i] :
                                                                              ( ( subset @ X1 @ X2 )
                                                                             => ( ( binintersect @ X1 @ X2 )
                                                                                = X1 ) )
                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                ( ( ( binintersect @ X1 @ X2 )
                                                                                  = X2 )
                                                                               => ( subset @ X2 @ X1 ) )
                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                  ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                 => ( in @ X3 @ X2 ) )
                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                    ( ! [X3: $i] :
                                                                                        ( ( in @ X3 @ X1 )
                                                                                       => ~ ( in @ X3 @ X2 ) )
                                                                                   => ( ( binintersect @ X1 @ X2 )
                                                                                      = emptyset ) )
                                                                               => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                        ( ( subset @ X2 @ X1 )
                                                                                       => ( ( binintersect @ X1 @ X2 )
                                                                                          = X2 ) )
                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                          ( ( ( binintersect @ X1 @ X2 )
                                                                                            = X1 )
                                                                                         => ( subset @ X1 @ X2 ) )
                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                            ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                                                            = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                              ( ( in @ X3 @ X1 )
                                                                                             => ( ~ ( in @ X3 @ X2 )
                                                                                               => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                               => ( in @ X3 @ X1 ) )
                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                  ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                 => ~ ( in @ X3 @ X2 ) )
                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                    ( ( subset @ X1 @ X2 )
                                                                                                   => ( ( setminus @ X1 @ X2 )
                                                                                                      = emptyset ) )
                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                      ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                     => ( ( in @ X3 @ X1 )
                                                                                                       => ( in @ X3 @ X2 ) ) )
                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                        ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                       => ( ~ ( in @ X3 @ X2 )
                                                                                                         => ~ ( in @ X3 @ X1 ) ) )
                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                          ( ~ ( in @ X3 @ X1 )
                                                                                                         => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                            ( ( in @ X3 @ X2 )
                                                                                                           => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                       => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                ( ( ( setminus @ X1 @ X2 )
                                                                                                                  = emptyset )
                                                                                                               => ( subset @ X1 @ X2 ) )
                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                  ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                                                 => ! [X4: $o] :
                                                                                                                      ( ( ( in @ X3 @ X1 )
                                                                                                                       => ( ~ ( in @ X3 @ X2 )
                                                                                                                         => X4 ) )
                                                                                                                     => ( ( ~ ( in @ X3 @ X1 )
                                                                                                                         => ( ( in @ X3 @ X2 )
                                                                                                                           => X4 ) )
                                                                                                                       => X4 ) ) )
                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                   => ( ~ ( in @ X3 @ X2 )
                                                                                                                     => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                      ( ~ ( in @ X3 @ X1 )
                                                                                                                     => ( ( in @ X3 @ X2 )
                                                                                                                       => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                       => ( ( in @ X3 @ X2 )
                                                                                                                         => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                          ( ~ ( in @ X3 @ X1 )
                                                                                                                         => ( ~ ( in @ X3 @ X2 )
                                                                                                                           => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                     => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                       => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                         => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                           => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                             => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                      ( ( in @ X2 @ X1 )
                                                                                                                                     => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                        ( ( in @ X2 @ X1 )
                                                                                                                                       => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                         => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                            ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                           => ( ( X3 != X1 )
                                                                                                                                             => ( X3 = X2 ) ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                                 => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                                   => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                                     => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                                       => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                                         => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                                           => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                         => ~ ! [X4: $i] :
                                                                                                                                                                ( ( in @ X4 @ X1 )
                                                                                                                                                               => ! [X5: $i] :
                                                                                                                                                                    ( ( in @ X5 @ X2 )
                                                                                                                                                                   => ( X3
                                                                                                                                                                     != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                                                     => ( sP5
                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                              ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                                                             => ~ ! [X3: $i] :
                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                   => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                                                         => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                                                           => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                             => ( ! [X1: $i] :
                                                                                                                                                                    ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                                                    = X1 )
                                                                                                                                                               => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                      ( ! [X3: $i] :
                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                              ( ( in @ X4 @ X1 )
                                                                                                                                                                             => ( ( X2 @ X3 )
                                                                                                                                                                               => ( ( X2 @ X4 )
                                                                                                                                                                                 => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                     => ( ~ ! [X3: $i] :
                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                             => ~ ( X2 @ X3 ) )
                                                                                                                                                                       => ~ ! [X3: $i] :
                                                                                                                                                                              ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                             => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                               != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                        ( ~ ! [X3: $i] :
                                                                                                                                                                              ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                             => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                               != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                                                       => ~ ! [X3: $i] :
                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                             => ~ ( X2 @ X3 ) ) )
                                                                                                                                                                   => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                         => ( ( X2 @ X3 )
                                                                                                                                                                           => ( ! [X4: $i] :
                                                                                                                                                                                  ( ( in @ X4 @ X1 )
                                                                                                                                                                                 => ( ( X2 @ X4 )
                                                                                                                                                                                   => ( X4 = X3 ) ) )
                                                                                                                                                                             => ~ ! [X4: $i] :
                                                                                                                                                                                    ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                   => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                     != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                            ( ! [X3: $i] :
                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                    ( ( in @ X4 @ X1 )
                                                                                                                                                                                   => ( ( X2 @ X3 )
                                                                                                                                                                                     => ( ( X2 @ X4 )
                                                                                                                                                                                       => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                           => ( ~ ! [X3: $i] :
                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                   => ~ ( X2 @ X3 ) )
                                                                                                                                                                             => ~ ! [X3: $i] :
                                                                                                                                                                                    ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                   => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                     != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                              ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                                                = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                             => ( X1 = X2 ) )
                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                               => ( X1 = X3 ) )
                                                                                                                                                                           => ( ! [X1: $i] :
                                                                                                                                                                                  ( ( iskpair @ X1 )
                                                                                                                                                                                 => ~ ! [X2: $i] :
                                                                                                                                                                                        ( ( in @ X2
                                                                                                                                                                                          @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                            @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                                                       => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                            @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                                                         != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                             => ( ! [X1: $i] :
                                                                                                                                                                                    ( ~ ! [X2: $i] :
                                                                                                                                                                                          ( ( in @ X2 @ X1 )
                                                                                                                                                                                         => ( X1
                                                                                                                                                                                           != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                   => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                      ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                      = X1 )
                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                       => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                          ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                            = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                         => ( X1 = X3 ) )
                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                            ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                              = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                           => ( X1 = X3 ) )
                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                              ( ( X1 = X2 )
                                                                                                                                                                                             => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                ( ( X1 = X2 )
                                                                                                                                                                                               => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                  = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                  ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                    = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                 => ( ( X3 = X4 )
                                                                                                                                                                                                   => ( X2 = X4 ) ) )
                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                    ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                      = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                                                   => ( X1 = X2 ) )
                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                      ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                        = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                     => ( X2 = X4 ) )
                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                        ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                          = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                       => ( X2 = X4 ) )
                                                                                                                                                                                                   => ( ! [X1: $i] :
                                                                                                                                                                                                          ( ( iskpair @ X1 )
                                                                                                                                                                                                         => ~ ! [X2: $i] :
                                                                                                                                                                                                                ( ( in @ X2
                                                                                                                                                                                                                  @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                    @ ^ [X3: $i] :
                                                                                                                                                                                                                        ( X1
                                                                                                                                                                                                                        = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                                               => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                    @ ^ [X3: $i] :
                                                                                                                                                                                                                        ( X1
                                                                                                                                                                                                                        = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                                                 != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                            ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                            = X2 )
                                                                                                                                                                                                       => ( sP8
                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                               => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                  ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                 => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                    ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                   => ( in @ X4 @ X2 ) )
                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                         => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                            = X3 ) ) )
                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                           => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                              = X4 ) ) )
                                                                                                                                                                                                                   => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                       => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                                                          = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h125,assumption,
    ! [X1: $i,X2: $i] :
      ( ! [X3: $i] :
          ( ( in @ X3 @ X1 )
         => ( in @ X3 @ X2 ) )
     => ( subset @ X1 @ X2 ) ),
    introduced(assumption,[]) ).

thf(h126,assumption,
    ~ ( ! [X1: $i,X2: $i] :
          ( ( X1 = X2 )
         => ( subset @ X2 @ X1 ) )
     => ( ! [X1: $i,X2: $i] :
            ( ( X1 = X2 )
           => ( subset @ X1 @ X2 ) )
       => ( ! [X1: $i,X2: $i] :
              ( ! [X3: $i] :
                  ( ( in @ X3 @ X1 )
                 => ( in @ X3 @ X2 ) )
             => ( subset @ X1 @ X2 ) )
         => ( ! [X1: $i] : ( subset @ emptyset @ X1 )
           => ( ! [X1: $i,X2: $i,X3: $i] :
                  ( ( subset @ X1 @ X2 )
                 => ( ( in @ X3 @ X1 )
                   => ( in @ X3 @ X2 ) ) )
             => ( ! [X1: $i,X2: $i,X3: $i] :
                    ( ( subset @ X1 @ X2 )
                   => ( ~ ( in @ X3 @ X2 )
                     => ~ ( in @ X3 @ X1 ) ) )
               => ( ! [X1: $i,X2: $i,X3: $i] :
                      ( ( in @ X3 @ X1 )
                     => ( ~ ( in @ X3 @ X2 )
                       => ~ ( subset @ X1 @ X2 ) ) )
                 => ( ! [X1: $i,X2: $i] :
                        ( ~ ( subset @ X1 @ X2 )
                       => ( X1 != X2 ) )
                   => ( ! [X1: $i,X2: $i,X3: $i] :
                          ( ( in @ X3 @ X1 )
                         => ( ~ ( in @ X3 @ X2 )
                           => ( X1 != X2 ) ) )
                     => ( ! [X1: $i] : ( subset @ X1 @ X1 )
                       => ( ! [X1: $i,X2: $i,X3: $i] :
                              ( ( subset @ X1 @ X2 )
                             => ( ( subset @ X2 @ X3 )
                               => ( subset @ X1 @ X3 ) ) )
                         => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) )
                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                  ( ( subset @ X1 @ X3 )
                                 => ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
                             => ( ! [X1: $i,X2: $i] :
                                    ( ( subset @ X1 @ X2 )
                                   => ( in @ X1 @ ( powerset @ X2 ) ) )
                               => ( ! [X1: $i,X2: $i] :
                                      ( ( subset @ X1 @ X2 )
                                     => ( ( subset @ X2 @ X1 )
                                       => ( X1 = X2 ) ) )
                                 => ( ! [X1: $i] :
                                        ( ( subset @ X1 @ emptyset )
                                       => ( X1 = emptyset ) )
                                   => ( ! [X1: $i,X2: $i] :
                                          ( ( subset @ X2 @ X1 )
                                         => ( in @ X2 @ ( powerset @ X1 ) ) )
                                     => ( ! [X1: $i,X2: $i] :
                                            ( ( in @ X2 @ ( powerset @ X1 ) )
                                           => ( subset @ X2 @ X1 ) )
                                       => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
                                         => ( ! [X1: $i,X2: $i] :
                                                ( ( subset @ X1 @ X2 )
                                               => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
                                           => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                                             => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                      ( ( in @ X3 @ X1 )
                                                     => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                 => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                          ( ( in @ X3 @ X2 )
                                                         => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                                            ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                           => ( ( ( in @ X3 @ X1 )
                                                               => X4 )
                                                             => ( ( ( in @ X3 @ X2 )
                                                                 => X4 )
                                                               => X4 ) ) )
                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                              ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                             => ( ~ ( in @ X3 @ X1 )
                                                               => ( in @ X3 @ X2 ) ) )
                                                         => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                                                           => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                    ( ( in @ X3 @ X1 )
                                                                   => ( ( in @ X3 @ X2 )
                                                                     => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                      ( ( subset @ X3 @ X1 )
                                                                     => ( ( subset @ X3 @ X2 )
                                                                       => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                        ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                       => ( in @ X3 @ X1 ) )
                                                                   => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                                                     => ( ! [X1: $i,X2: $i] :
                                                                            ( ( subset @ X1 @ X2 )
                                                                           => ( ( binintersect @ X1 @ X2 )
                                                                              = X1 ) )
                                                                       => ( ! [X1: $i,X2: $i] :
                                                                              ( ( ( binintersect @ X1 @ X2 )
                                                                                = X2 )
                                                                             => ( subset @ X2 @ X1 ) )
                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                               => ( in @ X3 @ X2 ) )
                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                  ( ! [X3: $i] :
                                                                                      ( ( in @ X3 @ X1 )
                                                                                     => ~ ( in @ X3 @ X2 ) )
                                                                                 => ( ( binintersect @ X1 @ X2 )
                                                                                    = emptyset ) )
                                                                             => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                      ( ( subset @ X2 @ X1 )
                                                                                     => ( ( binintersect @ X1 @ X2 )
                                                                                        = X2 ) )
                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                        ( ( ( binintersect @ X1 @ X2 )
                                                                                          = X1 )
                                                                                       => ( subset @ X1 @ X2 ) )
                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                          ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                                                          = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                            ( ( in @ X3 @ X1 )
                                                                                           => ( ~ ( in @ X3 @ X2 )
                                                                                             => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                              ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                             => ( in @ X3 @ X1 ) )
                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                               => ~ ( in @ X3 @ X2 ) )
                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                  ( ( subset @ X1 @ X2 )
                                                                                                 => ( ( setminus @ X1 @ X2 )
                                                                                                    = emptyset ) )
                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                    ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                   => ( ( in @ X3 @ X1 )
                                                                                                     => ( in @ X3 @ X2 ) ) )
                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                      ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                     => ( ~ ( in @ X3 @ X2 )
                                                                                                       => ~ ( in @ X3 @ X1 ) ) )
                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                        ( ~ ( in @ X3 @ X1 )
                                                                                                       => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                          ( ( in @ X3 @ X2 )
                                                                                                         => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                     => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                              ( ( ( setminus @ X1 @ X2 )
                                                                                                                = emptyset )
                                                                                                             => ( subset @ X1 @ X2 ) )
                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                                               => ! [X4: $o] :
                                                                                                                    ( ( ( in @ X3 @ X1 )
                                                                                                                     => ( ~ ( in @ X3 @ X2 )
                                                                                                                       => X4 ) )
                                                                                                                   => ( ( ~ ( in @ X3 @ X1 )
                                                                                                                       => ( ( in @ X3 @ X2 )
                                                                                                                         => X4 ) )
                                                                                                                     => X4 ) ) )
                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                 => ( ~ ( in @ X3 @ X2 )
                                                                                                                   => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                    ( ~ ( in @ X3 @ X1 )
                                                                                                                   => ( ( in @ X3 @ X2 )
                                                                                                                     => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                     => ( ( in @ X3 @ X2 )
                                                                                                                       => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                        ( ~ ( in @ X3 @ X1 )
                                                                                                                       => ( ~ ( in @ X3 @ X2 )
                                                                                                                         => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                   => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                     => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                       => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                         => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                           => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                    ( ( in @ X2 @ X1 )
                                                                                                                                   => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                      ( ( in @ X2 @ X1 )
                                                                                                                                     => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                       => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                          ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                         => ( ( X3 != X1 )
                                                                                                                                           => ( X3 = X2 ) ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                                               => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                                 => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                                   => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                                     => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                                       => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                                         => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                       => ~ ! [X4: $i] :
                                                                                                                                                              ( ( in @ X4 @ X1 )
                                                                                                                                                             => ! [X5: $i] :
                                                                                                                                                                  ( ( in @ X5 @ X2 )
                                                                                                                                                                 => ( X3
                                                                                                                                                                   != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                                                   => ( sP5
                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                            ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                                                           => ~ ! [X3: $i] :
                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                 => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                                                       => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                                                         => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                           => ( ! [X1: $i] :
                                                                                                                                                                  ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                                                  = X1 )
                                                                                                                                                             => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                    ( ! [X3: $i] :
                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                            ( ( in @ X4 @ X1 )
                                                                                                                                                                           => ( ( X2 @ X3 )
                                                                                                                                                                             => ( ( X2 @ X4 )
                                                                                                                                                                               => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                   => ( ~ ! [X3: $i] :
                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                           => ~ ( X2 @ X3 ) )
                                                                                                                                                                     => ~ ! [X3: $i] :
                                                                                                                                                                            ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                           => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                             != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                               => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                      ( ~ ! [X3: $i] :
                                                                                                                                                                            ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                           => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                             != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                                                     => ~ ! [X3: $i] :
                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                           => ~ ( X2 @ X3 ) ) )
                                                                                                                                                                 => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                       => ( ( X2 @ X3 )
                                                                                                                                                                         => ( ! [X4: $i] :
                                                                                                                                                                                ( ( in @ X4 @ X1 )
                                                                                                                                                                               => ( ( X2 @ X4 )
                                                                                                                                                                                 => ( X4 = X3 ) ) )
                                                                                                                                                                           => ~ ! [X4: $i] :
                                                                                                                                                                                  ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                 => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                   != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                          ( ! [X3: $i] :
                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                  ( ( in @ X4 @ X1 )
                                                                                                                                                                                 => ( ( X2 @ X3 )
                                                                                                                                                                                   => ( ( X2 @ X4 )
                                                                                                                                                                                     => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                         => ( ~ ! [X3: $i] :
                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                 => ~ ( X2 @ X3 ) )
                                                                                                                                                                           => ~ ! [X3: $i] :
                                                                                                                                                                                  ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                 => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                   != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                            ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                                              = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                           => ( X1 = X2 ) )
                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                              ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                             => ( X1 = X3 ) )
                                                                                                                                                                         => ( ! [X1: $i] :
                                                                                                                                                                                ( ( iskpair @ X1 )
                                                                                                                                                                               => ~ ! [X2: $i] :
                                                                                                                                                                                      ( ( in @ X2
                                                                                                                                                                                        @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                          @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                                                     => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                          @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                                                       != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                           => ( ! [X1: $i] :
                                                                                                                                                                                  ( ~ ! [X2: $i] :
                                                                                                                                                                                        ( ( in @ X2 @ X1 )
                                                                                                                                                                                       => ( X1
                                                                                                                                                                                         != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                 => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                    ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                    = X1 )
                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                      ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                     => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                        ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                          = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                       => ( X1 = X3 ) )
                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                          ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                            = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                         => ( X1 = X3 ) )
                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                            ( ( X1 = X2 )
                                                                                                                                                                                           => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                              = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                              ( ( X1 = X2 )
                                                                                                                                                                                             => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                  = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                               => ( ( X3 = X4 )
                                                                                                                                                                                                 => ( X2 = X4 ) ) )
                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                  ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                    = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                                                 => ( X1 = X2 ) )
                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                    ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                      = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                   => ( X2 = X4 ) )
                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                      ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                        = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                     => ( X2 = X4 ) )
                                                                                                                                                                                                 => ( ! [X1: $i] :
                                                                                                                                                                                                        ( ( iskpair @ X1 )
                                                                                                                                                                                                       => ~ ! [X2: $i] :
                                                                                                                                                                                                              ( ( in @ X2
                                                                                                                                                                                                                @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                  @ ^ [X3: $i] :
                                                                                                                                                                                                                      ( X1
                                                                                                                                                                                                                      = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                                             => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                  @ ^ [X3: $i] :
                                                                                                                                                                                                                      ( X1
                                                                                                                                                                                                                      = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                                               != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                          ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                          = X2 )
                                                                                                                                                                                                     => ( sP8
                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                              ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                             => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                               => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                  ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                 => ( in @ X4 @ X2 ) )
                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                       => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                          = X3 ) ) )
                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                         => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                            = X4 ) ) )
                                                                                                                                                                                                                 => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                      ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                     => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                                                        = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h127,assumption,
    ! [X1: $i,X2: $i] :
      ( ( X1 = X2 )
     => ( subset @ X2 @ X1 ) ),
    introduced(assumption,[]) ).

thf(h128,assumption,
    ~ ( ! [X1: $i,X2: $i] :
          ( ( X1 = X2 )
         => ( subset @ X1 @ X2 ) )
     => ( ! [X1: $i,X2: $i] :
            ( ! [X3: $i] :
                ( ( in @ X3 @ X1 )
               => ( in @ X3 @ X2 ) )
           => ( subset @ X1 @ X2 ) )
       => ( ! [X1: $i] : ( subset @ emptyset @ X1 )
         => ( ! [X1: $i,X2: $i,X3: $i] :
                ( ( subset @ X1 @ X2 )
               => ( ( in @ X3 @ X1 )
                 => ( in @ X3 @ X2 ) ) )
           => ( ! [X1: $i,X2: $i,X3: $i] :
                  ( ( subset @ X1 @ X2 )
                 => ( ~ ( in @ X3 @ X2 )
                   => ~ ( in @ X3 @ X1 ) ) )
             => ( ! [X1: $i,X2: $i,X3: $i] :
                    ( ( in @ X3 @ X1 )
                   => ( ~ ( in @ X3 @ X2 )
                     => ~ ( subset @ X1 @ X2 ) ) )
               => ( ! [X1: $i,X2: $i] :
                      ( ~ ( subset @ X1 @ X2 )
                     => ( X1 != X2 ) )
                 => ( ! [X1: $i,X2: $i,X3: $i] :
                        ( ( in @ X3 @ X1 )
                       => ( ~ ( in @ X3 @ X2 )
                         => ( X1 != X2 ) ) )
                   => ( ! [X1: $i] : ( subset @ X1 @ X1 )
                     => ( ! [X1: $i,X2: $i,X3: $i] :
                            ( ( subset @ X1 @ X2 )
                           => ( ( subset @ X2 @ X3 )
                             => ( subset @ X1 @ X3 ) ) )
                       => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) )
                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                ( ( subset @ X1 @ X3 )
                               => ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
                           => ( ! [X1: $i,X2: $i] :
                                  ( ( subset @ X1 @ X2 )
                                 => ( in @ X1 @ ( powerset @ X2 ) ) )
                             => ( ! [X1: $i,X2: $i] :
                                    ( ( subset @ X1 @ X2 )
                                   => ( ( subset @ X2 @ X1 )
                                     => ( X1 = X2 ) ) )
                               => ( ! [X1: $i] :
                                      ( ( subset @ X1 @ emptyset )
                                     => ( X1 = emptyset ) )
                                 => ( ! [X1: $i,X2: $i] :
                                        ( ( subset @ X2 @ X1 )
                                       => ( in @ X2 @ ( powerset @ X1 ) ) )
                                   => ( ! [X1: $i,X2: $i] :
                                          ( ( in @ X2 @ ( powerset @ X1 ) )
                                         => ( subset @ X2 @ X1 ) )
                                     => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
                                       => ( ! [X1: $i,X2: $i] :
                                              ( ( subset @ X1 @ X2 )
                                             => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
                                         => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                                           => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                    ( ( in @ X3 @ X1 )
                                                   => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                               => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                        ( ( in @ X3 @ X2 )
                                                       => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                                          ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                         => ( ( ( in @ X3 @ X1 )
                                                             => X4 )
                                                           => ( ( ( in @ X3 @ X2 )
                                                               => X4 )
                                                             => X4 ) ) )
                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                            ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                           => ( ~ ( in @ X3 @ X1 )
                                                             => ( in @ X3 @ X2 ) ) )
                                                       => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                                                         => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                  ( ( in @ X3 @ X1 )
                                                                 => ( ( in @ X3 @ X2 )
                                                                   => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                    ( ( subset @ X3 @ X1 )
                                                                   => ( ( subset @ X3 @ X2 )
                                                                     => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                      ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                     => ( in @ X3 @ X1 ) )
                                                                 => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                                                   => ( ! [X1: $i,X2: $i] :
                                                                          ( ( subset @ X1 @ X2 )
                                                                         => ( ( binintersect @ X1 @ X2 )
                                                                            = X1 ) )
                                                                     => ( ! [X1: $i,X2: $i] :
                                                                            ( ( ( binintersect @ X1 @ X2 )
                                                                              = X2 )
                                                                           => ( subset @ X2 @ X1 ) )
                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                              ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                             => ( in @ X3 @ X2 ) )
                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                ( ! [X3: $i] :
                                                                                    ( ( in @ X3 @ X1 )
                                                                                   => ~ ( in @ X3 @ X2 ) )
                                                                               => ( ( binintersect @ X1 @ X2 )
                                                                                  = emptyset ) )
                                                                           => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                    ( ( subset @ X2 @ X1 )
                                                                                   => ( ( binintersect @ X1 @ X2 )
                                                                                      = X2 ) )
                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                      ( ( ( binintersect @ X1 @ X2 )
                                                                                        = X1 )
                                                                                     => ( subset @ X1 @ X2 ) )
                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                        ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                                                        = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                          ( ( in @ X3 @ X1 )
                                                                                         => ( ~ ( in @ X3 @ X2 )
                                                                                           => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                            ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                           => ( in @ X3 @ X1 ) )
                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                              ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                             => ~ ( in @ X3 @ X2 ) )
                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                ( ( subset @ X1 @ X2 )
                                                                                               => ( ( setminus @ X1 @ X2 )
                                                                                                  = emptyset ) )
                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                  ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                 => ( ( in @ X3 @ X1 )
                                                                                                   => ( in @ X3 @ X2 ) ) )
                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                    ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                   => ( ~ ( in @ X3 @ X2 )
                                                                                                     => ~ ( in @ X3 @ X1 ) ) )
                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                      ( ~ ( in @ X3 @ X1 )
                                                                                                     => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                        ( ( in @ X3 @ X2 )
                                                                                                       => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                   => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                            ( ( ( setminus @ X1 @ X2 )
                                                                                                              = emptyset )
                                                                                                           => ( subset @ X1 @ X2 ) )
                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                              ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                                             => ! [X4: $o] :
                                                                                                                  ( ( ( in @ X3 @ X1 )
                                                                                                                   => ( ~ ( in @ X3 @ X2 )
                                                                                                                     => X4 ) )
                                                                                                                 => ( ( ~ ( in @ X3 @ X1 )
                                                                                                                     => ( ( in @ X3 @ X2 )
                                                                                                                       => X4 ) )
                                                                                                                   => X4 ) ) )
                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                               => ( ~ ( in @ X3 @ X2 )
                                                                                                                 => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                  ( ~ ( in @ X3 @ X1 )
                                                                                                                 => ( ( in @ X3 @ X2 )
                                                                                                                   => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                   => ( ( in @ X3 @ X2 )
                                                                                                                     => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                      ( ~ ( in @ X3 @ X1 )
                                                                                                                     => ( ~ ( in @ X3 @ X2 )
                                                                                                                       => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                 => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                   => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                     => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                       => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                         => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                  ( ( in @ X2 @ X1 )
                                                                                                                                 => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                    ( ( in @ X2 @ X1 )
                                                                                                                                   => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                     => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                        ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                       => ( ( X3 != X1 )
                                                                                                                                         => ( X3 = X2 ) ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                         => ! [X4: $i] :
                                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                                             => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                                               => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                                 => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                                   => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                                     => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                                       => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                      ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                     => ~ ! [X4: $i] :
                                                                                                                                                            ( ( in @ X4 @ X1 )
                                                                                                                                                           => ! [X5: $i] :
                                                                                                                                                                ( ( in @ X5 @ X2 )
                                                                                                                                                               => ( X3
                                                                                                                                                                 != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                                                 => ( sP5
                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                          ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                                                         => ~ ! [X3: $i] :
                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                               => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                                                     => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                                                       => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                         => ( ! [X1: $i] :
                                                                                                                                                                ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                                                = X1 )
                                                                                                                                                           => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                  ( ! [X3: $i] :
                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                          ( ( in @ X4 @ X1 )
                                                                                                                                                                         => ( ( X2 @ X3 )
                                                                                                                                                                           => ( ( X2 @ X4 )
                                                                                                                                                                             => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                 => ( ~ ! [X3: $i] :
                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                         => ~ ( X2 @ X3 ) )
                                                                                                                                                                   => ~ ! [X3: $i] :
                                                                                                                                                                          ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                         => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                           != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                             => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                    ( ~ ! [X3: $i] :
                                                                                                                                                                          ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                         => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                           != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                                                   => ~ ! [X3: $i] :
                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                         => ~ ( X2 @ X3 ) ) )
                                                                                                                                                               => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                     => ( ( X2 @ X3 )
                                                                                                                                                                       => ( ! [X4: $i] :
                                                                                                                                                                              ( ( in @ X4 @ X1 )
                                                                                                                                                                             => ( ( X2 @ X4 )
                                                                                                                                                                               => ( X4 = X3 ) ) )
                                                                                                                                                                         => ~ ! [X4: $i] :
                                                                                                                                                                                ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                               => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                 != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                        ( ! [X3: $i] :
                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                                ( ( in @ X4 @ X1 )
                                                                                                                                                                               => ( ( X2 @ X3 )
                                                                                                                                                                                 => ( ( X2 @ X4 )
                                                                                                                                                                                   => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                       => ( ~ ! [X3: $i] :
                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                               => ~ ( X2 @ X3 ) )
                                                                                                                                                                         => ~ ! [X3: $i] :
                                                                                                                                                                                ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                               => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                 != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                          ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                                            = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                         => ( X1 = X2 ) )
                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                            ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                           => ( X1 = X3 ) )
                                                                                                                                                                       => ( ! [X1: $i] :
                                                                                                                                                                              ( ( iskpair @ X1 )
                                                                                                                                                                             => ~ ! [X2: $i] :
                                                                                                                                                                                    ( ( in @ X2
                                                                                                                                                                                      @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                        @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                                                   => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                        @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                                                     != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                         => ( ! [X1: $i] :
                                                                                                                                                                                ( ~ ! [X2: $i] :
                                                                                                                                                                                      ( ( in @ X2 @ X1 )
                                                                                                                                                                                     => ( X1
                                                                                                                                                                                       != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                               => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                  ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                  = X1 )
                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                    ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                   => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                      ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                        = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                     => ( X1 = X3 ) )
                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                        ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                          = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                       => ( X1 = X3 ) )
                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                          ( ( X1 = X2 )
                                                                                                                                                                                         => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                            = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                            ( ( X1 = X2 )
                                                                                                                                                                                           => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                              = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                              ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                             => ( ( X3 = X4 )
                                                                                                                                                                                               => ( X2 = X4 ) ) )
                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                  = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                                               => ( X1 = X2 ) )
                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                  ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                    = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                 => ( X2 = X4 ) )
                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                    ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                      = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                   => ( X2 = X4 ) )
                                                                                                                                                                                               => ( ! [X1: $i] :
                                                                                                                                                                                                      ( ( iskpair @ X1 )
                                                                                                                                                                                                     => ~ ! [X2: $i] :
                                                                                                                                                                                                            ( ( in @ X2
                                                                                                                                                                                                              @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                @ ^ [X3: $i] :
                                                                                                                                                                                                                    ( X1
                                                                                                                                                                                                                    = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                                           => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                @ ^ [X3: $i] :
                                                                                                                                                                                                                    ( X1
                                                                                                                                                                                                                    = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                                             != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                        ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                        = X2 )
                                                                                                                                                                                                   => ( sP8
                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                            ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                           => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                              ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                             => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                               => ( in @ X4 @ X2 ) )
                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                     => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                        = X3 ) ) )
                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                       => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                          = X4 ) ) )
                                                                                                                                                                                                               => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                    ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                   => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                                                      = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h129,assumption,
    ! [X1: $i,X2: $i] :
      ( ( X1 = X2 )
     => ( subset @ X1 @ X2 ) ),
    introduced(assumption,[]) ).

thf(h130,assumption,
    ~ ( ! [X1: $i,X2: $i] :
          ( ! [X3: $i] :
              ( ( in @ X3 @ X1 )
             => ( in @ X3 @ X2 ) )
         => ( subset @ X1 @ X2 ) )
     => ( ! [X1: $i] : ( subset @ emptyset @ X1 )
       => ( ! [X1: $i,X2: $i,X3: $i] :
              ( ( subset @ X1 @ X2 )
             => ( ( in @ X3 @ X1 )
               => ( in @ X3 @ X2 ) ) )
         => ( ! [X1: $i,X2: $i,X3: $i] :
                ( ( subset @ X1 @ X2 )
               => ( ~ ( in @ X3 @ X2 )
                 => ~ ( in @ X3 @ X1 ) ) )
           => ( ! [X1: $i,X2: $i,X3: $i] :
                  ( ( in @ X3 @ X1 )
                 => ( ~ ( in @ X3 @ X2 )
                   => ~ ( subset @ X1 @ X2 ) ) )
             => ( ! [X1: $i,X2: $i] :
                    ( ~ ( subset @ X1 @ X2 )
                   => ( X1 != X2 ) )
               => ( ! [X1: $i,X2: $i,X3: $i] :
                      ( ( in @ X3 @ X1 )
                     => ( ~ ( in @ X3 @ X2 )
                       => ( X1 != X2 ) ) )
                 => ( ! [X1: $i] : ( subset @ X1 @ X1 )
                   => ( ! [X1: $i,X2: $i,X3: $i] :
                          ( ( subset @ X1 @ X2 )
                         => ( ( subset @ X2 @ X3 )
                           => ( subset @ X1 @ X3 ) ) )
                     => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) )
                       => ( ! [X1: $i,X2: $i,X3: $i] :
                              ( ( subset @ X1 @ X3 )
                             => ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
                         => ( ! [X1: $i,X2: $i] :
                                ( ( subset @ X1 @ X2 )
                               => ( in @ X1 @ ( powerset @ X2 ) ) )
                           => ( ! [X1: $i,X2: $i] :
                                  ( ( subset @ X1 @ X2 )
                                 => ( ( subset @ X2 @ X1 )
                                   => ( X1 = X2 ) ) )
                             => ( ! [X1: $i] :
                                    ( ( subset @ X1 @ emptyset )
                                   => ( X1 = emptyset ) )
                               => ( ! [X1: $i,X2: $i] :
                                      ( ( subset @ X2 @ X1 )
                                     => ( in @ X2 @ ( powerset @ X1 ) ) )
                                 => ( ! [X1: $i,X2: $i] :
                                        ( ( in @ X2 @ ( powerset @ X1 ) )
                                       => ( subset @ X2 @ X1 ) )
                                   => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
                                     => ( ! [X1: $i,X2: $i] :
                                            ( ( subset @ X1 @ X2 )
                                           => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
                                       => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                                         => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                  ( ( in @ X3 @ X1 )
                                                 => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                             => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                      ( ( in @ X3 @ X2 )
                                                     => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                                        ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                       => ( ( ( in @ X3 @ X1 )
                                                           => X4 )
                                                         => ( ( ( in @ X3 @ X2 )
                                                             => X4 )
                                                           => X4 ) ) )
                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                          ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                         => ( ~ ( in @ X3 @ X1 )
                                                           => ( in @ X3 @ X2 ) ) )
                                                     => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                                                       => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                ( ( in @ X3 @ X1 )
                                                               => ( ( in @ X3 @ X2 )
                                                                 => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                  ( ( subset @ X3 @ X1 )
                                                                 => ( ( subset @ X3 @ X2 )
                                                                   => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                    ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                   => ( in @ X3 @ X1 ) )
                                                               => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                                                 => ( ! [X1: $i,X2: $i] :
                                                                        ( ( subset @ X1 @ X2 )
                                                                       => ( ( binintersect @ X1 @ X2 )
                                                                          = X1 ) )
                                                                   => ( ! [X1: $i,X2: $i] :
                                                                          ( ( ( binintersect @ X1 @ X2 )
                                                                            = X2 )
                                                                         => ( subset @ X2 @ X1 ) )
                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                            ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                           => ( in @ X3 @ X2 ) )
                                                                       => ( ! [X1: $i,X2: $i] :
                                                                              ( ! [X3: $i] :
                                                                                  ( ( in @ X3 @ X1 )
                                                                                 => ~ ( in @ X3 @ X2 ) )
                                                                             => ( ( binintersect @ X1 @ X2 )
                                                                                = emptyset ) )
                                                                         => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                  ( ( subset @ X2 @ X1 )
                                                                                 => ( ( binintersect @ X1 @ X2 )
                                                                                    = X2 ) )
                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                    ( ( ( binintersect @ X1 @ X2 )
                                                                                      = X1 )
                                                                                   => ( subset @ X1 @ X2 ) )
                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                      ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                                                      = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                        ( ( in @ X3 @ X1 )
                                                                                       => ( ~ ( in @ X3 @ X2 )
                                                                                         => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                          ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                         => ( in @ X3 @ X1 ) )
                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                            ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                           => ~ ( in @ X3 @ X2 ) )
                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                              ( ( subset @ X1 @ X2 )
                                                                                             => ( ( setminus @ X1 @ X2 )
                                                                                                = emptyset ) )
                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                               => ( ( in @ X3 @ X1 )
                                                                                                 => ( in @ X3 @ X2 ) ) )
                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                  ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                 => ( ~ ( in @ X3 @ X2 )
                                                                                                   => ~ ( in @ X3 @ X1 ) ) )
                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                    ( ~ ( in @ X3 @ X1 )
                                                                                                   => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                      ( ( in @ X3 @ X2 )
                                                                                                     => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                 => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                          ( ( ( setminus @ X1 @ X2 )
                                                                                                            = emptyset )
                                                                                                         => ( subset @ X1 @ X2 ) )
                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                            ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                                           => ! [X4: $o] :
                                                                                                                ( ( ( in @ X3 @ X1 )
                                                                                                                 => ( ~ ( in @ X3 @ X2 )
                                                                                                                   => X4 ) )
                                                                                                               => ( ( ~ ( in @ X3 @ X1 )
                                                                                                                   => ( ( in @ X3 @ X2 )
                                                                                                                     => X4 ) )
                                                                                                                 => X4 ) ) )
                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                             => ( ~ ( in @ X3 @ X2 )
                                                                                                               => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                ( ~ ( in @ X3 @ X1 )
                                                                                                               => ( ( in @ X3 @ X2 )
                                                                                                                 => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                 => ( ( in @ X3 @ X2 )
                                                                                                                   => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                    ( ~ ( in @ X3 @ X1 )
                                                                                                                   => ( ~ ( in @ X3 @ X2 )
                                                                                                                     => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                               => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                 => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                   => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                     => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                       => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                ( ( in @ X2 @ X1 )
                                                                                                                               => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                  ( ( in @ X2 @ X1 )
                                                                                                                                 => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                   => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                      ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                     => ( ( X3 != X1 )
                                                                                                                                       => ( X3 = X2 ) ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                       => ! [X4: $i] :
                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                           => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                         => ! [X4: $i] :
                                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                                             => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                                               => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                                 => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                                   => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                                     => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                    ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                   => ~ ! [X4: $i] :
                                                                                                                                                          ( ( in @ X4 @ X1 )
                                                                                                                                                         => ! [X5: $i] :
                                                                                                                                                              ( ( in @ X5 @ X2 )
                                                                                                                                                             => ( X3
                                                                                                                                                               != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                                               => ( sP5
                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                        ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                                                       => ~ ! [X3: $i] :
                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                             => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                                                   => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                                                     => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                       => ( ! [X1: $i] :
                                                                                                                                                              ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                                              = X1 )
                                                                                                                                                         => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                ( ! [X3: $i] :
                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                        ( ( in @ X4 @ X1 )
                                                                                                                                                                       => ( ( X2 @ X3 )
                                                                                                                                                                         => ( ( X2 @ X4 )
                                                                                                                                                                           => ( X3 = X4 ) ) ) ) )
                                                                                                                                                               => ( ~ ! [X3: $i] :
                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                       => ~ ( X2 @ X3 ) )
                                                                                                                                                                 => ~ ! [X3: $i] :
                                                                                                                                                                        ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                       => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                         != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                           => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                  ( ~ ! [X3: $i] :
                                                                                                                                                                        ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                       => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                         != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                                                 => ~ ! [X3: $i] :
                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                       => ~ ( X2 @ X3 ) ) )
                                                                                                                                                             => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                   => ( ( X2 @ X3 )
                                                                                                                                                                     => ( ! [X4: $i] :
                                                                                                                                                                            ( ( in @ X4 @ X1 )
                                                                                                                                                                           => ( ( X2 @ X4 )
                                                                                                                                                                             => ( X4 = X3 ) ) )
                                                                                                                                                                       => ~ ! [X4: $i] :
                                                                                                                                                                              ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                             => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                               != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                                               => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                      ( ! [X3: $i] :
                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                              ( ( in @ X4 @ X1 )
                                                                                                                                                                             => ( ( X2 @ X3 )
                                                                                                                                                                               => ( ( X2 @ X4 )
                                                                                                                                                                                 => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                     => ( ~ ! [X3: $i] :
                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                             => ~ ( X2 @ X3 ) )
                                                                                                                                                                       => ~ ! [X3: $i] :
                                                                                                                                                                              ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                             => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                               != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                        ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                                          = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                       => ( X1 = X2 ) )
                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                          ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                         => ( X1 = X3 ) )
                                                                                                                                                                     => ( ! [X1: $i] :
                                                                                                                                                                            ( ( iskpair @ X1 )
                                                                                                                                                                           => ~ ! [X2: $i] :
                                                                                                                                                                                  ( ( in @ X2
                                                                                                                                                                                    @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                      @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                                                 => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                      @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                                                   != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                       => ( ! [X1: $i] :
                                                                                                                                                                              ( ~ ! [X2: $i] :
                                                                                                                                                                                    ( ( in @ X2 @ X1 )
                                                                                                                                                                                   => ( X1
                                                                                                                                                                                     != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                             => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                = X1 )
                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                  ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                 => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                    ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                      = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                   => ( X1 = X3 ) )
                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                      ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                        = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                     => ( X1 = X3 ) )
                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                        ( ( X1 = X2 )
                                                                                                                                                                                       => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                          = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                          ( ( X1 = X2 )
                                                                                                                                                                                         => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                            = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                            ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                              = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                           => ( ( X3 = X4 )
                                                                                                                                                                                             => ( X2 = X4 ) ) )
                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                              ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                                             => ( X1 = X2 ) )
                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                  = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                               => ( X2 = X4 ) )
                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                  ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                    = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                 => ( X2 = X4 ) )
                                                                                                                                                                                             => ( ! [X1: $i] :
                                                                                                                                                                                                    ( ( iskpair @ X1 )
                                                                                                                                                                                                   => ~ ! [X2: $i] :
                                                                                                                                                                                                          ( ( in @ X2
                                                                                                                                                                                                            @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                              @ ^ [X3: $i] :
                                                                                                                                                                                                                  ( X1
                                                                                                                                                                                                                  = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                                         => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                              @ ^ [X3: $i] :
                                                                                                                                                                                                                  ( X1
                                                                                                                                                                                                                  = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                                           != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                      ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                      = X2 )
                                                                                                                                                                                                 => ( sP8
                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                         => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                            ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                           => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                              ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                             => ( in @ X4 @ X2 ) )
                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                   => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                      = X3 ) ) )
                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                     => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                        = X4 ) ) )
                                                                                                                                                                                                             => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                  ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                 => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                                                    = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h131,assumption,
    ~ ( ! [X1: $i] : ( subset @ emptyset @ X1 )
     => ( ! [X1: $i,X2: $i,X3: $i] :
            ( ( subset @ X1 @ X2 )
           => ( ( in @ X3 @ X1 )
             => ( in @ X3 @ X2 ) ) )
       => ( ! [X1: $i,X2: $i,X3: $i] :
              ( ( subset @ X1 @ X2 )
             => ( ~ ( in @ X3 @ X2 )
               => ~ ( in @ X3 @ X1 ) ) )
         => ( ! [X1: $i,X2: $i,X3: $i] :
                ( ( in @ X3 @ X1 )
               => ( ~ ( in @ X3 @ X2 )
                 => ~ ( subset @ X1 @ X2 ) ) )
           => ( ! [X1: $i,X2: $i] :
                  ( ~ ( subset @ X1 @ X2 )
                 => ( X1 != X2 ) )
             => ( ! [X1: $i,X2: $i,X3: $i] :
                    ( ( in @ X3 @ X1 )
                   => ( ~ ( in @ X3 @ X2 )
                     => ( X1 != X2 ) ) )
               => ( ! [X1: $i] : ( subset @ X1 @ X1 )
                 => ( ! [X1: $i,X2: $i,X3: $i] :
                        ( ( subset @ X1 @ X2 )
                       => ( ( subset @ X2 @ X3 )
                         => ( subset @ X1 @ X3 ) ) )
                   => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) )
                     => ( ! [X1: $i,X2: $i,X3: $i] :
                            ( ( subset @ X1 @ X3 )
                           => ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
                       => ( ! [X1: $i,X2: $i] :
                              ( ( subset @ X1 @ X2 )
                             => ( in @ X1 @ ( powerset @ X2 ) ) )
                         => ( ! [X1: $i,X2: $i] :
                                ( ( subset @ X1 @ X2 )
                               => ( ( subset @ X2 @ X1 )
                                 => ( X1 = X2 ) ) )
                           => ( ! [X1: $i] :
                                  ( ( subset @ X1 @ emptyset )
                                 => ( X1 = emptyset ) )
                             => ( ! [X1: $i,X2: $i] :
                                    ( ( subset @ X2 @ X1 )
                                   => ( in @ X2 @ ( powerset @ X1 ) ) )
                               => ( ! [X1: $i,X2: $i] :
                                      ( ( in @ X2 @ ( powerset @ X1 ) )
                                     => ( subset @ X2 @ X1 ) )
                                 => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
                                   => ( ! [X1: $i,X2: $i] :
                                          ( ( subset @ X1 @ X2 )
                                         => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
                                     => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                                       => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                ( ( in @ X3 @ X1 )
                                               => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                           => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                    ( ( in @ X3 @ X2 )
                                                   => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                                      ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                     => ( ( ( in @ X3 @ X1 )
                                                         => X4 )
                                                       => ( ( ( in @ X3 @ X2 )
                                                           => X4 )
                                                         => X4 ) ) )
                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                        ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                       => ( ~ ( in @ X3 @ X1 )
                                                         => ( in @ X3 @ X2 ) ) )
                                                   => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                                                     => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                              ( ( in @ X3 @ X1 )
                                                             => ( ( in @ X3 @ X2 )
                                                               => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                ( ( subset @ X3 @ X1 )
                                                               => ( ( subset @ X3 @ X2 )
                                                                 => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                  ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                 => ( in @ X3 @ X1 ) )
                                                             => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                                               => ( ! [X1: $i,X2: $i] :
                                                                      ( ( subset @ X1 @ X2 )
                                                                     => ( ( binintersect @ X1 @ X2 )
                                                                        = X1 ) )
                                                                 => ( ! [X1: $i,X2: $i] :
                                                                        ( ( ( binintersect @ X1 @ X2 )
                                                                          = X2 )
                                                                       => ( subset @ X2 @ X1 ) )
                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                          ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                         => ( in @ X3 @ X2 ) )
                                                                     => ( ! [X1: $i,X2: $i] :
                                                                            ( ! [X3: $i] :
                                                                                ( ( in @ X3 @ X1 )
                                                                               => ~ ( in @ X3 @ X2 ) )
                                                                           => ( ( binintersect @ X1 @ X2 )
                                                                              = emptyset ) )
                                                                       => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                ( ( subset @ X2 @ X1 )
                                                                               => ( ( binintersect @ X1 @ X2 )
                                                                                  = X2 ) )
                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                  ( ( ( binintersect @ X1 @ X2 )
                                                                                    = X1 )
                                                                                 => ( subset @ X1 @ X2 ) )
                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                    ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                                                    = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                      ( ( in @ X3 @ X1 )
                                                                                     => ( ~ ( in @ X3 @ X2 )
                                                                                       => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                        ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                       => ( in @ X3 @ X1 ) )
                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                          ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                         => ~ ( in @ X3 @ X2 ) )
                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                            ( ( subset @ X1 @ X2 )
                                                                                           => ( ( setminus @ X1 @ X2 )
                                                                                              = emptyset ) )
                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                              ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                             => ( ( in @ X3 @ X1 )
                                                                                               => ( in @ X3 @ X2 ) ) )
                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                               => ( ~ ( in @ X3 @ X2 )
                                                                                                 => ~ ( in @ X3 @ X1 ) ) )
                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                  ( ~ ( in @ X3 @ X1 )
                                                                                                 => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                    ( ( in @ X3 @ X2 )
                                                                                                   => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                               => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                        ( ( ( setminus @ X1 @ X2 )
                                                                                                          = emptyset )
                                                                                                       => ( subset @ X1 @ X2 ) )
                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                          ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                                         => ! [X4: $o] :
                                                                                                              ( ( ( in @ X3 @ X1 )
                                                                                                               => ( ~ ( in @ X3 @ X2 )
                                                                                                                 => X4 ) )
                                                                                                             => ( ( ~ ( in @ X3 @ X1 )
                                                                                                                 => ( ( in @ X3 @ X2 )
                                                                                                                   => X4 ) )
                                                                                                               => X4 ) ) )
                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                           => ( ~ ( in @ X3 @ X2 )
                                                                                                             => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                              ( ~ ( in @ X3 @ X1 )
                                                                                                             => ( ( in @ X3 @ X2 )
                                                                                                               => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                               => ( ( in @ X3 @ X2 )
                                                                                                                 => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                  ( ~ ( in @ X3 @ X1 )
                                                                                                                 => ( ~ ( in @ X3 @ X2 )
                                                                                                                   => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                             => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                               => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                 => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                   => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                     => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                              ( ( in @ X2 @ X1 )
                                                                                                                             => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                ( ( in @ X2 @ X1 )
                                                                                                                               => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                 => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                    ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                   => ( ( X3 != X1 )
                                                                                                                                     => ( X3 = X2 ) ) )
                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                     => ! [X4: $i] :
                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                         => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                       => ! [X4: $i] :
                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                           => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                         => ! [X4: $i] :
                                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                                             => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                                               => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                                 => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                                   => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                  ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                 => ~ ! [X4: $i] :
                                                                                                                                                        ( ( in @ X4 @ X1 )
                                                                                                                                                       => ! [X5: $i] :
                                                                                                                                                            ( ( in @ X5 @ X2 )
                                                                                                                                                           => ( X3
                                                                                                                                                             != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                                             => ( sP5
                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                      ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                                                     => ~ ! [X3: $i] :
                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                           => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                                                 => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                                                   => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                     => ( ! [X1: $i] :
                                                                                                                                                            ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                                            = X1 )
                                                                                                                                                       => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                              ( ! [X3: $i] :
                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                      ( ( in @ X4 @ X1 )
                                                                                                                                                                     => ( ( X2 @ X3 )
                                                                                                                                                                       => ( ( X2 @ X4 )
                                                                                                                                                                         => ( X3 = X4 ) ) ) ) )
                                                                                                                                                             => ( ~ ! [X3: $i] :
                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                     => ~ ( X2 @ X3 ) )
                                                                                                                                                               => ~ ! [X3: $i] :
                                                                                                                                                                      ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                     => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                       != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                         => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                ( ~ ! [X3: $i] :
                                                                                                                                                                      ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                     => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                       != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                                               => ~ ! [X3: $i] :
                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                     => ~ ( X2 @ X3 ) ) )
                                                                                                                                                           => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                 => ( ( X2 @ X3 )
                                                                                                                                                                   => ( ! [X4: $i] :
                                                                                                                                                                          ( ( in @ X4 @ X1 )
                                                                                                                                                                         => ( ( X2 @ X4 )
                                                                                                                                                                           => ( X4 = X3 ) ) )
                                                                                                                                                                     => ~ ! [X4: $i] :
                                                                                                                                                                            ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                           => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                             != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                                             => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                    ( ! [X3: $i] :
                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                            ( ( in @ X4 @ X1 )
                                                                                                                                                                           => ( ( X2 @ X3 )
                                                                                                                                                                             => ( ( X2 @ X4 )
                                                                                                                                                                               => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                   => ( ~ ! [X3: $i] :
                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                           => ~ ( X2 @ X3 ) )
                                                                                                                                                                     => ~ ! [X3: $i] :
                                                                                                                                                                            ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                           => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                             != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                      ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                                        = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                     => ( X1 = X2 ) )
                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                        ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                       => ( X1 = X3 ) )
                                                                                                                                                                   => ( ! [X1: $i] :
                                                                                                                                                                          ( ( iskpair @ X1 )
                                                                                                                                                                         => ~ ! [X2: $i] :
                                                                                                                                                                                ( ( in @ X2
                                                                                                                                                                                  @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                    @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                                               => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                    @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                                                 != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                     => ( ! [X1: $i] :
                                                                                                                                                                            ( ~ ! [X2: $i] :
                                                                                                                                                                                  ( ( in @ X2 @ X1 )
                                                                                                                                                                                 => ( X1
                                                                                                                                                                                   != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                           => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                              ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                              = X1 )
                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                               => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                  ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                    = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                 => ( X1 = X3 ) )
                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                    ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                      = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                   => ( X1 = X3 ) )
                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                      ( ( X1 = X2 )
                                                                                                                                                                                     => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                        = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                        ( ( X1 = X2 )
                                                                                                                                                                                       => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                          = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                          ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                            = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                         => ( ( X3 = X4 )
                                                                                                                                                                                           => ( X2 = X4 ) ) )
                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                            ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                              = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                                           => ( X1 = X2 ) )
                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                              ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                             => ( X2 = X4 ) )
                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                  = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                               => ( X2 = X4 ) )
                                                                                                                                                                                           => ( ! [X1: $i] :
                                                                                                                                                                                                  ( ( iskpair @ X1 )
                                                                                                                                                                                                 => ~ ! [X2: $i] :
                                                                                                                                                                                                        ( ( in @ X2
                                                                                                                                                                                                          @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                            @ ^ [X3: $i] :
                                                                                                                                                                                                                ( X1
                                                                                                                                                                                                                = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                                       => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                            @ ^ [X3: $i] :
                                                                                                                                                                                                                ( X1
                                                                                                                                                                                                                = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                                         != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                    ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                    = X2 )
                                                                                                                                                                                               => ( sP8
                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                       => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                          ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                         => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                            ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                           => ( in @ X4 @ X2 ) )
                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                 => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                    = X3 ) ) )
                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                   => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                      = X4 ) ) )
                                                                                                                                                                                                           => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                               => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                                                  = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h132,assumption,
    ! [X1: $i] : ( subset @ emptyset @ X1 ),
    introduced(assumption,[]) ).

thf(h133,assumption,
    ~ ( ! [X1: $i,X2: $i,X3: $i] :
          ( ( subset @ X1 @ X2 )
         => ( ( in @ X3 @ X1 )
           => ( in @ X3 @ X2 ) ) )
     => ( ! [X1: $i,X2: $i,X3: $i] :
            ( ( subset @ X1 @ X2 )
           => ( ~ ( in @ X3 @ X2 )
             => ~ ( in @ X3 @ X1 ) ) )
       => ( ! [X1: $i,X2: $i,X3: $i] :
              ( ( in @ X3 @ X1 )
             => ( ~ ( in @ X3 @ X2 )
               => ~ ( subset @ X1 @ X2 ) ) )
         => ( ! [X1: $i,X2: $i] :
                ( ~ ( subset @ X1 @ X2 )
               => ( X1 != X2 ) )
           => ( ! [X1: $i,X2: $i,X3: $i] :
                  ( ( in @ X3 @ X1 )
                 => ( ~ ( in @ X3 @ X2 )
                   => ( X1 != X2 ) ) )
             => ( ! [X1: $i] : ( subset @ X1 @ X1 )
               => ( ! [X1: $i,X2: $i,X3: $i] :
                      ( ( subset @ X1 @ X2 )
                     => ( ( subset @ X2 @ X3 )
                       => ( subset @ X1 @ X3 ) ) )
                 => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) )
                   => ( ! [X1: $i,X2: $i,X3: $i] :
                          ( ( subset @ X1 @ X3 )
                         => ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
                     => ( ! [X1: $i,X2: $i] :
                            ( ( subset @ X1 @ X2 )
                           => ( in @ X1 @ ( powerset @ X2 ) ) )
                       => ( ! [X1: $i,X2: $i] :
                              ( ( subset @ X1 @ X2 )
                             => ( ( subset @ X2 @ X1 )
                               => ( X1 = X2 ) ) )
                         => ( ! [X1: $i] :
                                ( ( subset @ X1 @ emptyset )
                               => ( X1 = emptyset ) )
                           => ( ! [X1: $i,X2: $i] :
                                  ( ( subset @ X2 @ X1 )
                                 => ( in @ X2 @ ( powerset @ X1 ) ) )
                             => ( ! [X1: $i,X2: $i] :
                                    ( ( in @ X2 @ ( powerset @ X1 ) )
                                   => ( subset @ X2 @ X1 ) )
                               => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
                                 => ( ! [X1: $i,X2: $i] :
                                        ( ( subset @ X1 @ X2 )
                                       => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
                                   => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                                     => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                              ( ( in @ X3 @ X1 )
                                             => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                         => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                  ( ( in @ X3 @ X2 )
                                                 => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                                    ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                   => ( ( ( in @ X3 @ X1 )
                                                       => X4 )
                                                     => ( ( ( in @ X3 @ X2 )
                                                         => X4 )
                                                       => X4 ) ) )
                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                      ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                     => ( ~ ( in @ X3 @ X1 )
                                                       => ( in @ X3 @ X2 ) ) )
                                                 => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                                                   => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                            ( ( in @ X3 @ X1 )
                                                           => ( ( in @ X3 @ X2 )
                                                             => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                              ( ( subset @ X3 @ X1 )
                                                             => ( ( subset @ X3 @ X2 )
                                                               => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                               => ( in @ X3 @ X1 ) )
                                                           => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                                             => ( ! [X1: $i,X2: $i] :
                                                                    ( ( subset @ X1 @ X2 )
                                                                   => ( ( binintersect @ X1 @ X2 )
                                                                      = X1 ) )
                                                               => ( ! [X1: $i,X2: $i] :
                                                                      ( ( ( binintersect @ X1 @ X2 )
                                                                        = X2 )
                                                                     => ( subset @ X2 @ X1 ) )
                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                        ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                       => ( in @ X3 @ X2 ) )
                                                                   => ( ! [X1: $i,X2: $i] :
                                                                          ( ! [X3: $i] :
                                                                              ( ( in @ X3 @ X1 )
                                                                             => ~ ( in @ X3 @ X2 ) )
                                                                         => ( ( binintersect @ X1 @ X2 )
                                                                            = emptyset ) )
                                                                     => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                                       => ( ! [X1: $i,X2: $i] :
                                                                              ( ( subset @ X2 @ X1 )
                                                                             => ( ( binintersect @ X1 @ X2 )
                                                                                = X2 ) )
                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                ( ( ( binintersect @ X1 @ X2 )
                                                                                  = X1 )
                                                                               => ( subset @ X1 @ X2 ) )
                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                  ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                                                  = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                    ( ( in @ X3 @ X1 )
                                                                                   => ( ~ ( in @ X3 @ X2 )
                                                                                     => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                      ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                     => ( in @ X3 @ X1 ) )
                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                        ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                       => ~ ( in @ X3 @ X2 ) )
                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                          ( ( subset @ X1 @ X2 )
                                                                                         => ( ( setminus @ X1 @ X2 )
                                                                                            = emptyset ) )
                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                            ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                           => ( ( in @ X3 @ X1 )
                                                                                             => ( in @ X3 @ X2 ) ) )
                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                              ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                             => ( ~ ( in @ X3 @ X2 )
                                                                                               => ~ ( in @ X3 @ X1 ) ) )
                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                ( ~ ( in @ X3 @ X1 )
                                                                                               => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                  ( ( in @ X3 @ X2 )
                                                                                                 => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                             => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                      ( ( ( setminus @ X1 @ X2 )
                                                                                                        = emptyset )
                                                                                                     => ( subset @ X1 @ X2 ) )
                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                        ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                                       => ! [X4: $o] :
                                                                                                            ( ( ( in @ X3 @ X1 )
                                                                                                             => ( ~ ( in @ X3 @ X2 )
                                                                                                               => X4 ) )
                                                                                                           => ( ( ~ ( in @ X3 @ X1 )
                                                                                                               => ( ( in @ X3 @ X2 )
                                                                                                                 => X4 ) )
                                                                                                             => X4 ) ) )
                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                         => ( ~ ( in @ X3 @ X2 )
                                                                                                           => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                            ( ~ ( in @ X3 @ X1 )
                                                                                                           => ( ( in @ X3 @ X2 )
                                                                                                             => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                             => ( ( in @ X3 @ X2 )
                                                                                                               => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                ( ~ ( in @ X3 @ X1 )
                                                                                                               => ( ~ ( in @ X3 @ X2 )
                                                                                                                 => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                           => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                             => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                               => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                 => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                   => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                            ( ( in @ X2 @ X1 )
                                                                                                                           => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                              ( ( in @ X2 @ X1 )
                                                                                                                             => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                               => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                  ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                 => ( ( X3 != X1 )
                                                                                                                                   => ( X3 = X2 ) ) )
                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                   => ! [X4: $i] :
                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                       => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                     => ! [X4: $i] :
                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                         => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                       => ! [X4: $i] :
                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                           => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                         => ! [X4: $i] :
                                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                                             => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                                               => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                                 => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                               => ~ ! [X4: $i] :
                                                                                                                                                      ( ( in @ X4 @ X1 )
                                                                                                                                                     => ! [X5: $i] :
                                                                                                                                                          ( ( in @ X5 @ X2 )
                                                                                                                                                         => ( X3
                                                                                                                                                           != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                                           => ( sP5
                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                    ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                                                   => ~ ! [X3: $i] :
                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                         => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                                               => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                                                 => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                   => ( ! [X1: $i] :
                                                                                                                                                          ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                                          = X1 )
                                                                                                                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                            ( ! [X3: $i] :
                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                    ( ( in @ X4 @ X1 )
                                                                                                                                                                   => ( ( X2 @ X3 )
                                                                                                                                                                     => ( ( X2 @ X4 )
                                                                                                                                                                       => ( X3 = X4 ) ) ) ) )
                                                                                                                                                           => ( ~ ! [X3: $i] :
                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                   => ~ ( X2 @ X3 ) )
                                                                                                                                                             => ~ ! [X3: $i] :
                                                                                                                                                                    ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                   => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                     != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                       => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                              ( ~ ! [X3: $i] :
                                                                                                                                                                    ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                   => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                     != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                                             => ~ ! [X3: $i] :
                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                   => ~ ( X2 @ X3 ) ) )
                                                                                                                                                         => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                               => ( ( X2 @ X3 )
                                                                                                                                                                 => ( ! [X4: $i] :
                                                                                                                                                                        ( ( in @ X4 @ X1 )
                                                                                                                                                                       => ( ( X2 @ X4 )
                                                                                                                                                                         => ( X4 = X3 ) ) )
                                                                                                                                                                   => ~ ! [X4: $i] :
                                                                                                                                                                          ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                         => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                           != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                                           => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                  ( ! [X3: $i] :
                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                          ( ( in @ X4 @ X1 )
                                                                                                                                                                         => ( ( X2 @ X3 )
                                                                                                                                                                           => ( ( X2 @ X4 )
                                                                                                                                                                             => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                 => ( ~ ! [X3: $i] :
                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                         => ~ ( X2 @ X3 ) )
                                                                                                                                                                   => ~ ! [X3: $i] :
                                                                                                                                                                          ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                         => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                           != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                    ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                                      = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                   => ( X1 = X2 ) )
                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                      ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                     => ( X1 = X3 ) )
                                                                                                                                                                 => ( ! [X1: $i] :
                                                                                                                                                                        ( ( iskpair @ X1 )
                                                                                                                                                                       => ~ ! [X2: $i] :
                                                                                                                                                                              ( ( in @ X2
                                                                                                                                                                                @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                  @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                                             => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                  @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                                               != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                   => ( ! [X1: $i] :
                                                                                                                                                                          ( ~ ! [X2: $i] :
                                                                                                                                                                                ( ( in @ X2 @ X1 )
                                                                                                                                                                               => ( X1
                                                                                                                                                                                 != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                         => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                            ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                            = X1 )
                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                              ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                             => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                  = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                               => ( X1 = X3 ) )
                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                  ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                    = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                 => ( X1 = X3 ) )
                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                    ( ( X1 = X2 )
                                                                                                                                                                                   => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                      = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                      ( ( X1 = X2 )
                                                                                                                                                                                     => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                        = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                        ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                          = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                       => ( ( X3 = X4 )
                                                                                                                                                                                         => ( X2 = X4 ) ) )
                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                          ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                            = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                                         => ( X1 = X2 ) )
                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                            ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                              = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                           => ( X2 = X4 ) )
                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                              ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                             => ( X2 = X4 ) )
                                                                                                                                                                                         => ( ! [X1: $i] :
                                                                                                                                                                                                ( ( iskpair @ X1 )
                                                                                                                                                                                               => ~ ! [X2: $i] :
                                                                                                                                                                                                      ( ( in @ X2
                                                                                                                                                                                                        @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                          @ ^ [X3: $i] :
                                                                                                                                                                                                              ( X1
                                                                                                                                                                                                              = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                                     => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                          @ ^ [X3: $i] :
                                                                                                                                                                                                              ( X1
                                                                                                                                                                                                              = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                                       != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                  ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                  = X2 )
                                                                                                                                                                                             => ( sP8
                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                      ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                     => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                        ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                       => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                          ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                         => ( in @ X4 @ X2 ) )
                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                                                                                                               => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                  = X3 ) ) )
                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                 => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                    = X4 ) ) )
                                                                                                                                                                                                         => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                              ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                             => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                                                = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h134,assumption,
    ! [X1: $i,X2: $i,X3: $i] :
      ( ( subset @ X1 @ X2 )
     => ( ( in @ X3 @ X1 )
       => ( in @ X3 @ X2 ) ) ),
    introduced(assumption,[]) ).

thf(h135,assumption,
    ~ ( ! [X1: $i,X2: $i,X3: $i] :
          ( ( subset @ X1 @ X2 )
         => ( ~ ( in @ X3 @ X2 )
           => ~ ( in @ X3 @ X1 ) ) )
     => ( ! [X1: $i,X2: $i,X3: $i] :
            ( ( in @ X3 @ X1 )
           => ( ~ ( in @ X3 @ X2 )
             => ~ ( subset @ X1 @ X2 ) ) )
       => ( ! [X1: $i,X2: $i] :
              ( ~ ( subset @ X1 @ X2 )
             => ( X1 != X2 ) )
         => ( ! [X1: $i,X2: $i,X3: $i] :
                ( ( in @ X3 @ X1 )
               => ( ~ ( in @ X3 @ X2 )
                 => ( X1 != X2 ) ) )
           => ( ! [X1: $i] : ( subset @ X1 @ X1 )
             => ( ! [X1: $i,X2: $i,X3: $i] :
                    ( ( subset @ X1 @ X2 )
                   => ( ( subset @ X2 @ X3 )
                     => ( subset @ X1 @ X3 ) ) )
               => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) )
                 => ( ! [X1: $i,X2: $i,X3: $i] :
                        ( ( subset @ X1 @ X3 )
                       => ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
                   => ( ! [X1: $i,X2: $i] :
                          ( ( subset @ X1 @ X2 )
                         => ( in @ X1 @ ( powerset @ X2 ) ) )
                     => ( ! [X1: $i,X2: $i] :
                            ( ( subset @ X1 @ X2 )
                           => ( ( subset @ X2 @ X1 )
                             => ( X1 = X2 ) ) )
                       => ( ! [X1: $i] :
                              ( ( subset @ X1 @ emptyset )
                             => ( X1 = emptyset ) )
                         => ( ! [X1: $i,X2: $i] :
                                ( ( subset @ X2 @ X1 )
                               => ( in @ X2 @ ( powerset @ X1 ) ) )
                           => ( ! [X1: $i,X2: $i] :
                                  ( ( in @ X2 @ ( powerset @ X1 ) )
                                 => ( subset @ X2 @ X1 ) )
                             => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
                               => ( ! [X1: $i,X2: $i] :
                                      ( ( subset @ X1 @ X2 )
                                     => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
                                 => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                                   => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                            ( ( in @ X3 @ X1 )
                                           => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                       => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                ( ( in @ X3 @ X2 )
                                               => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                                  ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                 => ( ( ( in @ X3 @ X1 )
                                                     => X4 )
                                                   => ( ( ( in @ X3 @ X2 )
                                                       => X4 )
                                                     => X4 ) ) )
                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                    ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                   => ( ~ ( in @ X3 @ X1 )
                                                     => ( in @ X3 @ X2 ) ) )
                                               => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                                                 => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                          ( ( in @ X3 @ X1 )
                                                         => ( ( in @ X3 @ X2 )
                                                           => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                            ( ( subset @ X3 @ X1 )
                                                           => ( ( subset @ X3 @ X2 )
                                                             => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                              ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                             => ( in @ X3 @ X1 ) )
                                                         => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                                           => ( ! [X1: $i,X2: $i] :
                                                                  ( ( subset @ X1 @ X2 )
                                                                 => ( ( binintersect @ X1 @ X2 )
                                                                    = X1 ) )
                                                             => ( ! [X1: $i,X2: $i] :
                                                                    ( ( ( binintersect @ X1 @ X2 )
                                                                      = X2 )
                                                                   => ( subset @ X2 @ X1 ) )
                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                      ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                     => ( in @ X3 @ X2 ) )
                                                                 => ( ! [X1: $i,X2: $i] :
                                                                        ( ! [X3: $i] :
                                                                            ( ( in @ X3 @ X1 )
                                                                           => ~ ( in @ X3 @ X2 ) )
                                                                       => ( ( binintersect @ X1 @ X2 )
                                                                          = emptyset ) )
                                                                   => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                                     => ( ! [X1: $i,X2: $i] :
                                                                            ( ( subset @ X2 @ X1 )
                                                                           => ( ( binintersect @ X1 @ X2 )
                                                                              = X2 ) )
                                                                       => ( ! [X1: $i,X2: $i] :
                                                                              ( ( ( binintersect @ X1 @ X2 )
                                                                                = X1 )
                                                                             => ( subset @ X1 @ X2 ) )
                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                                                = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                  ( ( in @ X3 @ X1 )
                                                                                 => ( ~ ( in @ X3 @ X2 )
                                                                                   => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                    ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                   => ( in @ X3 @ X1 ) )
                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                      ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                     => ~ ( in @ X3 @ X2 ) )
                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                        ( ( subset @ X1 @ X2 )
                                                                                       => ( ( setminus @ X1 @ X2 )
                                                                                          = emptyset ) )
                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                          ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                         => ( ( in @ X3 @ X1 )
                                                                                           => ( in @ X3 @ X2 ) ) )
                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                            ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                           => ( ~ ( in @ X3 @ X2 )
                                                                                             => ~ ( in @ X3 @ X1 ) ) )
                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                              ( ~ ( in @ X3 @ X1 )
                                                                                             => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                ( ( in @ X3 @ X2 )
                                                                                               => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                           => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                    ( ( ( setminus @ X1 @ X2 )
                                                                                                      = emptyset )
                                                                                                   => ( subset @ X1 @ X2 ) )
                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                      ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                                     => ! [X4: $o] :
                                                                                                          ( ( ( in @ X3 @ X1 )
                                                                                                           => ( ~ ( in @ X3 @ X2 )
                                                                                                             => X4 ) )
                                                                                                         => ( ( ~ ( in @ X3 @ X1 )
                                                                                                             => ( ( in @ X3 @ X2 )
                                                                                                               => X4 ) )
                                                                                                           => X4 ) ) )
                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                       => ( ~ ( in @ X3 @ X2 )
                                                                                                         => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                          ( ~ ( in @ X3 @ X1 )
                                                                                                         => ( ( in @ X3 @ X2 )
                                                                                                           => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                           => ( ( in @ X3 @ X2 )
                                                                                                             => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                              ( ~ ( in @ X3 @ X1 )
                                                                                                             => ( ~ ( in @ X3 @ X2 )
                                                                                                               => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                         => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                           => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                             => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                               => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                 => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                          ( ( in @ X2 @ X1 )
                                                                                                                         => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                            ( ( in @ X2 @ X1 )
                                                                                                                           => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                             => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                               => ( ( X3 != X1 )
                                                                                                                                 => ( X3 = X2 ) ) )
                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                 => ! [X4: $i] :
                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                     => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                   => ! [X4: $i] :
                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                       => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                     => ! [X4: $i] :
                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                         => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                       => ! [X4: $i] :
                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                           => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                         => ! [X4: $i] :
                                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                                             => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                                               => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                              ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                             => ~ ! [X4: $i] :
                                                                                                                                                    ( ( in @ X4 @ X1 )
                                                                                                                                                   => ! [X5: $i] :
                                                                                                                                                        ( ( in @ X5 @ X2 )
                                                                                                                                                       => ( X3
                                                                                                                                                         != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                                         => ( sP5
                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                  ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                                                 => ~ ! [X3: $i] :
                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                       => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                                             => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                                               => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                 => ( ! [X1: $i] :
                                                                                                                                                        ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                                        = X1 )
                                                                                                                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                          ( ! [X3: $i] :
                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                  ( ( in @ X4 @ X1 )
                                                                                                                                                                 => ( ( X2 @ X3 )
                                                                                                                                                                   => ( ( X2 @ X4 )
                                                                                                                                                                     => ( X3 = X4 ) ) ) ) )
                                                                                                                                                         => ( ~ ! [X3: $i] :
                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                 => ~ ( X2 @ X3 ) )
                                                                                                                                                           => ~ ! [X3: $i] :
                                                                                                                                                                  ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                 => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                   != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                            ( ~ ! [X3: $i] :
                                                                                                                                                                  ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                 => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                   != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                                           => ~ ! [X3: $i] :
                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                 => ~ ( X2 @ X3 ) ) )
                                                                                                                                                       => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                             => ( ( X2 @ X3 )
                                                                                                                                                               => ( ! [X4: $i] :
                                                                                                                                                                      ( ( in @ X4 @ X1 )
                                                                                                                                                                     => ( ( X2 @ X4 )
                                                                                                                                                                       => ( X4 = X3 ) ) )
                                                                                                                                                                 => ~ ! [X4: $i] :
                                                                                                                                                                        ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                       => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                         != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                                         => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                ( ! [X3: $i] :
                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                        ( ( in @ X4 @ X1 )
                                                                                                                                                                       => ( ( X2 @ X3 )
                                                                                                                                                                         => ( ( X2 @ X4 )
                                                                                                                                                                           => ( X3 = X4 ) ) ) ) )
                                                                                                                                                               => ( ~ ! [X3: $i] :
                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                       => ~ ( X2 @ X3 ) )
                                                                                                                                                                 => ~ ! [X3: $i] :
                                                                                                                                                                        ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                       => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                         != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                  ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                                    = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                 => ( X1 = X2 ) )
                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                    ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                   => ( X1 = X3 ) )
                                                                                                                                                               => ( ! [X1: $i] :
                                                                                                                                                                      ( ( iskpair @ X1 )
                                                                                                                                                                     => ~ ! [X2: $i] :
                                                                                                                                                                            ( ( in @ X2
                                                                                                                                                                              @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                                           => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                                             != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                 => ( ! [X1: $i] :
                                                                                                                                                                        ( ~ ! [X2: $i] :
                                                                                                                                                                              ( ( in @ X2 @ X1 )
                                                                                                                                                                             => ( X1
                                                                                                                                                                               != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                       => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                          ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                          = X1 )
                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                            ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                           => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                              ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                             => ( X1 = X3 ) )
                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                  = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                               => ( X1 = X3 ) )
                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                  ( ( X1 = X2 )
                                                                                                                                                                                 => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                    = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                    ( ( X1 = X2 )
                                                                                                                                                                                   => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                      = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                      ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                        = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                     => ( ( X3 = X4 )
                                                                                                                                                                                       => ( X2 = X4 ) ) )
                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                        ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                          = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                                       => ( X1 = X2 ) )
                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                          ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                            = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                         => ( X2 = X4 ) )
                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                            ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                              = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                           => ( X2 = X4 ) )
                                                                                                                                                                                       => ( ! [X1: $i] :
                                                                                                                                                                                              ( ( iskpair @ X1 )
                                                                                                                                                                                             => ~ ! [X2: $i] :
                                                                                                                                                                                                    ( ( in @ X2
                                                                                                                                                                                                      @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                        @ ^ [X3: $i] :
                                                                                                                                                                                                            ( X1
                                                                                                                                                                                                            = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                                   => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                        @ ^ [X3: $i] :
                                                                                                                                                                                                            ( X1
                                                                                                                                                                                                            = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                                     != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                = X2 )
                                                                                                                                                                                           => ( sP8
                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                    ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                   => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                      ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                     => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                        ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                       => ( in @ X4 @ X2 ) )
                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                                                                                                             => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                = X3 ) ) )
                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                                                                                                               => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                  = X4 ) ) )
                                                                                                                                                                                                       => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                            ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                           => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                                              = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h136,assumption,
    ! [X1: $i,X2: $i,X3: $i] :
      ( ( subset @ X1 @ X2 )
     => ( ~ ( in @ X3 @ X2 )
       => ~ ( in @ X3 @ X1 ) ) ),
    introduced(assumption,[]) ).

thf(h137,assumption,
    ~ ( ! [X1: $i,X2: $i,X3: $i] :
          ( ( in @ X3 @ X1 )
         => ( ~ ( in @ X3 @ X2 )
           => ~ ( subset @ X1 @ X2 ) ) )
     => ( ! [X1: $i,X2: $i] :
            ( ~ ( subset @ X1 @ X2 )
           => ( X1 != X2 ) )
       => ( ! [X1: $i,X2: $i,X3: $i] :
              ( ( in @ X3 @ X1 )
             => ( ~ ( in @ X3 @ X2 )
               => ( X1 != X2 ) ) )
         => ( ! [X1: $i] : ( subset @ X1 @ X1 )
           => ( ! [X1: $i,X2: $i,X3: $i] :
                  ( ( subset @ X1 @ X2 )
                 => ( ( subset @ X2 @ X3 )
                   => ( subset @ X1 @ X3 ) ) )
             => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) )
               => ( ! [X1: $i,X2: $i,X3: $i] :
                      ( ( subset @ X1 @ X3 )
                     => ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
                 => ( ! [X1: $i,X2: $i] :
                        ( ( subset @ X1 @ X2 )
                       => ( in @ X1 @ ( powerset @ X2 ) ) )
                   => ( ! [X1: $i,X2: $i] :
                          ( ( subset @ X1 @ X2 )
                         => ( ( subset @ X2 @ X1 )
                           => ( X1 = X2 ) ) )
                     => ( ! [X1: $i] :
                            ( ( subset @ X1 @ emptyset )
                           => ( X1 = emptyset ) )
                       => ( ! [X1: $i,X2: $i] :
                              ( ( subset @ X2 @ X1 )
                             => ( in @ X2 @ ( powerset @ X1 ) ) )
                         => ( ! [X1: $i,X2: $i] :
                                ( ( in @ X2 @ ( powerset @ X1 ) )
                               => ( subset @ X2 @ X1 ) )
                           => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
                             => ( ! [X1: $i,X2: $i] :
                                    ( ( subset @ X1 @ X2 )
                                   => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
                               => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                                 => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                          ( ( in @ X3 @ X1 )
                                         => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                     => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                              ( ( in @ X3 @ X2 )
                                             => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                                ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                               => ( ( ( in @ X3 @ X1 )
                                                   => X4 )
                                                 => ( ( ( in @ X3 @ X2 )
                                                     => X4 )
                                                   => X4 ) ) )
                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                  ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                 => ( ~ ( in @ X3 @ X1 )
                                                   => ( in @ X3 @ X2 ) ) )
                                             => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                                               => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                        ( ( in @ X3 @ X1 )
                                                       => ( ( in @ X3 @ X2 )
                                                         => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                          ( ( subset @ X3 @ X1 )
                                                         => ( ( subset @ X3 @ X2 )
                                                           => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                            ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                           => ( in @ X3 @ X1 ) )
                                                       => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                                         => ( ! [X1: $i,X2: $i] :
                                                                ( ( subset @ X1 @ X2 )
                                                               => ( ( binintersect @ X1 @ X2 )
                                                                  = X1 ) )
                                                           => ( ! [X1: $i,X2: $i] :
                                                                  ( ( ( binintersect @ X1 @ X2 )
                                                                    = X2 )
                                                                 => ( subset @ X2 @ X1 ) )
                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                    ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                   => ( in @ X3 @ X2 ) )
                                                               => ( ! [X1: $i,X2: $i] :
                                                                      ( ! [X3: $i] :
                                                                          ( ( in @ X3 @ X1 )
                                                                         => ~ ( in @ X3 @ X2 ) )
                                                                     => ( ( binintersect @ X1 @ X2 )
                                                                        = emptyset ) )
                                                                 => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                                   => ( ! [X1: $i,X2: $i] :
                                                                          ( ( subset @ X2 @ X1 )
                                                                         => ( ( binintersect @ X1 @ X2 )
                                                                            = X2 ) )
                                                                     => ( ! [X1: $i,X2: $i] :
                                                                            ( ( ( binintersect @ X1 @ X2 )
                                                                              = X1 )
                                                                           => ( subset @ X1 @ X2 ) )
                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                              ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                                              = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                ( ( in @ X3 @ X1 )
                                                                               => ( ~ ( in @ X3 @ X2 )
                                                                                 => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                  ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                 => ( in @ X3 @ X1 ) )
                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                    ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                   => ~ ( in @ X3 @ X2 ) )
                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                      ( ( subset @ X1 @ X2 )
                                                                                     => ( ( setminus @ X1 @ X2 )
                                                                                        = emptyset ) )
                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                        ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                       => ( ( in @ X3 @ X1 )
                                                                                         => ( in @ X3 @ X2 ) ) )
                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                          ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                         => ( ~ ( in @ X3 @ X2 )
                                                                                           => ~ ( in @ X3 @ X1 ) ) )
                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                            ( ~ ( in @ X3 @ X1 )
                                                                                           => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                              ( ( in @ X3 @ X2 )
                                                                                             => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                         => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                  ( ( ( setminus @ X1 @ X2 )
                                                                                                    = emptyset )
                                                                                                 => ( subset @ X1 @ X2 ) )
                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                    ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                                   => ! [X4: $o] :
                                                                                                        ( ( ( in @ X3 @ X1 )
                                                                                                         => ( ~ ( in @ X3 @ X2 )
                                                                                                           => X4 ) )
                                                                                                       => ( ( ~ ( in @ X3 @ X1 )
                                                                                                           => ( ( in @ X3 @ X2 )
                                                                                                             => X4 ) )
                                                                                                         => X4 ) ) )
                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                     => ( ~ ( in @ X3 @ X2 )
                                                                                                       => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                        ( ~ ( in @ X3 @ X1 )
                                                                                                       => ( ( in @ X3 @ X2 )
                                                                                                         => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                         => ( ( in @ X3 @ X2 )
                                                                                                           => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                            ( ~ ( in @ X3 @ X1 )
                                                                                                           => ( ~ ( in @ X3 @ X2 )
                                                                                                             => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                       => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                         => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                           => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                             => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                               => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                        ( ( in @ X2 @ X1 )
                                                                                                                       => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                          ( ( in @ X2 @ X1 )
                                                                                                                         => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                           => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                              ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                             => ( ( X3 != X1 )
                                                                                                                               => ( X3 = X2 ) ) )
                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                               => ! [X4: $i] :
                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                   => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                 => ! [X4: $i] :
                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                     => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                   => ! [X4: $i] :
                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                       => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                     => ! [X4: $i] :
                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                         => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                       => ! [X4: $i] :
                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                           => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                         => ! [X4: $i] :
                                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                                             => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                            ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                           => ~ ! [X4: $i] :
                                                                                                                                                  ( ( in @ X4 @ X1 )
                                                                                                                                                 => ! [X5: $i] :
                                                                                                                                                      ( ( in @ X5 @ X2 )
                                                                                                                                                     => ( X3
                                                                                                                                                       != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                                       => ( sP5
                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                                               => ~ ! [X3: $i] :
                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                     => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                                           => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                                             => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                               => ( ! [X1: $i] :
                                                                                                                                                      ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                                      = X1 )
                                                                                                                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                        ( ! [X3: $i] :
                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                ( ( in @ X4 @ X1 )
                                                                                                                                                               => ( ( X2 @ X3 )
                                                                                                                                                                 => ( ( X2 @ X4 )
                                                                                                                                                                   => ( X3 = X4 ) ) ) ) )
                                                                                                                                                       => ( ~ ! [X3: $i] :
                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                               => ~ ( X2 @ X3 ) )
                                                                                                                                                         => ~ ! [X3: $i] :
                                                                                                                                                                ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                               => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                 != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                          ( ~ ! [X3: $i] :
                                                                                                                                                                ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                               => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                 != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                                         => ~ ! [X3: $i] :
                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                               => ~ ( X2 @ X3 ) ) )
                                                                                                                                                     => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                           => ( ( X2 @ X3 )
                                                                                                                                                             => ( ! [X4: $i] :
                                                                                                                                                                    ( ( in @ X4 @ X1 )
                                                                                                                                                                   => ( ( X2 @ X4 )
                                                                                                                                                                     => ( X4 = X3 ) ) )
                                                                                                                                                               => ~ ! [X4: $i] :
                                                                                                                                                                      ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                     => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                       != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                                       => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                              ( ! [X3: $i] :
                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                      ( ( in @ X4 @ X1 )
                                                                                                                                                                     => ( ( X2 @ X3 )
                                                                                                                                                                       => ( ( X2 @ X4 )
                                                                                                                                                                         => ( X3 = X4 ) ) ) ) )
                                                                                                                                                             => ( ~ ! [X3: $i] :
                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                     => ~ ( X2 @ X3 ) )
                                                                                                                                                               => ~ ! [X3: $i] :
                                                                                                                                                                      ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                     => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                       != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                                  = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                               => ( X1 = X2 ) )
                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                  ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                 => ( X1 = X3 ) )
                                                                                                                                                             => ( ! [X1: $i] :
                                                                                                                                                                    ( ( iskpair @ X1 )
                                                                                                                                                                   => ~ ! [X2: $i] :
                                                                                                                                                                          ( ( in @ X2
                                                                                                                                                                            @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                              @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                                         => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                              @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                                           != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                               => ( ! [X1: $i] :
                                                                                                                                                                      ( ~ ! [X2: $i] :
                                                                                                                                                                            ( ( in @ X2 @ X1 )
                                                                                                                                                                           => ( X1
                                                                                                                                                                             != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                     => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                        ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                        = X1 )
                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                         => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                            ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                              = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                           => ( X1 = X3 ) )
                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                              ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                             => ( X1 = X3 ) )
                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                ( ( X1 = X2 )
                                                                                                                                                                               => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                  = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                  ( ( X1 = X2 )
                                                                                                                                                                                 => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                    = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                    ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                      = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                   => ( ( X3 = X4 )
                                                                                                                                                                                     => ( X2 = X4 ) ) )
                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                      ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                        = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                                     => ( X1 = X2 ) )
                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                        ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                          = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                       => ( X2 = X4 ) )
                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                          ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                            = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                         => ( X2 = X4 ) )
                                                                                                                                                                                     => ( ! [X1: $i] :
                                                                                                                                                                                            ( ( iskpair @ X1 )
                                                                                                                                                                                           => ~ ! [X2: $i] :
                                                                                                                                                                                                  ( ( in @ X2
                                                                                                                                                                                                    @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                      @ ^ [X3: $i] :
                                                                                                                                                                                                          ( X1
                                                                                                                                                                                                          = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                                 => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                      @ ^ [X3: $i] :
                                                                                                                                                                                                          ( X1
                                                                                                                                                                                                          = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                                   != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                              ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                              = X2 )
                                                                                                                                                                                         => ( sP8
                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                  ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                 => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                    ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                   => ( in @ X3 @ X1 ) )
                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                      ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                     => ( in @ X4 @ X2 ) )
                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                                                                                           => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                              = X3 ) ) )
                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                                                                                                             => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                = X4 ) ) )
                                                                                                                                                                                                     => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                         => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                                            = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h138,assumption,
    ! [X1: $i,X2: $i,X3: $i] :
      ( ( in @ X3 @ X1 )
     => ( ~ ( in @ X3 @ X2 )
       => ~ ( subset @ X1 @ X2 ) ) ),
    introduced(assumption,[]) ).

thf(h139,assumption,
    ~ ( ! [X1: $i,X2: $i] :
          ( ~ ( subset @ X1 @ X2 )
         => ( X1 != X2 ) )
     => ( ! [X1: $i,X2: $i,X3: $i] :
            ( ( in @ X3 @ X1 )
           => ( ~ ( in @ X3 @ X2 )
             => ( X1 != X2 ) ) )
       => ( ! [X1: $i] : ( subset @ X1 @ X1 )
         => ( ! [X1: $i,X2: $i,X3: $i] :
                ( ( subset @ X1 @ X2 )
               => ( ( subset @ X2 @ X3 )
                 => ( subset @ X1 @ X3 ) ) )
           => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) )
             => ( ! [X1: $i,X2: $i,X3: $i] :
                    ( ( subset @ X1 @ X3 )
                   => ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
               => ( ! [X1: $i,X2: $i] :
                      ( ( subset @ X1 @ X2 )
                     => ( in @ X1 @ ( powerset @ X2 ) ) )
                 => ( ! [X1: $i,X2: $i] :
                        ( ( subset @ X1 @ X2 )
                       => ( ( subset @ X2 @ X1 )
                         => ( X1 = X2 ) ) )
                   => ( ! [X1: $i] :
                          ( ( subset @ X1 @ emptyset )
                         => ( X1 = emptyset ) )
                     => ( ! [X1: $i,X2: $i] :
                            ( ( subset @ X2 @ X1 )
                           => ( in @ X2 @ ( powerset @ X1 ) ) )
                       => ( ! [X1: $i,X2: $i] :
                              ( ( in @ X2 @ ( powerset @ X1 ) )
                             => ( subset @ X2 @ X1 ) )
                         => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
                           => ( ! [X1: $i,X2: $i] :
                                  ( ( subset @ X1 @ X2 )
                                 => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
                             => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                               => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                        ( ( in @ X3 @ X1 )
                                       => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                   => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                            ( ( in @ X3 @ X2 )
                                           => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                              ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                             => ( ( ( in @ X3 @ X1 )
                                                 => X4 )
                                               => ( ( ( in @ X3 @ X2 )
                                                   => X4 )
                                                 => X4 ) ) )
                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                               => ( ~ ( in @ X3 @ X1 )
                                                 => ( in @ X3 @ X2 ) ) )
                                           => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                                             => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                      ( ( in @ X3 @ X1 )
                                                     => ( ( in @ X3 @ X2 )
                                                       => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                        ( ( subset @ X3 @ X1 )
                                                       => ( ( subset @ X3 @ X2 )
                                                         => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                          ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                         => ( in @ X3 @ X1 ) )
                                                     => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                                       => ( ! [X1: $i,X2: $i] :
                                                              ( ( subset @ X1 @ X2 )
                                                             => ( ( binintersect @ X1 @ X2 )
                                                                = X1 ) )
                                                         => ( ! [X1: $i,X2: $i] :
                                                                ( ( ( binintersect @ X1 @ X2 )
                                                                  = X2 )
                                                               => ( subset @ X2 @ X1 ) )
                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                  ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                 => ( in @ X3 @ X2 ) )
                                                             => ( ! [X1: $i,X2: $i] :
                                                                    ( ! [X3: $i] :
                                                                        ( ( in @ X3 @ X1 )
                                                                       => ~ ( in @ X3 @ X2 ) )
                                                                   => ( ( binintersect @ X1 @ X2 )
                                                                      = emptyset ) )
                                                               => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                                 => ( ! [X1: $i,X2: $i] :
                                                                        ( ( subset @ X2 @ X1 )
                                                                       => ( ( binintersect @ X1 @ X2 )
                                                                          = X2 ) )
                                                                   => ( ! [X1: $i,X2: $i] :
                                                                          ( ( ( binintersect @ X1 @ X2 )
                                                                            = X1 )
                                                                         => ( subset @ X1 @ X2 ) )
                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                            ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                                            = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                              ( ( in @ X3 @ X1 )
                                                                             => ( ~ ( in @ X3 @ X2 )
                                                                               => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                               => ( in @ X3 @ X1 ) )
                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                  ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                 => ~ ( in @ X3 @ X2 ) )
                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                    ( ( subset @ X1 @ X2 )
                                                                                   => ( ( setminus @ X1 @ X2 )
                                                                                      = emptyset ) )
                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                      ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                     => ( ( in @ X3 @ X1 )
                                                                                       => ( in @ X3 @ X2 ) ) )
                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                        ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                       => ( ~ ( in @ X3 @ X2 )
                                                                                         => ~ ( in @ X3 @ X1 ) ) )
                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                          ( ~ ( in @ X3 @ X1 )
                                                                                         => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                            ( ( in @ X3 @ X2 )
                                                                                           => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                       => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                ( ( ( setminus @ X1 @ X2 )
                                                                                                  = emptyset )
                                                                                               => ( subset @ X1 @ X2 ) )
                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                  ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                                 => ! [X4: $o] :
                                                                                                      ( ( ( in @ X3 @ X1 )
                                                                                                       => ( ~ ( in @ X3 @ X2 )
                                                                                                         => X4 ) )
                                                                                                     => ( ( ~ ( in @ X3 @ X1 )
                                                                                                         => ( ( in @ X3 @ X2 )
                                                                                                           => X4 ) )
                                                                                                       => X4 ) ) )
                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                   => ( ~ ( in @ X3 @ X2 )
                                                                                                     => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                      ( ~ ( in @ X3 @ X1 )
                                                                                                     => ( ( in @ X3 @ X2 )
                                                                                                       => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                       => ( ( in @ X3 @ X2 )
                                                                                                         => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                          ( ~ ( in @ X3 @ X1 )
                                                                                                         => ( ~ ( in @ X3 @ X2 )
                                                                                                           => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                     => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                       => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                         => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                           => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                             => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                      ( ( in @ X2 @ X1 )
                                                                                                                     => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                        ( ( in @ X2 @ X1 )
                                                                                                                       => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                         => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                            ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                           => ( ( X3 != X1 )
                                                                                                                             => ( X3 = X2 ) ) )
                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                             => ! [X4: $i] :
                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                 => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                               => ! [X4: $i] :
                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                   => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                 => ! [X4: $i] :
                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                     => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                   => ! [X4: $i] :
                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                       => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                     => ! [X4: $i] :
                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                         => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                       => ! [X4: $i] :
                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                           => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                         => ~ ! [X4: $i] :
                                                                                                                                                ( ( in @ X4 @ X1 )
                                                                                                                                               => ! [X5: $i] :
                                                                                                                                                    ( ( in @ X5 @ X2 )
                                                                                                                                                   => ( X3
                                                                                                                                                     != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                                     => ( sP5
                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                              ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                                             => ~ ! [X3: $i] :
                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                   => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                                         => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                                           => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                             => ( ! [X1: $i] :
                                                                                                                                                    ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                                    = X1 )
                                                                                                                                               => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                      ( ! [X3: $i] :
                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                              ( ( in @ X4 @ X1 )
                                                                                                                                                             => ( ( X2 @ X3 )
                                                                                                                                                               => ( ( X2 @ X4 )
                                                                                                                                                                 => ( X3 = X4 ) ) ) ) )
                                                                                                                                                     => ( ~ ! [X3: $i] :
                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                             => ~ ( X2 @ X3 ) )
                                                                                                                                                       => ~ ! [X3: $i] :
                                                                                                                                                              ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                             => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                               != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                        ( ~ ! [X3: $i] :
                                                                                                                                                              ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                             => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                               != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                                       => ~ ! [X3: $i] :
                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                             => ~ ( X2 @ X3 ) ) )
                                                                                                                                                   => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                         => ( ( X2 @ X3 )
                                                                                                                                                           => ( ! [X4: $i] :
                                                                                                                                                                  ( ( in @ X4 @ X1 )
                                                                                                                                                                 => ( ( X2 @ X4 )
                                                                                                                                                                   => ( X4 = X3 ) ) )
                                                                                                                                                             => ~ ! [X4: $i] :
                                                                                                                                                                    ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                   => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                     != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                            ( ! [X3: $i] :
                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                    ( ( in @ X4 @ X1 )
                                                                                                                                                                   => ( ( X2 @ X3 )
                                                                                                                                                                     => ( ( X2 @ X4 )
                                                                                                                                                                       => ( X3 = X4 ) ) ) ) )
                                                                                                                                                           => ( ~ ! [X3: $i] :
                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                   => ~ ( X2 @ X3 ) )
                                                                                                                                                             => ~ ! [X3: $i] :
                                                                                                                                                                    ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                   => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                     != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                              ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                                = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                             => ( X1 = X2 ) )
                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                               => ( X1 = X3 ) )
                                                                                                                                                           => ( ! [X1: $i] :
                                                                                                                                                                  ( ( iskpair @ X1 )
                                                                                                                                                                 => ~ ! [X2: $i] :
                                                                                                                                                                        ( ( in @ X2
                                                                                                                                                                          @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                            @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                                       => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                            @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                                         != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                             => ( ! [X1: $i] :
                                                                                                                                                                    ( ~ ! [X2: $i] :
                                                                                                                                                                          ( ( in @ X2 @ X1 )
                                                                                                                                                                         => ( X1
                                                                                                                                                                           != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                   => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                      ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                      = X1 )
                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                       => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                          ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                            = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                         => ( X1 = X3 ) )
                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                            ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                              = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                           => ( X1 = X3 ) )
                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                              ( ( X1 = X2 )
                                                                                                                                                                             => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                ( ( X1 = X2 )
                                                                                                                                                                               => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                  = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                  ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                    = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                 => ( ( X3 = X4 )
                                                                                                                                                                                   => ( X2 = X4 ) ) )
                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                    ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                      = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                                   => ( X1 = X2 ) )
                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                      ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                        = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                     => ( X2 = X4 ) )
                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                        ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                          = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                       => ( X2 = X4 ) )
                                                                                                                                                                                   => ( ! [X1: $i] :
                                                                                                                                                                                          ( ( iskpair @ X1 )
                                                                                                                                                                                         => ~ ! [X2: $i] :
                                                                                                                                                                                                ( ( in @ X2
                                                                                                                                                                                                  @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                    @ ^ [X3: $i] :
                                                                                                                                                                                                        ( X1
                                                                                                                                                                                                        = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                               => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                    @ ^ [X3: $i] :
                                                                                                                                                                                                        ( X1
                                                                                                                                                                                                        = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                                 != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                            ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                            = X2 )
                                                                                                                                                                                       => ( sP8
                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                               => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                  ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                 => ( in @ X3 @ X1 ) )
                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                    ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                   => ( in @ X4 @ X2 ) )
                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                                                                                         => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                            = X3 ) ) )
                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                                                                                           => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                              = X4 ) ) )
                                                                                                                                                                                                   => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                       => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                                          = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h140,assumption,
    ! [X1: $i,X2: $i] :
      ( ~ ( subset @ X1 @ X2 )
     => ( X1 != X2 ) ),
    introduced(assumption,[]) ).

thf(h141,assumption,
    ~ ( ! [X1: $i,X2: $i,X3: $i] :
          ( ( in @ X3 @ X1 )
         => ( ~ ( in @ X3 @ X2 )
           => ( X1 != X2 ) ) )
     => ( ! [X1: $i] : ( subset @ X1 @ X1 )
       => ( ! [X1: $i,X2: $i,X3: $i] :
              ( ( subset @ X1 @ X2 )
             => ( ( subset @ X2 @ X3 )
               => ( subset @ X1 @ X3 ) ) )
         => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) )
           => ( ! [X1: $i,X2: $i,X3: $i] :
                  ( ( subset @ X1 @ X3 )
                 => ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
             => ( ! [X1: $i,X2: $i] :
                    ( ( subset @ X1 @ X2 )
                   => ( in @ X1 @ ( powerset @ X2 ) ) )
               => ( ! [X1: $i,X2: $i] :
                      ( ( subset @ X1 @ X2 )
                     => ( ( subset @ X2 @ X1 )
                       => ( X1 = X2 ) ) )
                 => ( ! [X1: $i] :
                        ( ( subset @ X1 @ emptyset )
                       => ( X1 = emptyset ) )
                   => ( ! [X1: $i,X2: $i] :
                          ( ( subset @ X2 @ X1 )
                         => ( in @ X2 @ ( powerset @ X1 ) ) )
                     => ( ! [X1: $i,X2: $i] :
                            ( ( in @ X2 @ ( powerset @ X1 ) )
                           => ( subset @ X2 @ X1 ) )
                       => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
                         => ( ! [X1: $i,X2: $i] :
                                ( ( subset @ X1 @ X2 )
                               => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
                           => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                             => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                      ( ( in @ X3 @ X1 )
                                     => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                 => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                          ( ( in @ X3 @ X2 )
                                         => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                            ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                           => ( ( ( in @ X3 @ X1 )
                                               => X4 )
                                             => ( ( ( in @ X3 @ X2 )
                                                 => X4 )
                                               => X4 ) ) )
                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                              ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                             => ( ~ ( in @ X3 @ X1 )
                                               => ( in @ X3 @ X2 ) ) )
                                         => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                                           => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                    ( ( in @ X3 @ X1 )
                                                   => ( ( in @ X3 @ X2 )
                                                     => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                      ( ( subset @ X3 @ X1 )
                                                     => ( ( subset @ X3 @ X2 )
                                                       => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                        ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                       => ( in @ X3 @ X1 ) )
                                                   => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                                     => ( ! [X1: $i,X2: $i] :
                                                            ( ( subset @ X1 @ X2 )
                                                           => ( ( binintersect @ X1 @ X2 )
                                                              = X1 ) )
                                                       => ( ! [X1: $i,X2: $i] :
                                                              ( ( ( binintersect @ X1 @ X2 )
                                                                = X2 )
                                                             => ( subset @ X2 @ X1 ) )
                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                               => ( in @ X3 @ X2 ) )
                                                           => ( ! [X1: $i,X2: $i] :
                                                                  ( ! [X3: $i] :
                                                                      ( ( in @ X3 @ X1 )
                                                                     => ~ ( in @ X3 @ X2 ) )
                                                                 => ( ( binintersect @ X1 @ X2 )
                                                                    = emptyset ) )
                                                             => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                               => ( ! [X1: $i,X2: $i] :
                                                                      ( ( subset @ X2 @ X1 )
                                                                     => ( ( binintersect @ X1 @ X2 )
                                                                        = X2 ) )
                                                                 => ( ! [X1: $i,X2: $i] :
                                                                        ( ( ( binintersect @ X1 @ X2 )
                                                                          = X1 )
                                                                       => ( subset @ X1 @ X2 ) )
                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                          ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                                          = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                            ( ( in @ X3 @ X1 )
                                                                           => ( ~ ( in @ X3 @ X2 )
                                                                             => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                              ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                             => ( in @ X3 @ X1 ) )
                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                               => ~ ( in @ X3 @ X2 ) )
                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                  ( ( subset @ X1 @ X2 )
                                                                                 => ( ( setminus @ X1 @ X2 )
                                                                                    = emptyset ) )
                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                    ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                   => ( ( in @ X3 @ X1 )
                                                                                     => ( in @ X3 @ X2 ) ) )
                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                      ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                     => ( ~ ( in @ X3 @ X2 )
                                                                                       => ~ ( in @ X3 @ X1 ) ) )
                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                        ( ~ ( in @ X3 @ X1 )
                                                                                       => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                          ( ( in @ X3 @ X2 )
                                                                                         => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                     => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                              ( ( ( setminus @ X1 @ X2 )
                                                                                                = emptyset )
                                                                                             => ( subset @ X1 @ X2 ) )
                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                               => ! [X4: $o] :
                                                                                                    ( ( ( in @ X3 @ X1 )
                                                                                                     => ( ~ ( in @ X3 @ X2 )
                                                                                                       => X4 ) )
                                                                                                   => ( ( ~ ( in @ X3 @ X1 )
                                                                                                       => ( ( in @ X3 @ X2 )
                                                                                                         => X4 ) )
                                                                                                     => X4 ) ) )
                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                 => ( ~ ( in @ X3 @ X2 )
                                                                                                   => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                    ( ~ ( in @ X3 @ X1 )
                                                                                                   => ( ( in @ X3 @ X2 )
                                                                                                     => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                     => ( ( in @ X3 @ X2 )
                                                                                                       => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                        ( ~ ( in @ X3 @ X1 )
                                                                                                       => ( ~ ( in @ X3 @ X2 )
                                                                                                         => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                   => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                     => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                       => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                         => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                           => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                    ( ( in @ X2 @ X1 )
                                                                                                                   => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                      ( ( in @ X2 @ X1 )
                                                                                                                     => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                       => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                          ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                         => ( ( X3 != X1 )
                                                                                                                           => ( X3 = X2 ) ) )
                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                           => ! [X4: $i] :
                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                               => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                             => ! [X4: $i] :
                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                 => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                               => ! [X4: $i] :
                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                   => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                 => ! [X4: $i] :
                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                     => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                   => ! [X4: $i] :
                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                       => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                     => ! [X4: $i] :
                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                         => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                       => ~ ! [X4: $i] :
                                                                                                                                              ( ( in @ X4 @ X1 )
                                                                                                                                             => ! [X5: $i] :
                                                                                                                                                  ( ( in @ X5 @ X2 )
                                                                                                                                                 => ( X3
                                                                                                                                                   != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                                   => ( sP5
                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                            ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                                           => ~ ! [X3: $i] :
                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                 => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                                       => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                                         => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                           => ( ! [X1: $i] :
                                                                                                                                                  ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                                  = X1 )
                                                                                                                                             => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                    ( ! [X3: $i] :
                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                            ( ( in @ X4 @ X1 )
                                                                                                                                                           => ( ( X2 @ X3 )
                                                                                                                                                             => ( ( X2 @ X4 )
                                                                                                                                                               => ( X3 = X4 ) ) ) ) )
                                                                                                                                                   => ( ~ ! [X3: $i] :
                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                           => ~ ( X2 @ X3 ) )
                                                                                                                                                     => ~ ! [X3: $i] :
                                                                                                                                                            ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                           => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                             != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                               => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                      ( ~ ! [X3: $i] :
                                                                                                                                                            ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                           => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                             != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                                     => ~ ! [X3: $i] :
                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                           => ~ ( X2 @ X3 ) ) )
                                                                                                                                                 => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                       => ( ( X2 @ X3 )
                                                                                                                                                         => ( ! [X4: $i] :
                                                                                                                                                                ( ( in @ X4 @ X1 )
                                                                                                                                                               => ( ( X2 @ X4 )
                                                                                                                                                                 => ( X4 = X3 ) ) )
                                                                                                                                                           => ~ ! [X4: $i] :
                                                                                                                                                                  ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                 => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                   != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                          ( ! [X3: $i] :
                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                  ( ( in @ X4 @ X1 )
                                                                                                                                                                 => ( ( X2 @ X3 )
                                                                                                                                                                   => ( ( X2 @ X4 )
                                                                                                                                                                     => ( X3 = X4 ) ) ) ) )
                                                                                                                                                         => ( ~ ! [X3: $i] :
                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                 => ~ ( X2 @ X3 ) )
                                                                                                                                                           => ~ ! [X3: $i] :
                                                                                                                                                                  ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                 => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                   != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                            ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                              = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                           => ( X1 = X2 ) )
                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                              ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                             => ( X1 = X3 ) )
                                                                                                                                                         => ( ! [X1: $i] :
                                                                                                                                                                ( ( iskpair @ X1 )
                                                                                                                                                               => ~ ! [X2: $i] :
                                                                                                                                                                      ( ( in @ X2
                                                                                                                                                                        @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                          @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                                     => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                          @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                                       != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                           => ( ! [X1: $i] :
                                                                                                                                                                  ( ~ ! [X2: $i] :
                                                                                                                                                                        ( ( in @ X2 @ X1 )
                                                                                                                                                                       => ( X1
                                                                                                                                                                         != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                 => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                    ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                    = X1 )
                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                      ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                     => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                        ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                          = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                       => ( X1 = X3 ) )
                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                          ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                            = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                         => ( X1 = X3 ) )
                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                            ( ( X1 = X2 )
                                                                                                                                                                           => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                              = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                              ( ( X1 = X2 )
                                                                                                                                                                             => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                  = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                               => ( ( X3 = X4 )
                                                                                                                                                                                 => ( X2 = X4 ) ) )
                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                  ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                    = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                                 => ( X1 = X2 ) )
                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                    ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                      = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                   => ( X2 = X4 ) )
                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                      ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                        = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                     => ( X2 = X4 ) )
                                                                                                                                                                                 => ( ! [X1: $i] :
                                                                                                                                                                                        ( ( iskpair @ X1 )
                                                                                                                                                                                       => ~ ! [X2: $i] :
                                                                                                                                                                                              ( ( in @ X2
                                                                                                                                                                                                @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                  @ ^ [X3: $i] :
                                                                                                                                                                                                      ( X1
                                                                                                                                                                                                      = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                             => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                  @ ^ [X3: $i] :
                                                                                                                                                                                                      ( X1
                                                                                                                                                                                                      = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                               != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                          ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                          = X2 )
                                                                                                                                                                                     => ( sP8
                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                              ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                             => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                               => ( in @ X3 @ X1 ) )
                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                  ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                 => ( in @ X4 @ X2 ) )
                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                                                                                       => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                          = X3 ) ) )
                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                                                                                         => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                            = X4 ) ) )
                                                                                                                                                                                                 => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                      ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                     => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                                        = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h142,assumption,
    ! [X1: $i,X2: $i,X3: $i] :
      ( ( in @ X3 @ X1 )
     => ( ~ ( in @ X3 @ X2 )
       => ( X1 != X2 ) ) ),
    introduced(assumption,[]) ).

thf(h143,assumption,
    ~ ( ! [X1: $i] : ( subset @ X1 @ X1 )
     => ( ! [X1: $i,X2: $i,X3: $i] :
            ( ( subset @ X1 @ X2 )
           => ( ( subset @ X2 @ X3 )
             => ( subset @ X1 @ X3 ) ) )
       => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) )
         => ( ! [X1: $i,X2: $i,X3: $i] :
                ( ( subset @ X1 @ X3 )
               => ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
           => ( ! [X1: $i,X2: $i] :
                  ( ( subset @ X1 @ X2 )
                 => ( in @ X1 @ ( powerset @ X2 ) ) )
             => ( ! [X1: $i,X2: $i] :
                    ( ( subset @ X1 @ X2 )
                   => ( ( subset @ X2 @ X1 )
                     => ( X1 = X2 ) ) )
               => ( ! [X1: $i] :
                      ( ( subset @ X1 @ emptyset )
                     => ( X1 = emptyset ) )
                 => ( ! [X1: $i,X2: $i] :
                        ( ( subset @ X2 @ X1 )
                       => ( in @ X2 @ ( powerset @ X1 ) ) )
                   => ( ! [X1: $i,X2: $i] :
                          ( ( in @ X2 @ ( powerset @ X1 ) )
                         => ( subset @ X2 @ X1 ) )
                     => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
                       => ( ! [X1: $i,X2: $i] :
                              ( ( subset @ X1 @ X2 )
                             => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
                         => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                           => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                    ( ( in @ X3 @ X1 )
                                   => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                               => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                        ( ( in @ X3 @ X2 )
                                       => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                          ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                         => ( ( ( in @ X3 @ X1 )
                                             => X4 )
                                           => ( ( ( in @ X3 @ X2 )
                                               => X4 )
                                             => X4 ) ) )
                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                            ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                           => ( ~ ( in @ X3 @ X1 )
                                             => ( in @ X3 @ X2 ) ) )
                                       => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                                         => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                  ( ( in @ X3 @ X1 )
                                                 => ( ( in @ X3 @ X2 )
                                                   => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                    ( ( subset @ X3 @ X1 )
                                                   => ( ( subset @ X3 @ X2 )
                                                     => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                      ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                     => ( in @ X3 @ X1 ) )
                                                 => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                                   => ( ! [X1: $i,X2: $i] :
                                                          ( ( subset @ X1 @ X2 )
                                                         => ( ( binintersect @ X1 @ X2 )
                                                            = X1 ) )
                                                     => ( ! [X1: $i,X2: $i] :
                                                            ( ( ( binintersect @ X1 @ X2 )
                                                              = X2 )
                                                           => ( subset @ X2 @ X1 ) )
                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                              ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                             => ( in @ X3 @ X2 ) )
                                                         => ( ! [X1: $i,X2: $i] :
                                                                ( ! [X3: $i] :
                                                                    ( ( in @ X3 @ X1 )
                                                                   => ~ ( in @ X3 @ X2 ) )
                                                               => ( ( binintersect @ X1 @ X2 )
                                                                  = emptyset ) )
                                                           => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                             => ( ! [X1: $i,X2: $i] :
                                                                    ( ( subset @ X2 @ X1 )
                                                                   => ( ( binintersect @ X1 @ X2 )
                                                                      = X2 ) )
                                                               => ( ! [X1: $i,X2: $i] :
                                                                      ( ( ( binintersect @ X1 @ X2 )
                                                                        = X1 )
                                                                     => ( subset @ X1 @ X2 ) )
                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                        ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                                        = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                          ( ( in @ X3 @ X1 )
                                                                         => ( ~ ( in @ X3 @ X2 )
                                                                           => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                            ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                           => ( in @ X3 @ X1 ) )
                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                              ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                             => ~ ( in @ X3 @ X2 ) )
                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                ( ( subset @ X1 @ X2 )
                                                                               => ( ( setminus @ X1 @ X2 )
                                                                                  = emptyset ) )
                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                  ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                 => ( ( in @ X3 @ X1 )
                                                                                   => ( in @ X3 @ X2 ) ) )
                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                    ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                   => ( ~ ( in @ X3 @ X2 )
                                                                                     => ~ ( in @ X3 @ X1 ) ) )
                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                      ( ~ ( in @ X3 @ X1 )
                                                                                     => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                        ( ( in @ X3 @ X2 )
                                                                                       => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                   => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                            ( ( ( setminus @ X1 @ X2 )
                                                                                              = emptyset )
                                                                                           => ( subset @ X1 @ X2 ) )
                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                              ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                             => ! [X4: $o] :
                                                                                                  ( ( ( in @ X3 @ X1 )
                                                                                                   => ( ~ ( in @ X3 @ X2 )
                                                                                                     => X4 ) )
                                                                                                 => ( ( ~ ( in @ X3 @ X1 )
                                                                                                     => ( ( in @ X3 @ X2 )
                                                                                                       => X4 ) )
                                                                                                   => X4 ) ) )
                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                ( ( in @ X3 @ X1 )
                                                                                               => ( ~ ( in @ X3 @ X2 )
                                                                                                 => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                  ( ~ ( in @ X3 @ X1 )
                                                                                                 => ( ( in @ X3 @ X2 )
                                                                                                   => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                   => ( ( in @ X3 @ X2 )
                                                                                                     => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                      ( ~ ( in @ X3 @ X1 )
                                                                                                     => ( ~ ( in @ X3 @ X2 )
                                                                                                       => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                 => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                   => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                     => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                       => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                         => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                  ( ( in @ X2 @ X1 )
                                                                                                                 => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                    ( ( in @ X2 @ X1 )
                                                                                                                   => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                     => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                        ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                       => ( ( X3 != X1 )
                                                                                                                         => ( X3 = X2 ) ) )
                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                         => ! [X4: $i] :
                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                             => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                           => ! [X4: $i] :
                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                               => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                             => ! [X4: $i] :
                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                 => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                               => ! [X4: $i] :
                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                   => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                 => ! [X4: $i] :
                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                     => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                   => ! [X4: $i] :
                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                       => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                      ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                     => ~ ! [X4: $i] :
                                                                                                                                            ( ( in @ X4 @ X1 )
                                                                                                                                           => ! [X5: $i] :
                                                                                                                                                ( ( in @ X5 @ X2 )
                                                                                                                                               => ( X3
                                                                                                                                                 != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                                 => ( sP5
                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                          ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                                         => ~ ! [X3: $i] :
                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                               => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                                     => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                                       => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                         => ( ! [X1: $i] :
                                                                                                                                                ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                                = X1 )
                                                                                                                                           => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                  ( ! [X3: $i] :
                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                          ( ( in @ X4 @ X1 )
                                                                                                                                                         => ( ( X2 @ X3 )
                                                                                                                                                           => ( ( X2 @ X4 )
                                                                                                                                                             => ( X3 = X4 ) ) ) ) )
                                                                                                                                                 => ( ~ ! [X3: $i] :
                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                         => ~ ( X2 @ X3 ) )
                                                                                                                                                   => ~ ! [X3: $i] :
                                                                                                                                                          ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                         => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                           != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                             => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                    ( ~ ! [X3: $i] :
                                                                                                                                                          ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                         => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                           != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                                   => ~ ! [X3: $i] :
                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                         => ~ ( X2 @ X3 ) ) )
                                                                                                                                               => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                     => ( ( X2 @ X3 )
                                                                                                                                                       => ( ! [X4: $i] :
                                                                                                                                                              ( ( in @ X4 @ X1 )
                                                                                                                                                             => ( ( X2 @ X4 )
                                                                                                                                                               => ( X4 = X3 ) ) )
                                                                                                                                                         => ~ ! [X4: $i] :
                                                                                                                                                                ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                               => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                 != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                        ( ! [X3: $i] :
                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                ( ( in @ X4 @ X1 )
                                                                                                                                                               => ( ( X2 @ X3 )
                                                                                                                                                                 => ( ( X2 @ X4 )
                                                                                                                                                                   => ( X3 = X4 ) ) ) ) )
                                                                                                                                                       => ( ~ ! [X3: $i] :
                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                               => ~ ( X2 @ X3 ) )
                                                                                                                                                         => ~ ! [X3: $i] :
                                                                                                                                                                ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                               => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                 != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                          ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                            = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                         => ( X1 = X2 ) )
                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                            ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                           => ( X1 = X3 ) )
                                                                                                                                                       => ( ! [X1: $i] :
                                                                                                                                                              ( ( iskpair @ X1 )
                                                                                                                                                             => ~ ! [X2: $i] :
                                                                                                                                                                    ( ( in @ X2
                                                                                                                                                                      @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                        @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                                   => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                        @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                                     != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                         => ( ! [X1: $i] :
                                                                                                                                                                ( ~ ! [X2: $i] :
                                                                                                                                                                      ( ( in @ X2 @ X1 )
                                                                                                                                                                     => ( X1
                                                                                                                                                                       != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                               => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                  ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                  = X1 )
                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                    ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                   => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                      ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                        = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                     => ( X1 = X3 ) )
                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                        ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                          = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                       => ( X1 = X3 ) )
                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                          ( ( X1 = X2 )
                                                                                                                                                                         => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                            = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                            ( ( X1 = X2 )
                                                                                                                                                                           => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                              = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                              ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                             => ( ( X3 = X4 )
                                                                                                                                                                               => ( X2 = X4 ) ) )
                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                  = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                               => ( X1 = X2 ) )
                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                  ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                    = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                 => ( X2 = X4 ) )
                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                    ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                      = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                   => ( X2 = X4 ) )
                                                                                                                                                                               => ( ! [X1: $i] :
                                                                                                                                                                                      ( ( iskpair @ X1 )
                                                                                                                                                                                     => ~ ! [X2: $i] :
                                                                                                                                                                                            ( ( in @ X2
                                                                                                                                                                                              @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                @ ^ [X3: $i] :
                                                                                                                                                                                                    ( X1
                                                                                                                                                                                                    = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                           => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                @ ^ [X3: $i] :
                                                                                                                                                                                                    ( X1
                                                                                                                                                                                                    = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                             != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                        ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                        = X2 )
                                                                                                                                                                                   => ( sP8
                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                            ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                           => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                              ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                             => ( in @ X3 @ X1 ) )
                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                               => ( in @ X4 @ X2 ) )
                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                                                                                     => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                        = X3 ) ) )
                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                                                                                       => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                          = X4 ) ) )
                                                                                                                                                                                               => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                    ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                   => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                                      = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h144,assumption,
    ! [X1: $i] : ( subset @ X1 @ X1 ),
    introduced(assumption,[]) ).

thf(h145,assumption,
    ~ ( ! [X1: $i,X2: $i,X3: $i] :
          ( ( subset @ X1 @ X2 )
         => ( ( subset @ X2 @ X3 )
           => ( subset @ X1 @ X3 ) ) )
     => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) )
       => ( ! [X1: $i,X2: $i,X3: $i] :
              ( ( subset @ X1 @ X3 )
             => ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
         => ( ! [X1: $i,X2: $i] :
                ( ( subset @ X1 @ X2 )
               => ( in @ X1 @ ( powerset @ X2 ) ) )
           => ( ! [X1: $i,X2: $i] :
                  ( ( subset @ X1 @ X2 )
                 => ( ( subset @ X2 @ X1 )
                   => ( X1 = X2 ) ) )
             => ( ! [X1: $i] :
                    ( ( subset @ X1 @ emptyset )
                   => ( X1 = emptyset ) )
               => ( ! [X1: $i,X2: $i] :
                      ( ( subset @ X2 @ X1 )
                     => ( in @ X2 @ ( powerset @ X1 ) ) )
                 => ( ! [X1: $i,X2: $i] :
                        ( ( in @ X2 @ ( powerset @ X1 ) )
                       => ( subset @ X2 @ X1 ) )
                   => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
                     => ( ! [X1: $i,X2: $i] :
                            ( ( subset @ X1 @ X2 )
                           => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
                       => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                         => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                  ( ( in @ X3 @ X1 )
                                 => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                             => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                      ( ( in @ X3 @ X2 )
                                     => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                        ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                       => ( ( ( in @ X3 @ X1 )
                                           => X4 )
                                         => ( ( ( in @ X3 @ X2 )
                                             => X4 )
                                           => X4 ) ) )
                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                          ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                         => ( ~ ( in @ X3 @ X1 )
                                           => ( in @ X3 @ X2 ) ) )
                                     => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                                       => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                ( ( in @ X3 @ X1 )
                                               => ( ( in @ X3 @ X2 )
                                                 => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                  ( ( subset @ X3 @ X1 )
                                                 => ( ( subset @ X3 @ X2 )
                                                   => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                    ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                   => ( in @ X3 @ X1 ) )
                                               => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                                 => ( ! [X1: $i,X2: $i] :
                                                        ( ( subset @ X1 @ X2 )
                                                       => ( ( binintersect @ X1 @ X2 )
                                                          = X1 ) )
                                                   => ( ! [X1: $i,X2: $i] :
                                                          ( ( ( binintersect @ X1 @ X2 )
                                                            = X2 )
                                                         => ( subset @ X2 @ X1 ) )
                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                            ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                           => ( in @ X3 @ X2 ) )
                                                       => ( ! [X1: $i,X2: $i] :
                                                              ( ! [X3: $i] :
                                                                  ( ( in @ X3 @ X1 )
                                                                 => ~ ( in @ X3 @ X2 ) )
                                                             => ( ( binintersect @ X1 @ X2 )
                                                                = emptyset ) )
                                                         => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                           => ( ! [X1: $i,X2: $i] :
                                                                  ( ( subset @ X2 @ X1 )
                                                                 => ( ( binintersect @ X1 @ X2 )
                                                                    = X2 ) )
                                                             => ( ! [X1: $i,X2: $i] :
                                                                    ( ( ( binintersect @ X1 @ X2 )
                                                                      = X1 )
                                                                   => ( subset @ X1 @ X2 ) )
                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                      ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                                      = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                        ( ( in @ X3 @ X1 )
                                                                       => ( ~ ( in @ X3 @ X2 )
                                                                         => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                          ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                         => ( in @ X3 @ X1 ) )
                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                            ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                           => ~ ( in @ X3 @ X2 ) )
                                                                       => ( ! [X1: $i,X2: $i] :
                                                                              ( ( subset @ X1 @ X2 )
                                                                             => ( ( setminus @ X1 @ X2 )
                                                                                = emptyset ) )
                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                               => ( ( in @ X3 @ X1 )
                                                                                 => ( in @ X3 @ X2 ) ) )
                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                  ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                 => ( ~ ( in @ X3 @ X2 )
                                                                                   => ~ ( in @ X3 @ X1 ) ) )
                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                    ( ~ ( in @ X3 @ X1 )
                                                                                   => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                      ( ( in @ X3 @ X2 )
                                                                                     => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                 => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                          ( ( ( setminus @ X1 @ X2 )
                                                                                            = emptyset )
                                                                                         => ( subset @ X1 @ X2 ) )
                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                            ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                           => ! [X4: $o] :
                                                                                                ( ( ( in @ X3 @ X1 )
                                                                                                 => ( ~ ( in @ X3 @ X2 )
                                                                                                   => X4 ) )
                                                                                               => ( ( ~ ( in @ X3 @ X1 )
                                                                                                   => ( ( in @ X3 @ X2 )
                                                                                                     => X4 ) )
                                                                                                 => X4 ) ) )
                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                              ( ( in @ X3 @ X1 )
                                                                                             => ( ~ ( in @ X3 @ X2 )
                                                                                               => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                ( ~ ( in @ X3 @ X1 )
                                                                                               => ( ( in @ X3 @ X2 )
                                                                                                 => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                 => ( ( in @ X3 @ X2 )
                                                                                                   => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                    ( ~ ( in @ X3 @ X1 )
                                                                                                   => ( ~ ( in @ X3 @ X2 )
                                                                                                     => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                               => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                 => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                   => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                     => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                       => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                ( ( in @ X2 @ X1 )
                                                                                                               => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                  ( ( in @ X2 @ X1 )
                                                                                                                 => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                   => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                      ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                     => ( ( X3 != X1 )
                                                                                                                       => ( X3 = X2 ) ) )
                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                       => ! [X4: $i] :
                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                           => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                         => ! [X4: $i] :
                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                             => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                           => ! [X4: $i] :
                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                               => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                             => ! [X4: $i] :
                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                 => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                               => ! [X4: $i] :
                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                   => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                 => ! [X4: $i] :
                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                     => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                    ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                   => ~ ! [X4: $i] :
                                                                                                                                          ( ( in @ X4 @ X1 )
                                                                                                                                         => ! [X5: $i] :
                                                                                                                                              ( ( in @ X5 @ X2 )
                                                                                                                                             => ( X3
                                                                                                                                               != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                               => ( sP5
                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                        ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                                       => ~ ! [X3: $i] :
                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                             => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                                   => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                                     => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                       => ( ! [X1: $i] :
                                                                                                                                              ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                              = X1 )
                                                                                                                                         => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                ( ! [X3: $i] :
                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                        ( ( in @ X4 @ X1 )
                                                                                                                                                       => ( ( X2 @ X3 )
                                                                                                                                                         => ( ( X2 @ X4 )
                                                                                                                                                           => ( X3 = X4 ) ) ) ) )
                                                                                                                                               => ( ~ ! [X3: $i] :
                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                       => ~ ( X2 @ X3 ) )
                                                                                                                                                 => ~ ! [X3: $i] :
                                                                                                                                                        ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                       => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                         != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                           => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                  ( ~ ! [X3: $i] :
                                                                                                                                                        ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                       => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                         != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                                 => ~ ! [X3: $i] :
                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                       => ~ ( X2 @ X3 ) ) )
                                                                                                                                             => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                   => ( ( X2 @ X3 )
                                                                                                                                                     => ( ! [X4: $i] :
                                                                                                                                                            ( ( in @ X4 @ X1 )
                                                                                                                                                           => ( ( X2 @ X4 )
                                                                                                                                                             => ( X4 = X3 ) ) )
                                                                                                                                                       => ~ ! [X4: $i] :
                                                                                                                                                              ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                             => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                               != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                               => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                      ( ! [X3: $i] :
                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                              ( ( in @ X4 @ X1 )
                                                                                                                                                             => ( ( X2 @ X3 )
                                                                                                                                                               => ( ( X2 @ X4 )
                                                                                                                                                                 => ( X3 = X4 ) ) ) ) )
                                                                                                                                                     => ( ~ ! [X3: $i] :
                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                             => ~ ( X2 @ X3 ) )
                                                                                                                                                       => ~ ! [X3: $i] :
                                                                                                                                                              ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                             => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                               != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                        ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                          = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                       => ( X1 = X2 ) )
                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                          ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                         => ( X1 = X3 ) )
                                                                                                                                                     => ( ! [X1: $i] :
                                                                                                                                                            ( ( iskpair @ X1 )
                                                                                                                                                           => ~ ! [X2: $i] :
                                                                                                                                                                  ( ( in @ X2
                                                                                                                                                                    @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                      @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                                 => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                      @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                                   != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                       => ( ! [X1: $i] :
                                                                                                                                                              ( ~ ! [X2: $i] :
                                                                                                                                                                    ( ( in @ X2 @ X1 )
                                                                                                                                                                   => ( X1
                                                                                                                                                                     != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                             => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                = X1 )
                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                  ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                 => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                    ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                      = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                   => ( X1 = X3 ) )
                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                      ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                        = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                     => ( X1 = X3 ) )
                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                        ( ( X1 = X2 )
                                                                                                                                                                       => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                          = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                          ( ( X1 = X2 )
                                                                                                                                                                         => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                            = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                            ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                              = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                           => ( ( X3 = X4 )
                                                                                                                                                                             => ( X2 = X4 ) ) )
                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                              ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                             => ( X1 = X2 ) )
                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                  = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                               => ( X2 = X4 ) )
                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                  ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                    = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                 => ( X2 = X4 ) )
                                                                                                                                                                             => ( ! [X1: $i] :
                                                                                                                                                                                    ( ( iskpair @ X1 )
                                                                                                                                                                                   => ~ ! [X2: $i] :
                                                                                                                                                                                          ( ( in @ X2
                                                                                                                                                                                            @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                              @ ^ [X3: $i] :
                                                                                                                                                                                                  ( X1
                                                                                                                                                                                                  = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                         => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                              @ ^ [X3: $i] :
                                                                                                                                                                                                  ( X1
                                                                                                                                                                                                  = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                           != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                      ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                      = X2 )
                                                                                                                                                                                 => ( sP8
                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                         => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                            ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                           => ( in @ X3 @ X1 ) )
                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                              ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                             => ( in @ X4 @ X2 ) )
                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                                                                                   => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                      = X3 ) ) )
                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                                                                                     => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                        = X4 ) ) )
                                                                                                                                                                                             => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                  ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                 => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                                    = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h146,assumption,
    ! [X1: $i,X2: $i,X3: $i] :
      ( ( subset @ X1 @ X2 )
     => ( ( subset @ X2 @ X3 )
       => ( subset @ X1 @ X3 ) ) ),
    introduced(assumption,[]) ).

thf(h147,assumption,
    ~ ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) )
     => ( ! [X1: $i,X2: $i,X3: $i] :
            ( ( subset @ X1 @ X3 )
           => ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
       => ( ! [X1: $i,X2: $i] :
              ( ( subset @ X1 @ X2 )
             => ( in @ X1 @ ( powerset @ X2 ) ) )
         => ( ! [X1: $i,X2: $i] :
                ( ( subset @ X1 @ X2 )
               => ( ( subset @ X2 @ X1 )
                 => ( X1 = X2 ) ) )
           => ( ! [X1: $i] :
                  ( ( subset @ X1 @ emptyset )
                 => ( X1 = emptyset ) )
             => ( ! [X1: $i,X2: $i] :
                    ( ( subset @ X2 @ X1 )
                   => ( in @ X2 @ ( powerset @ X1 ) ) )
               => ( ! [X1: $i,X2: $i] :
                      ( ( in @ X2 @ ( powerset @ X1 ) )
                     => ( subset @ X2 @ X1 ) )
                 => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
                   => ( ! [X1: $i,X2: $i] :
                          ( ( subset @ X1 @ X2 )
                         => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
                     => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                       => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                ( ( in @ X3 @ X1 )
                               => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                           => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                    ( ( in @ X3 @ X2 )
                                   => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                      ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                     => ( ( ( in @ X3 @ X1 )
                                         => X4 )
                                       => ( ( ( in @ X3 @ X2 )
                                           => X4 )
                                         => X4 ) ) )
                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                        ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                       => ( ~ ( in @ X3 @ X1 )
                                         => ( in @ X3 @ X2 ) ) )
                                   => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                                     => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                              ( ( in @ X3 @ X1 )
                                             => ( ( in @ X3 @ X2 )
                                               => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                ( ( subset @ X3 @ X1 )
                                               => ( ( subset @ X3 @ X2 )
                                                 => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                  ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                 => ( in @ X3 @ X1 ) )
                                             => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                               => ( ! [X1: $i,X2: $i] :
                                                      ( ( subset @ X1 @ X2 )
                                                     => ( ( binintersect @ X1 @ X2 )
                                                        = X1 ) )
                                                 => ( ! [X1: $i,X2: $i] :
                                                        ( ( ( binintersect @ X1 @ X2 )
                                                          = X2 )
                                                       => ( subset @ X2 @ X1 ) )
                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                          ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                         => ( in @ X3 @ X2 ) )
                                                     => ( ! [X1: $i,X2: $i] :
                                                            ( ! [X3: $i] :
                                                                ( ( in @ X3 @ X1 )
                                                               => ~ ( in @ X3 @ X2 ) )
                                                           => ( ( binintersect @ X1 @ X2 )
                                                              = emptyset ) )
                                                       => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                         => ( ! [X1: $i,X2: $i] :
                                                                ( ( subset @ X2 @ X1 )
                                                               => ( ( binintersect @ X1 @ X2 )
                                                                  = X2 ) )
                                                           => ( ! [X1: $i,X2: $i] :
                                                                  ( ( ( binintersect @ X1 @ X2 )
                                                                    = X1 )
                                                                 => ( subset @ X1 @ X2 ) )
                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                    ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                                    = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                      ( ( in @ X3 @ X1 )
                                                                     => ( ~ ( in @ X3 @ X2 )
                                                                       => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                        ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                       => ( in @ X3 @ X1 ) )
                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                          ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                         => ~ ( in @ X3 @ X2 ) )
                                                                     => ( ! [X1: $i,X2: $i] :
                                                                            ( ( subset @ X1 @ X2 )
                                                                           => ( ( setminus @ X1 @ X2 )
                                                                              = emptyset ) )
                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                              ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                             => ( ( in @ X3 @ X1 )
                                                                               => ( in @ X3 @ X2 ) ) )
                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                               => ( ~ ( in @ X3 @ X2 )
                                                                                 => ~ ( in @ X3 @ X1 ) ) )
                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                  ( ~ ( in @ X3 @ X1 )
                                                                                 => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                    ( ( in @ X3 @ X2 )
                                                                                   => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                               => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                        ( ( ( setminus @ X1 @ X2 )
                                                                                          = emptyset )
                                                                                       => ( subset @ X1 @ X2 ) )
                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                          ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                         => ! [X4: $o] :
                                                                                              ( ( ( in @ X3 @ X1 )
                                                                                               => ( ~ ( in @ X3 @ X2 )
                                                                                                 => X4 ) )
                                                                                             => ( ( ~ ( in @ X3 @ X1 )
                                                                                                 => ( ( in @ X3 @ X2 )
                                                                                                   => X4 ) )
                                                                                               => X4 ) ) )
                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                            ( ( in @ X3 @ X1 )
                                                                                           => ( ~ ( in @ X3 @ X2 )
                                                                                             => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                              ( ~ ( in @ X3 @ X1 )
                                                                                             => ( ( in @ X3 @ X2 )
                                                                                               => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                ( ( in @ X3 @ X1 )
                                                                                               => ( ( in @ X3 @ X2 )
                                                                                                 => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                  ( ~ ( in @ X3 @ X1 )
                                                                                                 => ( ~ ( in @ X3 @ X2 )
                                                                                                   => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                             => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                               => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                 => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                   => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                     => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                              ( ( in @ X2 @ X1 )
                                                                                                             => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                ( ( in @ X2 @ X1 )
                                                                                                               => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                 => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                    ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                   => ( ( X3 != X1 )
                                                                                                                     => ( X3 = X2 ) ) )
                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                     => ! [X4: $i] :
                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                         => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                       => ! [X4: $i] :
                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                           => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                         => ! [X4: $i] :
                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                             => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                           => ! [X4: $i] :
                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                               => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                             => ! [X4: $i] :
                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                 => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                               => ! [X4: $i] :
                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                   => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                  ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                 => ~ ! [X4: $i] :
                                                                                                                                        ( ( in @ X4 @ X1 )
                                                                                                                                       => ! [X5: $i] :
                                                                                                                                            ( ( in @ X5 @ X2 )
                                                                                                                                           => ( X3
                                                                                                                                             != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                             => ( sP5
                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                      ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                                     => ~ ! [X3: $i] :
                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                           => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                                 => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                                   => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                     => ( ! [X1: $i] :
                                                                                                                                            ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                            = X1 )
                                                                                                                                       => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                              ( ! [X3: $i] :
                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                      ( ( in @ X4 @ X1 )
                                                                                                                                                     => ( ( X2 @ X3 )
                                                                                                                                                       => ( ( X2 @ X4 )
                                                                                                                                                         => ( X3 = X4 ) ) ) ) )
                                                                                                                                             => ( ~ ! [X3: $i] :
                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                     => ~ ( X2 @ X3 ) )
                                                                                                                                               => ~ ! [X3: $i] :
                                                                                                                                                      ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                     => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                       != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                         => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                ( ~ ! [X3: $i] :
                                                                                                                                                      ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                     => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                       != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                               => ~ ! [X3: $i] :
                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                     => ~ ( X2 @ X3 ) ) )
                                                                                                                                           => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                 => ( ( X2 @ X3 )
                                                                                                                                                   => ( ! [X4: $i] :
                                                                                                                                                          ( ( in @ X4 @ X1 )
                                                                                                                                                         => ( ( X2 @ X4 )
                                                                                                                                                           => ( X4 = X3 ) ) )
                                                                                                                                                     => ~ ! [X4: $i] :
                                                                                                                                                            ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                           => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                             != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                             => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                    ( ! [X3: $i] :
                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                            ( ( in @ X4 @ X1 )
                                                                                                                                                           => ( ( X2 @ X3 )
                                                                                                                                                             => ( ( X2 @ X4 )
                                                                                                                                                               => ( X3 = X4 ) ) ) ) )
                                                                                                                                                   => ( ~ ! [X3: $i] :
                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                           => ~ ( X2 @ X3 ) )
                                                                                                                                                     => ~ ! [X3: $i] :
                                                                                                                                                            ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                           => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                             != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                      ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                        = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                     => ( X1 = X2 ) )
                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                        ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                       => ( X1 = X3 ) )
                                                                                                                                                   => ( ! [X1: $i] :
                                                                                                                                                          ( ( iskpair @ X1 )
                                                                                                                                                         => ~ ! [X2: $i] :
                                                                                                                                                                ( ( in @ X2
                                                                                                                                                                  @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                    @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                               => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                    @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                                 != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                     => ( ! [X1: $i] :
                                                                                                                                                            ( ~ ! [X2: $i] :
                                                                                                                                                                  ( ( in @ X2 @ X1 )
                                                                                                                                                                 => ( X1
                                                                                                                                                                   != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                           => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                              ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                              = X1 )
                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                               => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                  ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                    = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                 => ( X1 = X3 ) )
                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                    ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                      = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                   => ( X1 = X3 ) )
                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                      ( ( X1 = X2 )
                                                                                                                                                                     => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                        = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                        ( ( X1 = X2 )
                                                                                                                                                                       => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                          = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                          ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                            = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                         => ( ( X3 = X4 )
                                                                                                                                                                           => ( X2 = X4 ) ) )
                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                            ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                              = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                           => ( X1 = X2 ) )
                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                              ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                             => ( X2 = X4 ) )
                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                  = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                               => ( X2 = X4 ) )
                                                                                                                                                                           => ( ! [X1: $i] :
                                                                                                                                                                                  ( ( iskpair @ X1 )
                                                                                                                                                                                 => ~ ! [X2: $i] :
                                                                                                                                                                                        ( ( in @ X2
                                                                                                                                                                                          @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                            @ ^ [X3: $i] :
                                                                                                                                                                                                ( X1
                                                                                                                                                                                                = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                       => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                            @ ^ [X3: $i] :
                                                                                                                                                                                                ( X1
                                                                                                                                                                                                = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                         != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                    ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                    = X2 )
                                                                                                                                                                               => ( sP8
                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                       => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                          ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                         => ( in @ X3 @ X1 ) )
                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                            ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                           => ( in @ X4 @ X2 ) )
                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                                                                                 => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                    = X3 ) ) )
                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                                                                                   => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                      = X4 ) ) )
                                                                                                                                                                                           => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                               => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                                  = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h148,assumption,
    ! [X1: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) ),
    introduced(assumption,[]) ).

thf(h149,assumption,
    ~ ( ! [X1: $i,X2: $i,X3: $i] :
          ( ( subset @ X1 @ X3 )
         => ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
     => ( ! [X1: $i,X2: $i] :
            ( ( subset @ X1 @ X2 )
           => ( in @ X1 @ ( powerset @ X2 ) ) )
       => ( ! [X1: $i,X2: $i] :
              ( ( subset @ X1 @ X2 )
             => ( ( subset @ X2 @ X1 )
               => ( X1 = X2 ) ) )
         => ( ! [X1: $i] :
                ( ( subset @ X1 @ emptyset )
               => ( X1 = emptyset ) )
           => ( ! [X1: $i,X2: $i] :
                  ( ( subset @ X2 @ X1 )
                 => ( in @ X2 @ ( powerset @ X1 ) ) )
             => ( ! [X1: $i,X2: $i] :
                    ( ( in @ X2 @ ( powerset @ X1 ) )
                   => ( subset @ X2 @ X1 ) )
               => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
                 => ( ! [X1: $i,X2: $i] :
                        ( ( subset @ X1 @ X2 )
                       => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
                   => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                     => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                       => ( ! [X1: $i,X2: $i,X3: $i] :
                              ( ( in @ X3 @ X1 )
                             => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                         => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                  ( ( in @ X3 @ X2 )
                                 => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                    ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                   => ( ( ( in @ X3 @ X1 )
                                       => X4 )
                                     => ( ( ( in @ X3 @ X2 )
                                         => X4 )
                                       => X4 ) ) )
                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                      ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                     => ( ~ ( in @ X3 @ X1 )
                                       => ( in @ X3 @ X2 ) ) )
                                 => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                                   => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                            ( ( in @ X3 @ X1 )
                                           => ( ( in @ X3 @ X2 )
                                             => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                              ( ( subset @ X3 @ X1 )
                                             => ( ( subset @ X3 @ X2 )
                                               => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                               => ( in @ X3 @ X1 ) )
                                           => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                             => ( ! [X1: $i,X2: $i] :
                                                    ( ( subset @ X1 @ X2 )
                                                   => ( ( binintersect @ X1 @ X2 )
                                                      = X1 ) )
                                               => ( ! [X1: $i,X2: $i] :
                                                      ( ( ( binintersect @ X1 @ X2 )
                                                        = X2 )
                                                     => ( subset @ X2 @ X1 ) )
                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                        ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                       => ( in @ X3 @ X2 ) )
                                                   => ( ! [X1: $i,X2: $i] :
                                                          ( ! [X3: $i] :
                                                              ( ( in @ X3 @ X1 )
                                                             => ~ ( in @ X3 @ X2 ) )
                                                         => ( ( binintersect @ X1 @ X2 )
                                                            = emptyset ) )
                                                     => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                       => ( ! [X1: $i,X2: $i] :
                                                              ( ( subset @ X2 @ X1 )
                                                             => ( ( binintersect @ X1 @ X2 )
                                                                = X2 ) )
                                                         => ( ! [X1: $i,X2: $i] :
                                                                ( ( ( binintersect @ X1 @ X2 )
                                                                  = X1 )
                                                               => ( subset @ X1 @ X2 ) )
                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                  ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                                  = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                    ( ( in @ X3 @ X1 )
                                                                   => ( ~ ( in @ X3 @ X2 )
                                                                     => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                      ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                     => ( in @ X3 @ X1 ) )
                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                        ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                       => ~ ( in @ X3 @ X2 ) )
                                                                   => ( ! [X1: $i,X2: $i] :
                                                                          ( ( subset @ X1 @ X2 )
                                                                         => ( ( setminus @ X1 @ X2 )
                                                                            = emptyset ) )
                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                            ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                           => ( ( in @ X3 @ X1 )
                                                                             => ( in @ X3 @ X2 ) ) )
                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                              ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                             => ( ~ ( in @ X3 @ X2 )
                                                                               => ~ ( in @ X3 @ X1 ) ) )
                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                ( ~ ( in @ X3 @ X1 )
                                                                               => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                  ( ( in @ X3 @ X2 )
                                                                                 => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                             => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                      ( ( ( setminus @ X1 @ X2 )
                                                                                        = emptyset )
                                                                                     => ( subset @ X1 @ X2 ) )
                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                        ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                       => ! [X4: $o] :
                                                                                            ( ( ( in @ X3 @ X1 )
                                                                                             => ( ~ ( in @ X3 @ X2 )
                                                                                               => X4 ) )
                                                                                           => ( ( ~ ( in @ X3 @ X1 )
                                                                                               => ( ( in @ X3 @ X2 )
                                                                                                 => X4 ) )
                                                                                             => X4 ) ) )
                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                          ( ( in @ X3 @ X1 )
                                                                                         => ( ~ ( in @ X3 @ X2 )
                                                                                           => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                            ( ~ ( in @ X3 @ X1 )
                                                                                           => ( ( in @ X3 @ X2 )
                                                                                             => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                              ( ( in @ X3 @ X1 )
                                                                                             => ( ( in @ X3 @ X2 )
                                                                                               => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                ( ~ ( in @ X3 @ X1 )
                                                                                               => ( ~ ( in @ X3 @ X2 )
                                                                                                 => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                           => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                             => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                               => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                 => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                   => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                            ( ( in @ X2 @ X1 )
                                                                                                           => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                              ( ( in @ X2 @ X1 )
                                                                                                             => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                               => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                  ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                 => ( ( X3 != X1 )
                                                                                                                   => ( X3 = X2 ) ) )
                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                   => ! [X4: $i] :
                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                       => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                     => ! [X4: $i] :
                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                         => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                       => ! [X4: $i] :
                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                           => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                         => ! [X4: $i] :
                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                             => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                           => ! [X4: $i] :
                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                               => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                             => ! [X4: $i] :
                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                 => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                               => ~ ! [X4: $i] :
                                                                                                                                      ( ( in @ X4 @ X1 )
                                                                                                                                     => ! [X5: $i] :
                                                                                                                                          ( ( in @ X5 @ X2 )
                                                                                                                                         => ( X3
                                                                                                                                           != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                           => ( sP5
                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                    ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                                   => ~ ! [X3: $i] :
                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                         => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                               => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                                 => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                   => ( ! [X1: $i] :
                                                                                                                                          ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                          = X1 )
                                                                                                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                            ( ! [X3: $i] :
                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                    ( ( in @ X4 @ X1 )
                                                                                                                                                   => ( ( X2 @ X3 )
                                                                                                                                                     => ( ( X2 @ X4 )
                                                                                                                                                       => ( X3 = X4 ) ) ) ) )
                                                                                                                                           => ( ~ ! [X3: $i] :
                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                   => ~ ( X2 @ X3 ) )
                                                                                                                                             => ~ ! [X3: $i] :
                                                                                                                                                    ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                   => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                     != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                              ( ~ ! [X3: $i] :
                                                                                                                                                    ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                   => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                     != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                             => ~ ! [X3: $i] :
                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                   => ~ ( X2 @ X3 ) ) )
                                                                                                                                         => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                               => ( ( X2 @ X3 )
                                                                                                                                                 => ( ! [X4: $i] :
                                                                                                                                                        ( ( in @ X4 @ X1 )
                                                                                                                                                       => ( ( X2 @ X4 )
                                                                                                                                                         => ( X4 = X3 ) ) )
                                                                                                                                                   => ~ ! [X4: $i] :
                                                                                                                                                          ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                         => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                           != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                           => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                  ( ! [X3: $i] :
                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                          ( ( in @ X4 @ X1 )
                                                                                                                                                         => ( ( X2 @ X3 )
                                                                                                                                                           => ( ( X2 @ X4 )
                                                                                                                                                             => ( X3 = X4 ) ) ) ) )
                                                                                                                                                 => ( ~ ! [X3: $i] :
                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                         => ~ ( X2 @ X3 ) )
                                                                                                                                                   => ~ ! [X3: $i] :
                                                                                                                                                          ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                         => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                           != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                    ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                      = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                   => ( X1 = X2 ) )
                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                      ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                     => ( X1 = X3 ) )
                                                                                                                                                 => ( ! [X1: $i] :
                                                                                                                                                        ( ( iskpair @ X1 )
                                                                                                                                                       => ~ ! [X2: $i] :
                                                                                                                                                              ( ( in @ X2
                                                                                                                                                                @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                  @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                             => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                  @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                               != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                   => ( ! [X1: $i] :
                                                                                                                                                          ( ~ ! [X2: $i] :
                                                                                                                                                                ( ( in @ X2 @ X1 )
                                                                                                                                                               => ( X1
                                                                                                                                                                 != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                         => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                            ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                            = X1 )
                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                              ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                             => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                  = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                               => ( X1 = X3 ) )
                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                  ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                    = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                 => ( X1 = X3 ) )
                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                    ( ( X1 = X2 )
                                                                                                                                                                   => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                      = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                      ( ( X1 = X2 )
                                                                                                                                                                     => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                        = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                        ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                          = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                       => ( ( X3 = X4 )
                                                                                                                                                                         => ( X2 = X4 ) ) )
                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                          ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                            = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                         => ( X1 = X2 ) )
                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                            ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                              = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                           => ( X2 = X4 ) )
                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                              ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                             => ( X2 = X4 ) )
                                                                                                                                                                         => ( ! [X1: $i] :
                                                                                                                                                                                ( ( iskpair @ X1 )
                                                                                                                                                                               => ~ ! [X2: $i] :
                                                                                                                                                                                      ( ( in @ X2
                                                                                                                                                                                        @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                          @ ^ [X3: $i] :
                                                                                                                                                                                              ( X1
                                                                                                                                                                                              = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                     => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                          @ ^ [X3: $i] :
                                                                                                                                                                                              ( X1
                                                                                                                                                                                              = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                       != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                  ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                  = X2 )
                                                                                                                                                                             => ( sP8
                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                      ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                     => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                        ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                       => ( in @ X3 @ X1 ) )
                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                          ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                         => ( in @ X4 @ X2 ) )
                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                                                                                               => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                  = X3 ) ) )
                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                                                                                 => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                    = X4 ) ) )
                                                                                                                                                                                         => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                              ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                             => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                                = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h150,assumption,
    ! [X1: $i,X2: $i,X3: $i] :
      ( ( subset @ X1 @ X3 )
     => ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) ),
    introduced(assumption,[]) ).

thf(h151,assumption,
    ~ ( ! [X1: $i,X2: $i] :
          ( ( subset @ X1 @ X2 )
         => ( in @ X1 @ ( powerset @ X2 ) ) )
     => ( ! [X1: $i,X2: $i] :
            ( ( subset @ X1 @ X2 )
           => ( ( subset @ X2 @ X1 )
             => ( X1 = X2 ) ) )
       => ( ! [X1: $i] :
              ( ( subset @ X1 @ emptyset )
             => ( X1 = emptyset ) )
         => ( ! [X1: $i,X2: $i] :
                ( ( subset @ X2 @ X1 )
               => ( in @ X2 @ ( powerset @ X1 ) ) )
           => ( ! [X1: $i,X2: $i] :
                  ( ( in @ X2 @ ( powerset @ X1 ) )
                 => ( subset @ X2 @ X1 ) )
             => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
               => ( ! [X1: $i,X2: $i] :
                      ( ( subset @ X1 @ X2 )
                     => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
                 => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                   => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                     => ( ! [X1: $i,X2: $i,X3: $i] :
                            ( ( in @ X3 @ X1 )
                           => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                       => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                ( ( in @ X3 @ X2 )
                               => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                  ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                 => ( ( ( in @ X3 @ X1 )
                                     => X4 )
                                   => ( ( ( in @ X3 @ X2 )
                                       => X4 )
                                     => X4 ) ) )
                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                    ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                   => ( ~ ( in @ X3 @ X1 )
                                     => ( in @ X3 @ X2 ) ) )
                               => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                                 => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                          ( ( in @ X3 @ X1 )
                                         => ( ( in @ X3 @ X2 )
                                           => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                            ( ( subset @ X3 @ X1 )
                                           => ( ( subset @ X3 @ X2 )
                                             => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                              ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                             => ( in @ X3 @ X1 ) )
                                         => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                           => ( ! [X1: $i,X2: $i] :
                                                  ( ( subset @ X1 @ X2 )
                                                 => ( ( binintersect @ X1 @ X2 )
                                                    = X1 ) )
                                             => ( ! [X1: $i,X2: $i] :
                                                    ( ( ( binintersect @ X1 @ X2 )
                                                      = X2 )
                                                   => ( subset @ X2 @ X1 ) )
                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                      ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                     => ( in @ X3 @ X2 ) )
                                                 => ( ! [X1: $i,X2: $i] :
                                                        ( ! [X3: $i] :
                                                            ( ( in @ X3 @ X1 )
                                                           => ~ ( in @ X3 @ X2 ) )
                                                       => ( ( binintersect @ X1 @ X2 )
                                                          = emptyset ) )
                                                   => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                     => ( ! [X1: $i,X2: $i] :
                                                            ( ( subset @ X2 @ X1 )
                                                           => ( ( binintersect @ X1 @ X2 )
                                                              = X2 ) )
                                                       => ( ! [X1: $i,X2: $i] :
                                                              ( ( ( binintersect @ X1 @ X2 )
                                                                = X1 )
                                                             => ( subset @ X1 @ X2 ) )
                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                                = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                  ( ( in @ X3 @ X1 )
                                                                 => ( ~ ( in @ X3 @ X2 )
                                                                   => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                    ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                   => ( in @ X3 @ X1 ) )
                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                      ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                     => ~ ( in @ X3 @ X2 ) )
                                                                 => ( ! [X1: $i,X2: $i] :
                                                                        ( ( subset @ X1 @ X2 )
                                                                       => ( ( setminus @ X1 @ X2 )
                                                                          = emptyset ) )
                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                          ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                         => ( ( in @ X3 @ X1 )
                                                                           => ( in @ X3 @ X2 ) ) )
                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                            ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                           => ( ~ ( in @ X3 @ X2 )
                                                                             => ~ ( in @ X3 @ X1 ) ) )
                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                              ( ~ ( in @ X3 @ X1 )
                                                                             => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                ( ( in @ X3 @ X2 )
                                                                               => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                           => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                    ( ( ( setminus @ X1 @ X2 )
                                                                                      = emptyset )
                                                                                   => ( subset @ X1 @ X2 ) )
                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                      ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                     => ! [X4: $o] :
                                                                                          ( ( ( in @ X3 @ X1 )
                                                                                           => ( ~ ( in @ X3 @ X2 )
                                                                                             => X4 ) )
                                                                                         => ( ( ~ ( in @ X3 @ X1 )
                                                                                             => ( ( in @ X3 @ X2 )
                                                                                               => X4 ) )
                                                                                           => X4 ) ) )
                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                        ( ( in @ X3 @ X1 )
                                                                                       => ( ~ ( in @ X3 @ X2 )
                                                                                         => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                          ( ~ ( in @ X3 @ X1 )
                                                                                         => ( ( in @ X3 @ X2 )
                                                                                           => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                            ( ( in @ X3 @ X1 )
                                                                                           => ( ( in @ X3 @ X2 )
                                                                                             => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                              ( ~ ( in @ X3 @ X1 )
                                                                                             => ( ~ ( in @ X3 @ X2 )
                                                                                               => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                         => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                           => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                             => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                               => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                 => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                          ( ( in @ X2 @ X1 )
                                                                                                         => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                            ( ( in @ X2 @ X1 )
                                                                                                           => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                             => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                               => ( ( X3 != X1 )
                                                                                                                 => ( X3 = X2 ) ) )
                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                 => ! [X4: $i] :
                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                     => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                   => ! [X4: $i] :
                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                       => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                     => ! [X4: $i] :
                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                         => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                       => ! [X4: $i] :
                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                           => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                         => ! [X4: $i] :
                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                             => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                           => ! [X4: $i] :
                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                               => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                              ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                             => ~ ! [X4: $i] :
                                                                                                                                    ( ( in @ X4 @ X1 )
                                                                                                                                   => ! [X5: $i] :
                                                                                                                                        ( ( in @ X5 @ X2 )
                                                                                                                                       => ( X3
                                                                                                                                         != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                         => ( sP5
                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                  ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                                 => ~ ! [X3: $i] :
                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                       => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                             => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                               => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                 => ( ! [X1: $i] :
                                                                                                                                        ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                        = X1 )
                                                                                                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                          ( ! [X3: $i] :
                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                  ( ( in @ X4 @ X1 )
                                                                                                                                                 => ( ( X2 @ X3 )
                                                                                                                                                   => ( ( X2 @ X4 )
                                                                                                                                                     => ( X3 = X4 ) ) ) ) )
                                                                                                                                         => ( ~ ! [X3: $i] :
                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                 => ~ ( X2 @ X3 ) )
                                                                                                                                           => ~ ! [X3: $i] :
                                                                                                                                                  ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                 => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                   != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                            ( ~ ! [X3: $i] :
                                                                                                                                                  ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                 => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                   != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                           => ~ ! [X3: $i] :
                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                 => ~ ( X2 @ X3 ) ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                             => ( ( X2 @ X3 )
                                                                                                                                               => ( ! [X4: $i] :
                                                                                                                                                      ( ( in @ X4 @ X1 )
                                                                                                                                                     => ( ( X2 @ X4 )
                                                                                                                                                       => ( X4 = X3 ) ) )
                                                                                                                                                 => ~ ! [X4: $i] :
                                                                                                                                                        ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                       => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                         != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                         => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                ( ! [X3: $i] :
                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                        ( ( in @ X4 @ X1 )
                                                                                                                                                       => ( ( X2 @ X3 )
                                                                                                                                                         => ( ( X2 @ X4 )
                                                                                                                                                           => ( X3 = X4 ) ) ) ) )
                                                                                                                                               => ( ~ ! [X3: $i] :
                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                       => ~ ( X2 @ X3 ) )
                                                                                                                                                 => ~ ! [X3: $i] :
                                                                                                                                                        ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                       => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                         != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                  ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                    = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                 => ( X1 = X2 ) )
                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                    ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                   => ( X1 = X3 ) )
                                                                                                                                               => ( ! [X1: $i] :
                                                                                                                                                      ( ( iskpair @ X1 )
                                                                                                                                                     => ~ ! [X2: $i] :
                                                                                                                                                            ( ( in @ X2
                                                                                                                                                              @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                           => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                             != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                 => ( ! [X1: $i] :
                                                                                                                                                        ( ~ ! [X2: $i] :
                                                                                                                                                              ( ( in @ X2 @ X1 )
                                                                                                                                                             => ( X1
                                                                                                                                                               != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                       => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                          ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                          = X1 )
                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                            ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                           => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                              ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                             => ( X1 = X3 ) )
                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                  = ( kpair @ X3 @ X4 ) )
                                                                                                                                                               => ( X1 = X3 ) )
                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                  ( ( X1 = X2 )
                                                                                                                                                                 => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                    = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                    ( ( X1 = X2 )
                                                                                                                                                                   => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                      = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                      ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                        = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                     => ( ( X3 = X4 )
                                                                                                                                                                       => ( X2 = X4 ) ) )
                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                        ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                          = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                       => ( X1 = X2 ) )
                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                          ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                            = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                         => ( X2 = X4 ) )
                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                            ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                              = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                           => ( X2 = X4 ) )
                                                                                                                                                                       => ( ! [X1: $i] :
                                                                                                                                                                              ( ( iskpair @ X1 )
                                                                                                                                                                             => ~ ! [X2: $i] :
                                                                                                                                                                                    ( ( in @ X2
                                                                                                                                                                                      @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                        @ ^ [X3: $i] :
                                                                                                                                                                                            ( X1
                                                                                                                                                                                            = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                   => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                        @ ^ [X3: $i] :
                                                                                                                                                                                            ( X1
                                                                                                                                                                                            = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                     != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                = X2 )
                                                                                                                                                                           => ( sP8
                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                    ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                   => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                      ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                     => ( in @ X3 @ X1 ) )
                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                        ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                       => ( in @ X4 @ X2 ) )
                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                                                                                             => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                = X3 ) ) )
                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                                                                                               => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                  = X4 ) ) )
                                                                                                                                                                                       => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                            ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                           => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                              = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h152,assumption,
    ! [X1: $i,X2: $i] :
      ( ( subset @ X1 @ X2 )
     => ( in @ X1 @ ( powerset @ X2 ) ) ),
    introduced(assumption,[]) ).

thf(h153,assumption,
    ~ ( ! [X1: $i,X2: $i] :
          ( ( subset @ X1 @ X2 )
         => ( ( subset @ X2 @ X1 )
           => ( X1 = X2 ) ) )
     => ( ! [X1: $i] :
            ( ( subset @ X1 @ emptyset )
           => ( X1 = emptyset ) )
       => ( ! [X1: $i,X2: $i] :
              ( ( subset @ X2 @ X1 )
             => ( in @ X2 @ ( powerset @ X1 ) ) )
         => ( ! [X1: $i,X2: $i] :
                ( ( in @ X2 @ ( powerset @ X1 ) )
               => ( subset @ X2 @ X1 ) )
           => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
             => ( ! [X1: $i,X2: $i] :
                    ( ( subset @ X1 @ X2 )
                   => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
               => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                 => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                   => ( ! [X1: $i,X2: $i,X3: $i] :
                          ( ( in @ X3 @ X1 )
                         => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                     => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                       => ( ! [X1: $i,X2: $i,X3: $i] :
                              ( ( in @ X3 @ X2 )
                             => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                               => ( ( ( in @ X3 @ X1 )
                                   => X4 )
                                 => ( ( ( in @ X3 @ X2 )
                                     => X4 )
                                   => X4 ) ) )
                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                  ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                 => ( ~ ( in @ X3 @ X1 )
                                   => ( in @ X3 @ X2 ) ) )
                             => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                               => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                        ( ( in @ X3 @ X1 )
                                       => ( ( in @ X3 @ X2 )
                                         => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                          ( ( subset @ X3 @ X1 )
                                         => ( ( subset @ X3 @ X2 )
                                           => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                            ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                           => ( in @ X3 @ X1 ) )
                                       => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                         => ( ! [X1: $i,X2: $i] :
                                                ( ( subset @ X1 @ X2 )
                                               => ( ( binintersect @ X1 @ X2 )
                                                  = X1 ) )
                                           => ( ! [X1: $i,X2: $i] :
                                                  ( ( ( binintersect @ X1 @ X2 )
                                                    = X2 )
                                                 => ( subset @ X2 @ X1 ) )
                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                    ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                   => ( in @ X3 @ X2 ) )
                                               => ( ! [X1: $i,X2: $i] :
                                                      ( ! [X3: $i] :
                                                          ( ( in @ X3 @ X1 )
                                                         => ~ ( in @ X3 @ X2 ) )
                                                     => ( ( binintersect @ X1 @ X2 )
                                                        = emptyset ) )
                                                 => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                   => ( ! [X1: $i,X2: $i] :
                                                          ( ( subset @ X2 @ X1 )
                                                         => ( ( binintersect @ X1 @ X2 )
                                                            = X2 ) )
                                                     => ( ! [X1: $i,X2: $i] :
                                                            ( ( ( binintersect @ X1 @ X2 )
                                                              = X1 )
                                                           => ( subset @ X1 @ X2 ) )
                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                              ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                              = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                ( ( in @ X3 @ X1 )
                                                               => ( ~ ( in @ X3 @ X2 )
                                                                 => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                  ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                 => ( in @ X3 @ X1 ) )
                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                    ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                   => ~ ( in @ X3 @ X2 ) )
                                                               => ( ! [X1: $i,X2: $i] :
                                                                      ( ( subset @ X1 @ X2 )
                                                                     => ( ( setminus @ X1 @ X2 )
                                                                        = emptyset ) )
                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                        ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                       => ( ( in @ X3 @ X1 )
                                                                         => ( in @ X3 @ X2 ) ) )
                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                          ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                         => ( ~ ( in @ X3 @ X2 )
                                                                           => ~ ( in @ X3 @ X1 ) ) )
                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                            ( ~ ( in @ X3 @ X1 )
                                                                           => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                              ( ( in @ X3 @ X2 )
                                                                             => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                         => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                  ( ( ( setminus @ X1 @ X2 )
                                                                                    = emptyset )
                                                                                 => ( subset @ X1 @ X2 ) )
                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                    ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                   => ! [X4: $o] :
                                                                                        ( ( ( in @ X3 @ X1 )
                                                                                         => ( ~ ( in @ X3 @ X2 )
                                                                                           => X4 ) )
                                                                                       => ( ( ~ ( in @ X3 @ X1 )
                                                                                           => ( ( in @ X3 @ X2 )
                                                                                             => X4 ) )
                                                                                         => X4 ) ) )
                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                      ( ( in @ X3 @ X1 )
                                                                                     => ( ~ ( in @ X3 @ X2 )
                                                                                       => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                        ( ~ ( in @ X3 @ X1 )
                                                                                       => ( ( in @ X3 @ X2 )
                                                                                         => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                          ( ( in @ X3 @ X1 )
                                                                                         => ( ( in @ X3 @ X2 )
                                                                                           => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                            ( ~ ( in @ X3 @ X1 )
                                                                                           => ( ~ ( in @ X3 @ X2 )
                                                                                             => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                       => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                         => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                           => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                             => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                               => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                        ( ( in @ X2 @ X1 )
                                                                                                       => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                          ( ( in @ X2 @ X1 )
                                                                                                         => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                           => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                              ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                             => ( ( X3 != X1 )
                                                                                                               => ( X3 = X2 ) ) )
                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                               => ! [X4: $i] :
                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                   => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                 => ! [X4: $i] :
                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                     => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                   => ! [X4: $i] :
                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                       => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                     => ! [X4: $i] :
                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                         => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                       => ! [X4: $i] :
                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                           => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                         => ! [X4: $i] :
                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                             => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                            ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                           => ~ ! [X4: $i] :
                                                                                                                                  ( ( in @ X4 @ X1 )
                                                                                                                                 => ! [X5: $i] :
                                                                                                                                      ( ( in @ X5 @ X2 )
                                                                                                                                     => ( X3
                                                                                                                                       != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                       => ( sP5
                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                               => ~ ! [X3: $i] :
                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                     => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                           => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                             => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                               => ( ! [X1: $i] :
                                                                                                                                      ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                      = X1 )
                                                                                                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                        ( ! [X3: $i] :
                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                ( ( in @ X4 @ X1 )
                                                                                                                                               => ( ( X2 @ X3 )
                                                                                                                                                 => ( ( X2 @ X4 )
                                                                                                                                                   => ( X3 = X4 ) ) ) ) )
                                                                                                                                       => ( ~ ! [X3: $i] :
                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                               => ~ ( X2 @ X3 ) )
                                                                                                                                         => ~ ! [X3: $i] :
                                                                                                                                                ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                               => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                 != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                          ( ~ ! [X3: $i] :
                                                                                                                                                ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                               => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                 != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                         => ~ ! [X3: $i] :
                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                               => ~ ( X2 @ X3 ) ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                           => ( ( X2 @ X3 )
                                                                                                                                             => ( ! [X4: $i] :
                                                                                                                                                    ( ( in @ X4 @ X1 )
                                                                                                                                                   => ( ( X2 @ X4 )
                                                                                                                                                     => ( X4 = X3 ) ) )
                                                                                                                                               => ~ ! [X4: $i] :
                                                                                                                                                      ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                     => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                       != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                              ( ! [X3: $i] :
                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                      ( ( in @ X4 @ X1 )
                                                                                                                                                     => ( ( X2 @ X3 )
                                                                                                                                                       => ( ( X2 @ X4 )
                                                                                                                                                         => ( X3 = X4 ) ) ) ) )
                                                                                                                                             => ( ~ ! [X3: $i] :
                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                     => ~ ( X2 @ X3 ) )
                                                                                                                                               => ~ ! [X3: $i] :
                                                                                                                                                      ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                     => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                       != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                  = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                               => ( X1 = X2 ) )
                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                  ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                 => ( X1 = X3 ) )
                                                                                                                                             => ( ! [X1: $i] :
                                                                                                                                                    ( ( iskpair @ X1 )
                                                                                                                                                   => ~ ! [X2: $i] :
                                                                                                                                                          ( ( in @ X2
                                                                                                                                                            @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                              @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                         => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                              @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                           != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                               => ( ! [X1: $i] :
                                                                                                                                                      ( ~ ! [X2: $i] :
                                                                                                                                                            ( ( in @ X2 @ X1 )
                                                                                                                                                           => ( X1
                                                                                                                                                             != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                     => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                        ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                        = X1 )
                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                         => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                            ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                              = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                           => ( X1 = X3 ) )
                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                              ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                = ( kpair @ X3 @ X4 ) )
                                                                                                                                                             => ( X1 = X3 ) )
                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                ( ( X1 = X2 )
                                                                                                                                                               => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                  = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                  ( ( X1 = X2 )
                                                                                                                                                                 => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                    = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                    ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                      = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                   => ( ( X3 = X4 )
                                                                                                                                                                     => ( X2 = X4 ) ) )
                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                      ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                        = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                     => ( X1 = X2 ) )
                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                        ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                          = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                       => ( X2 = X4 ) )
                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                          ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                            = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                         => ( X2 = X4 ) )
                                                                                                                                                                     => ( ! [X1: $i] :
                                                                                                                                                                            ( ( iskpair @ X1 )
                                                                                                                                                                           => ~ ! [X2: $i] :
                                                                                                                                                                                  ( ( in @ X2
                                                                                                                                                                                    @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                      @ ^ [X3: $i] :
                                                                                                                                                                                          ( X1
                                                                                                                                                                                          = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                 => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                      @ ^ [X3: $i] :
                                                                                                                                                                                          ( X1
                                                                                                                                                                                          = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                   != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                              ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                              = X2 )
                                                                                                                                                                         => ( sP8
                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                  ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                 => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                    ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                   => ( in @ X3 @ X1 ) )
                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                      ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                     => ( in @ X4 @ X2 ) )
                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                                                                           => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                              = X3 ) ) )
                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                                                                                             => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                = X4 ) ) )
                                                                                                                                                                                     => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                         => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                            = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h154,assumption,
    ! [X1: $i,X2: $i] :
      ( ( subset @ X1 @ X2 )
     => ( ( subset @ X2 @ X1 )
       => ( X1 = X2 ) ) ),
    introduced(assumption,[]) ).

thf(h155,assumption,
    ~ ( ! [X1: $i] :
          ( ( subset @ X1 @ emptyset )
         => ( X1 = emptyset ) )
     => ( ! [X1: $i,X2: $i] :
            ( ( subset @ X2 @ X1 )
           => ( in @ X2 @ ( powerset @ X1 ) ) )
       => ( ! [X1: $i,X2: $i] :
              ( ( in @ X2 @ ( powerset @ X1 ) )
             => ( subset @ X2 @ X1 ) )
         => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
           => ( ! [X1: $i,X2: $i] :
                  ( ( subset @ X1 @ X2 )
                 => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
             => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
               => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                 => ( ! [X1: $i,X2: $i,X3: $i] :
                        ( ( in @ X3 @ X1 )
                       => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                   => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                     => ( ! [X1: $i,X2: $i,X3: $i] :
                            ( ( in @ X3 @ X2 )
                           => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                              ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                             => ( ( ( in @ X3 @ X1 )
                                 => X4 )
                               => ( ( ( in @ X3 @ X2 )
                                   => X4 )
                                 => X4 ) ) )
                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                               => ( ~ ( in @ X3 @ X1 )
                                 => ( in @ X3 @ X2 ) ) )
                           => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                             => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                      ( ( in @ X3 @ X1 )
                                     => ( ( in @ X3 @ X2 )
                                       => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                        ( ( subset @ X3 @ X1 )
                                       => ( ( subset @ X3 @ X2 )
                                         => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                          ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                         => ( in @ X3 @ X1 ) )
                                     => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                       => ( ! [X1: $i,X2: $i] :
                                              ( ( subset @ X1 @ X2 )
                                             => ( ( binintersect @ X1 @ X2 )
                                                = X1 ) )
                                         => ( ! [X1: $i,X2: $i] :
                                                ( ( ( binintersect @ X1 @ X2 )
                                                  = X2 )
                                               => ( subset @ X2 @ X1 ) )
                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                  ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                 => ( in @ X3 @ X2 ) )
                                             => ( ! [X1: $i,X2: $i] :
                                                    ( ! [X3: $i] :
                                                        ( ( in @ X3 @ X1 )
                                                       => ~ ( in @ X3 @ X2 ) )
                                                   => ( ( binintersect @ X1 @ X2 )
                                                      = emptyset ) )
                                               => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                 => ( ! [X1: $i,X2: $i] :
                                                        ( ( subset @ X2 @ X1 )
                                                       => ( ( binintersect @ X1 @ X2 )
                                                          = X2 ) )
                                                   => ( ! [X1: $i,X2: $i] :
                                                          ( ( ( binintersect @ X1 @ X2 )
                                                            = X1 )
                                                         => ( subset @ X1 @ X2 ) )
                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                            ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                            = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                              ( ( in @ X3 @ X1 )
                                                             => ( ~ ( in @ X3 @ X2 )
                                                               => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                               => ( in @ X3 @ X1 ) )
                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                  ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                 => ~ ( in @ X3 @ X2 ) )
                                                             => ( ! [X1: $i,X2: $i] :
                                                                    ( ( subset @ X1 @ X2 )
                                                                   => ( ( setminus @ X1 @ X2 )
                                                                      = emptyset ) )
                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                      ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                     => ( ( in @ X3 @ X1 )
                                                                       => ( in @ X3 @ X2 ) ) )
                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                        ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                       => ( ~ ( in @ X3 @ X2 )
                                                                         => ~ ( in @ X3 @ X1 ) ) )
                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                          ( ~ ( in @ X3 @ X1 )
                                                                         => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                            ( ( in @ X3 @ X2 )
                                                                           => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                       => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                ( ( ( setminus @ X1 @ X2 )
                                                                                  = emptyset )
                                                                               => ( subset @ X1 @ X2 ) )
                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                  ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                 => ! [X4: $o] :
                                                                                      ( ( ( in @ X3 @ X1 )
                                                                                       => ( ~ ( in @ X3 @ X2 )
                                                                                         => X4 ) )
                                                                                     => ( ( ~ ( in @ X3 @ X1 )
                                                                                         => ( ( in @ X3 @ X2 )
                                                                                           => X4 ) )
                                                                                       => X4 ) ) )
                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                    ( ( in @ X3 @ X1 )
                                                                                   => ( ~ ( in @ X3 @ X2 )
                                                                                     => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                      ( ~ ( in @ X3 @ X1 )
                                                                                     => ( ( in @ X3 @ X2 )
                                                                                       => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                        ( ( in @ X3 @ X1 )
                                                                                       => ( ( in @ X3 @ X2 )
                                                                                         => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                          ( ~ ( in @ X3 @ X1 )
                                                                                         => ( ~ ( in @ X3 @ X2 )
                                                                                           => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                     => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                       => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                         => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                           => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                             => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                      ( ( in @ X2 @ X1 )
                                                                                                     => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                        ( ( in @ X2 @ X1 )
                                                                                                       => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                         => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                            ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                           => ( ( X3 != X1 )
                                                                                                             => ( X3 = X2 ) ) )
                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                             => ! [X4: $i] :
                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                 => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                               => ! [X4: $i] :
                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                   => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                 => ! [X4: $i] :
                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                     => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                   => ! [X4: $i] :
                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                       => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                     => ! [X4: $i] :
                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                         => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                       => ! [X4: $i] :
                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                           => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                         => ~ ! [X4: $i] :
                                                                                                                                ( ( in @ X4 @ X1 )
                                                                                                                               => ! [X5: $i] :
                                                                                                                                    ( ( in @ X5 @ X2 )
                                                                                                                                   => ( X3
                                                                                                                                     != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                     => ( sP5
                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                              ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                             => ~ ! [X3: $i] :
                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                   => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                         => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                           => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                             => ( ! [X1: $i] :
                                                                                                                                    ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                    = X1 )
                                                                                                                               => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                      ( ! [X3: $i] :
                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                         => ! [X4: $i] :
                                                                                                                                              ( ( in @ X4 @ X1 )
                                                                                                                                             => ( ( X2 @ X3 )
                                                                                                                                               => ( ( X2 @ X4 )
                                                                                                                                                 => ( X3 = X4 ) ) ) ) )
                                                                                                                                     => ( ~ ! [X3: $i] :
                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                             => ~ ( X2 @ X3 ) )
                                                                                                                                       => ~ ! [X3: $i] :
                                                                                                                                              ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                             => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                               != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                        ( ~ ! [X3: $i] :
                                                                                                                                              ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                             => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                               != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                       => ~ ! [X3: $i] :
                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                             => ~ ( X2 @ X3 ) ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                         => ( ( X2 @ X3 )
                                                                                                                                           => ( ! [X4: $i] :
                                                                                                                                                  ( ( in @ X4 @ X1 )
                                                                                                                                                 => ( ( X2 @ X4 )
                                                                                                                                                   => ( X4 = X3 ) ) )
                                                                                                                                             => ~ ! [X4: $i] :
                                                                                                                                                    ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                   => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                     != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                            ( ! [X3: $i] :
                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                    ( ( in @ X4 @ X1 )
                                                                                                                                                   => ( ( X2 @ X3 )
                                                                                                                                                     => ( ( X2 @ X4 )
                                                                                                                                                       => ( X3 = X4 ) ) ) ) )
                                                                                                                                           => ( ~ ! [X3: $i] :
                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                   => ~ ( X2 @ X3 ) )
                                                                                                                                             => ~ ! [X3: $i] :
                                                                                                                                                    ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                   => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                     != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                              ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                             => ( X1 = X2 ) )
                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                               => ( X1 = X3 ) )
                                                                                                                                           => ( ! [X1: $i] :
                                                                                                                                                  ( ( iskpair @ X1 )
                                                                                                                                                 => ~ ! [X2: $i] :
                                                                                                                                                        ( ( in @ X2
                                                                                                                                                          @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                            @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                       => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                            @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                         != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                             => ( ! [X1: $i] :
                                                                                                                                                    ( ~ ! [X2: $i] :
                                                                                                                                                          ( ( in @ X2 @ X1 )
                                                                                                                                                         => ( X1
                                                                                                                                                           != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                   => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                      ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                      = X1 )
                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                       => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                          ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                            = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                         => ( X1 = X3 ) )
                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                            ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                              = ( kpair @ X3 @ X4 ) )
                                                                                                                                                           => ( X1 = X3 ) )
                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                              ( ( X1 = X2 )
                                                                                                                                                             => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                ( ( X1 = X2 )
                                                                                                                                                               => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                  = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                  ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                    = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                 => ( ( X3 = X4 )
                                                                                                                                                                   => ( X2 = X4 ) ) )
                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                    ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                      = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                   => ( X1 = X2 ) )
                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                      ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                        = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                     => ( X2 = X4 ) )
                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                        ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                          = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                       => ( X2 = X4 ) )
                                                                                                                                                                   => ( ! [X1: $i] :
                                                                                                                                                                          ( ( iskpair @ X1 )
                                                                                                                                                                         => ~ ! [X2: $i] :
                                                                                                                                                                                ( ( in @ X2
                                                                                                                                                                                  @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                    @ ^ [X3: $i] :
                                                                                                                                                                                        ( X1
                                                                                                                                                                                        = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                               => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                    @ ^ [X3: $i] :
                                                                                                                                                                                        ( X1
                                                                                                                                                                                        = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                 != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                            ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                            = X2 )
                                                                                                                                                                       => ( sP8
                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                               => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                  ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                 => ( in @ X3 @ X1 ) )
                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                    ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                   => ( in @ X4 @ X2 ) )
                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                                                                         => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                            = X3 ) ) )
                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                                                                           => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                              = X4 ) ) )
                                                                                                                                                                                   => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                       => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                          = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h156,assumption,
    ! [X1: $i] :
      ( ( subset @ X1 @ emptyset )
     => ( X1 = emptyset ) ),
    introduced(assumption,[]) ).

thf(h157,assumption,
    ~ ( ! [X1: $i,X2: $i] :
          ( ( subset @ X2 @ X1 )
         => ( in @ X2 @ ( powerset @ X1 ) ) )
     => ( ! [X1: $i,X2: $i] :
            ( ( in @ X2 @ ( powerset @ X1 ) )
           => ( subset @ X2 @ X1 ) )
       => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
         => ( ! [X1: $i,X2: $i] :
                ( ( subset @ X1 @ X2 )
               => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
           => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
             => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
               => ( ! [X1: $i,X2: $i,X3: $i] :
                      ( ( in @ X3 @ X1 )
                     => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                 => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                   => ( ! [X1: $i,X2: $i,X3: $i] :
                          ( ( in @ X3 @ X2 )
                         => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                            ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                           => ( ( ( in @ X3 @ X1 )
                               => X4 )
                             => ( ( ( in @ X3 @ X2 )
                                 => X4 )
                               => X4 ) ) )
                       => ( ! [X1: $i,X2: $i,X3: $i] :
                              ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                             => ( ~ ( in @ X3 @ X1 )
                               => ( in @ X3 @ X2 ) ) )
                         => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                           => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                    ( ( in @ X3 @ X1 )
                                   => ( ( in @ X3 @ X2 )
                                     => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                      ( ( subset @ X3 @ X1 )
                                     => ( ( subset @ X3 @ X2 )
                                       => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                        ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                       => ( in @ X3 @ X1 ) )
                                   => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                     => ( ! [X1: $i,X2: $i] :
                                            ( ( subset @ X1 @ X2 )
                                           => ( ( binintersect @ X1 @ X2 )
                                              = X1 ) )
                                       => ( ! [X1: $i,X2: $i] :
                                              ( ( ( binintersect @ X1 @ X2 )
                                                = X2 )
                                             => ( subset @ X2 @ X1 ) )
                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                               => ( in @ X3 @ X2 ) )
                                           => ( ! [X1: $i,X2: $i] :
                                                  ( ! [X3: $i] :
                                                      ( ( in @ X3 @ X1 )
                                                     => ~ ( in @ X3 @ X2 ) )
                                                 => ( ( binintersect @ X1 @ X2 )
                                                    = emptyset ) )
                                             => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                               => ( ! [X1: $i,X2: $i] :
                                                      ( ( subset @ X2 @ X1 )
                                                     => ( ( binintersect @ X1 @ X2 )
                                                        = X2 ) )
                                                 => ( ! [X1: $i,X2: $i] :
                                                        ( ( ( binintersect @ X1 @ X2 )
                                                          = X1 )
                                                       => ( subset @ X1 @ X2 ) )
                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                          ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                          = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                            ( ( in @ X3 @ X1 )
                                                           => ( ~ ( in @ X3 @ X2 )
                                                             => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                              ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                             => ( in @ X3 @ X1 ) )
                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                               => ~ ( in @ X3 @ X2 ) )
                                                           => ( ! [X1: $i,X2: $i] :
                                                                  ( ( subset @ X1 @ X2 )
                                                                 => ( ( setminus @ X1 @ X2 )
                                                                    = emptyset ) )
                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                    ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                   => ( ( in @ X3 @ X1 )
                                                                     => ( in @ X3 @ X2 ) ) )
                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                      ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                     => ( ~ ( in @ X3 @ X2 )
                                                                       => ~ ( in @ X3 @ X1 ) ) )
                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                        ( ~ ( in @ X3 @ X1 )
                                                                       => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                          ( ( in @ X3 @ X2 )
                                                                         => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                     => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                       => ( ! [X1: $i,X2: $i] :
                                                                              ( ( ( setminus @ X1 @ X2 )
                                                                                = emptyset )
                                                                             => ( subset @ X1 @ X2 ) )
                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                               => ! [X4: $o] :
                                                                                    ( ( ( in @ X3 @ X1 )
                                                                                     => ( ~ ( in @ X3 @ X2 )
                                                                                       => X4 ) )
                                                                                   => ( ( ~ ( in @ X3 @ X1 )
                                                                                       => ( ( in @ X3 @ X2 )
                                                                                         => X4 ) )
                                                                                     => X4 ) ) )
                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                  ( ( in @ X3 @ X1 )
                                                                                 => ( ~ ( in @ X3 @ X2 )
                                                                                   => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                    ( ~ ( in @ X3 @ X1 )
                                                                                   => ( ( in @ X3 @ X2 )
                                                                                     => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                      ( ( in @ X3 @ X1 )
                                                                                     => ( ( in @ X3 @ X2 )
                                                                                       => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                        ( ~ ( in @ X3 @ X1 )
                                                                                       => ( ~ ( in @ X3 @ X2 )
                                                                                         => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                   => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                     => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                       => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                         => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                           => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                    ( ( in @ X2 @ X1 )
                                                                                                   => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                      ( ( in @ X2 @ X1 )
                                                                                                     => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                       => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                          ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                         => ( ( X3 != X1 )
                                                                                                           => ( X3 = X2 ) ) )
                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                           => ! [X4: $i] :
                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                               => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                             => ! [X4: $i] :
                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                 => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                               => ! [X4: $i] :
                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                   => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                 => ! [X4: $i] :
                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                     => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                   => ! [X4: $i] :
                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                       => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                     => ! [X4: $i] :
                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                         => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                       => ~ ! [X4: $i] :
                                                                                                                              ( ( in @ X4 @ X1 )
                                                                                                                             => ! [X5: $i] :
                                                                                                                                  ( ( in @ X5 @ X2 )
                                                                                                                                 => ( X3
                                                                                                                                   != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                   => ( sP5
                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                            ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                           => ~ ! [X3: $i] :
                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                 => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                       => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                         => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                           => ( ! [X1: $i] :
                                                                                                                                  ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                  = X1 )
                                                                                                                             => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                    ( ! [X3: $i] :
                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                       => ! [X4: $i] :
                                                                                                                                            ( ( in @ X4 @ X1 )
                                                                                                                                           => ( ( X2 @ X3 )
                                                                                                                                             => ( ( X2 @ X4 )
                                                                                                                                               => ( X3 = X4 ) ) ) ) )
                                                                                                                                   => ( ~ ! [X3: $i] :
                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                           => ~ ( X2 @ X3 ) )
                                                                                                                                     => ~ ! [X3: $i] :
                                                                                                                                            ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                           => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                             != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                               => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                      ( ~ ! [X3: $i] :
                                                                                                                                            ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                           => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                             != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                     => ~ ! [X3: $i] :
                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                           => ~ ( X2 @ X3 ) ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                       => ( ( X2 @ X3 )
                                                                                                                                         => ( ! [X4: $i] :
                                                                                                                                                ( ( in @ X4 @ X1 )
                                                                                                                                               => ( ( X2 @ X4 )
                                                                                                                                                 => ( X4 = X3 ) ) )
                                                                                                                                           => ~ ! [X4: $i] :
                                                                                                                                                  ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                 => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                   != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                          ( ! [X3: $i] :
                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                  ( ( in @ X4 @ X1 )
                                                                                                                                                 => ( ( X2 @ X3 )
                                                                                                                                                   => ( ( X2 @ X4 )
                                                                                                                                                     => ( X3 = X4 ) ) ) ) )
                                                                                                                                         => ( ~ ! [X3: $i] :
                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                 => ~ ( X2 @ X3 ) )
                                                                                                                                           => ~ ! [X3: $i] :
                                                                                                                                                  ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                 => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                   != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                            ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                              = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                           => ( X1 = X2 ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                              ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                             => ( X1 = X3 ) )
                                                                                                                                         => ( ! [X1: $i] :
                                                                                                                                                ( ( iskpair @ X1 )
                                                                                                                                               => ~ ! [X2: $i] :
                                                                                                                                                      ( ( in @ X2
                                                                                                                                                        @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                          @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                     => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                          @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                       != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                           => ( ! [X1: $i] :
                                                                                                                                                  ( ~ ! [X2: $i] :
                                                                                                                                                        ( ( in @ X2 @ X1 )
                                                                                                                                                       => ( X1
                                                                                                                                                         != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                 => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                    ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                    = X1 )
                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                      ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                     => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                        ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                          = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                       => ( X1 = X3 ) )
                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                          ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                            = ( kpair @ X3 @ X4 ) )
                                                                                                                                                         => ( X1 = X3 ) )
                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                            ( ( X1 = X2 )
                                                                                                                                                           => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                              = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                              ( ( X1 = X2 )
                                                                                                                                                             => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                  = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                               => ( ( X3 = X4 )
                                                                                                                                                                 => ( X2 = X4 ) ) )
                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                  ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                    = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                 => ( X1 = X2 ) )
                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                    ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                      = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                   => ( X2 = X4 ) )
                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                      ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                        = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                     => ( X2 = X4 ) )
                                                                                                                                                                 => ( ! [X1: $i] :
                                                                                                                                                                        ( ( iskpair @ X1 )
                                                                                                                                                                       => ~ ! [X2: $i] :
                                                                                                                                                                              ( ( in @ X2
                                                                                                                                                                                @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                  @ ^ [X3: $i] :
                                                                                                                                                                                      ( X1
                                                                                                                                                                                      = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                             => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                  @ ^ [X3: $i] :
                                                                                                                                                                                      ( X1
                                                                                                                                                                                      = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                               != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                          ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                          = X2 )
                                                                                                                                                                     => ( sP8
                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                              ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                             => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                               => ( in @ X3 @ X1 ) )
                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                  ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                 => ( in @ X4 @ X2 ) )
                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                                                                       => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                          = X3 ) ) )
                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                                                                         => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                            = X4 ) ) )
                                                                                                                                                                                 => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                      ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                     => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                        = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h158,assumption,
    ! [X1: $i,X2: $i] :
      ( ( subset @ X2 @ X1 )
     => ( in @ X2 @ ( powerset @ X1 ) ) ),
    introduced(assumption,[]) ).

thf(h159,assumption,
    ~ ( ! [X1: $i,X2: $i] :
          ( ( in @ X2 @ ( powerset @ X1 ) )
         => ( subset @ X2 @ X1 ) )
     => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
       => ( ! [X1: $i,X2: $i] :
              ( ( subset @ X1 @ X2 )
             => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
         => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
           => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
             => ( ! [X1: $i,X2: $i,X3: $i] :
                    ( ( in @ X3 @ X1 )
                   => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
               => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                 => ( ! [X1: $i,X2: $i,X3: $i] :
                        ( ( in @ X3 @ X2 )
                       => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                          ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                         => ( ( ( in @ X3 @ X1 )
                             => X4 )
                           => ( ( ( in @ X3 @ X2 )
                               => X4 )
                             => X4 ) ) )
                     => ( ! [X1: $i,X2: $i,X3: $i] :
                            ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                           => ( ~ ( in @ X3 @ X1 )
                             => ( in @ X3 @ X2 ) ) )
                       => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                         => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                  ( ( in @ X3 @ X1 )
                                 => ( ( in @ X3 @ X2 )
                                   => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                    ( ( subset @ X3 @ X1 )
                                   => ( ( subset @ X3 @ X2 )
                                     => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                      ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                     => ( in @ X3 @ X1 ) )
                                 => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                   => ( ! [X1: $i,X2: $i] :
                                          ( ( subset @ X1 @ X2 )
                                         => ( ( binintersect @ X1 @ X2 )
                                            = X1 ) )
                                     => ( ! [X1: $i,X2: $i] :
                                            ( ( ( binintersect @ X1 @ X2 )
                                              = X2 )
                                           => ( subset @ X2 @ X1 ) )
                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                              ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                             => ( in @ X3 @ X2 ) )
                                         => ( ! [X1: $i,X2: $i] :
                                                ( ! [X3: $i] :
                                                    ( ( in @ X3 @ X1 )
                                                   => ~ ( in @ X3 @ X2 ) )
                                               => ( ( binintersect @ X1 @ X2 )
                                                  = emptyset ) )
                                           => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                             => ( ! [X1: $i,X2: $i] :
                                                    ( ( subset @ X2 @ X1 )
                                                   => ( ( binintersect @ X1 @ X2 )
                                                      = X2 ) )
                                               => ( ! [X1: $i,X2: $i] :
                                                      ( ( ( binintersect @ X1 @ X2 )
                                                        = X1 )
                                                     => ( subset @ X1 @ X2 ) )
                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                        ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                        = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                          ( ( in @ X3 @ X1 )
                                                         => ( ~ ( in @ X3 @ X2 )
                                                           => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                            ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                           => ( in @ X3 @ X1 ) )
                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                              ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                             => ~ ( in @ X3 @ X2 ) )
                                                         => ( ! [X1: $i,X2: $i] :
                                                                ( ( subset @ X1 @ X2 )
                                                               => ( ( setminus @ X1 @ X2 )
                                                                  = emptyset ) )
                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                  ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                 => ( ( in @ X3 @ X1 )
                                                                   => ( in @ X3 @ X2 ) ) )
                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                    ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                   => ( ~ ( in @ X3 @ X2 )
                                                                     => ~ ( in @ X3 @ X1 ) ) )
                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                      ( ~ ( in @ X3 @ X1 )
                                                                     => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                        ( ( in @ X3 @ X2 )
                                                                       => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                   => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                     => ( ! [X1: $i,X2: $i] :
                                                                            ( ( ( setminus @ X1 @ X2 )
                                                                              = emptyset )
                                                                           => ( subset @ X1 @ X2 ) )
                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                              ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                             => ! [X4: $o] :
                                                                                  ( ( ( in @ X3 @ X1 )
                                                                                   => ( ~ ( in @ X3 @ X2 )
                                                                                     => X4 ) )
                                                                                 => ( ( ~ ( in @ X3 @ X1 )
                                                                                     => ( ( in @ X3 @ X2 )
                                                                                       => X4 ) )
                                                                                   => X4 ) ) )
                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                ( ( in @ X3 @ X1 )
                                                                               => ( ~ ( in @ X3 @ X2 )
                                                                                 => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                  ( ~ ( in @ X3 @ X1 )
                                                                                 => ( ( in @ X3 @ X2 )
                                                                                   => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                    ( ( in @ X3 @ X1 )
                                                                                   => ( ( in @ X3 @ X2 )
                                                                                     => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                      ( ~ ( in @ X3 @ X1 )
                                                                                     => ( ~ ( in @ X3 @ X2 )
                                                                                       => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                 => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                   => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                     => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                       => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                         => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                  ( ( in @ X2 @ X1 )
                                                                                                 => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                    ( ( in @ X2 @ X1 )
                                                                                                   => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                     => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                        ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                       => ( ( X3 != X1 )
                                                                                                         => ( X3 = X2 ) ) )
                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                         => ! [X4: $i] :
                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                             => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                           => ! [X4: $i] :
                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                               => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                             => ! [X4: $i] :
                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                 => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                               => ! [X4: $i] :
                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                   => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                 => ! [X4: $i] :
                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                     => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                   => ! [X4: $i] :
                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                       => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                      ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                     => ~ ! [X4: $i] :
                                                                                                                            ( ( in @ X4 @ X1 )
                                                                                                                           => ! [X5: $i] :
                                                                                                                                ( ( in @ X5 @ X2 )
                                                                                                                               => ( X3
                                                                                                                                 != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                 => ( sP5
                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                          ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                         => ~ ! [X3: $i] :
                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                               => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                     => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                       => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                         => ( ! [X1: $i] :
                                                                                                                                ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                = X1 )
                                                                                                                           => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                  ( ! [X3: $i] :
                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                     => ! [X4: $i] :
                                                                                                                                          ( ( in @ X4 @ X1 )
                                                                                                                                         => ( ( X2 @ X3 )
                                                                                                                                           => ( ( X2 @ X4 )
                                                                                                                                             => ( X3 = X4 ) ) ) ) )
                                                                                                                                 => ( ~ ! [X3: $i] :
                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                         => ~ ( X2 @ X3 ) )
                                                                                                                                   => ~ ! [X3: $i] :
                                                                                                                                          ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                         => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                           != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                             => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                    ( ~ ! [X3: $i] :
                                                                                                                                          ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                         => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                           != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                   => ~ ! [X3: $i] :
                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                         => ~ ( X2 @ X3 ) ) )
                                                                                                                               => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                     => ( ( X2 @ X3 )
                                                                                                                                       => ( ! [X4: $i] :
                                                                                                                                              ( ( in @ X4 @ X1 )
                                                                                                                                             => ( ( X2 @ X4 )
                                                                                                                                               => ( X4 = X3 ) ) )
                                                                                                                                         => ~ ! [X4: $i] :
                                                                                                                                                ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                               => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                 != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                        ( ! [X3: $i] :
                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                ( ( in @ X4 @ X1 )
                                                                                                                                               => ( ( X2 @ X3 )
                                                                                                                                                 => ( ( X2 @ X4 )
                                                                                                                                                   => ( X3 = X4 ) ) ) ) )
                                                                                                                                       => ( ~ ! [X3: $i] :
                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                               => ~ ( X2 @ X3 ) )
                                                                                                                                         => ~ ! [X3: $i] :
                                                                                                                                                ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                               => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                 != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                          ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                            = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                         => ( X1 = X2 ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                            ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                           => ( X1 = X3 ) )
                                                                                                                                       => ( ! [X1: $i] :
                                                                                                                                              ( ( iskpair @ X1 )
                                                                                                                                             => ~ ! [X2: $i] :
                                                                                                                                                    ( ( in @ X2
                                                                                                                                                      @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                        @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                   => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                        @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                     != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                         => ( ! [X1: $i] :
                                                                                                                                                ( ~ ! [X2: $i] :
                                                                                                                                                      ( ( in @ X2 @ X1 )
                                                                                                                                                     => ( X1
                                                                                                                                                       != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                               => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                  ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                  = X1 )
                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                    ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                   => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                      ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                        = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                     => ( X1 = X3 ) )
                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                        ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                          = ( kpair @ X3 @ X4 ) )
                                                                                                                                                       => ( X1 = X3 ) )
                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                          ( ( X1 = X2 )
                                                                                                                                                         => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                            = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                            ( ( X1 = X2 )
                                                                                                                                                           => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                              = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                              ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                             => ( ( X3 = X4 )
                                                                                                                                                               => ( X2 = X4 ) ) )
                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                  = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                               => ( X1 = X2 ) )
                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                  ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                    = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                 => ( X2 = X4 ) )
                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                    ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                      = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                   => ( X2 = X4 ) )
                                                                                                                                                               => ( ! [X1: $i] :
                                                                                                                                                                      ( ( iskpair @ X1 )
                                                                                                                                                                     => ~ ! [X2: $i] :
                                                                                                                                                                            ( ( in @ X2
                                                                                                                                                                              @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                @ ^ [X3: $i] :
                                                                                                                                                                                    ( X1
                                                                                                                                                                                    = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                           => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                @ ^ [X3: $i] :
                                                                                                                                                                                    ( X1
                                                                                                                                                                                    = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                             != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                        ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                        = X2 )
                                                                                                                                                                   => ( sP8
                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                            ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                           => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                              ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                             => ( in @ X3 @ X1 ) )
                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                               => ( in @ X4 @ X2 ) )
                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                                                                     => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                        = X3 ) ) )
                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                                                                       => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                          = X4 ) ) )
                                                                                                                                                                               => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                    ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                   => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                      = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h160,assumption,
    ! [X1: $i,X2: $i] :
      ( ( in @ X2 @ ( powerset @ X1 ) )
     => ( subset @ X2 @ X1 ) ),
    introduced(assumption,[]) ).

thf(h161,assumption,
    ~ ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
     => ( ! [X1: $i,X2: $i] :
            ( ( subset @ X1 @ X2 )
           => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
       => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
         => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
           => ( ! [X1: $i,X2: $i,X3: $i] :
                  ( ( in @ X3 @ X1 )
                 => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
             => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
               => ( ! [X1: $i,X2: $i,X3: $i] :
                      ( ( in @ X3 @ X2 )
                     => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                        ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                       => ( ( ( in @ X3 @ X1 )
                           => X4 )
                         => ( ( ( in @ X3 @ X2 )
                             => X4 )
                           => X4 ) ) )
                   => ( ! [X1: $i,X2: $i,X3: $i] :
                          ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                         => ( ~ ( in @ X3 @ X1 )
                           => ( in @ X3 @ X2 ) ) )
                     => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                       => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                ( ( in @ X3 @ X1 )
                               => ( ( in @ X3 @ X2 )
                                 => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                  ( ( subset @ X3 @ X1 )
                                 => ( ( subset @ X3 @ X2 )
                                   => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                    ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                   => ( in @ X3 @ X1 ) )
                               => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                 => ( ! [X1: $i,X2: $i] :
                                        ( ( subset @ X1 @ X2 )
                                       => ( ( binintersect @ X1 @ X2 )
                                          = X1 ) )
                                   => ( ! [X1: $i,X2: $i] :
                                          ( ( ( binintersect @ X1 @ X2 )
                                            = X2 )
                                         => ( subset @ X2 @ X1 ) )
                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                            ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                           => ( in @ X3 @ X2 ) )
                                       => ( ! [X1: $i,X2: $i] :
                                              ( ! [X3: $i] :
                                                  ( ( in @ X3 @ X1 )
                                                 => ~ ( in @ X3 @ X2 ) )
                                             => ( ( binintersect @ X1 @ X2 )
                                                = emptyset ) )
                                         => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                           => ( ! [X1: $i,X2: $i] :
                                                  ( ( subset @ X2 @ X1 )
                                                 => ( ( binintersect @ X1 @ X2 )
                                                    = X2 ) )
                                             => ( ! [X1: $i,X2: $i] :
                                                    ( ( ( binintersect @ X1 @ X2 )
                                                      = X1 )
                                                   => ( subset @ X1 @ X2 ) )
                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                      ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                      = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                        ( ( in @ X3 @ X1 )
                                                       => ( ~ ( in @ X3 @ X2 )
                                                         => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                          ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                         => ( in @ X3 @ X1 ) )
                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                            ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                           => ~ ( in @ X3 @ X2 ) )
                                                       => ( ! [X1: $i,X2: $i] :
                                                              ( ( subset @ X1 @ X2 )
                                                             => ( ( setminus @ X1 @ X2 )
                                                                = emptyset ) )
                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                               => ( ( in @ X3 @ X1 )
                                                                 => ( in @ X3 @ X2 ) ) )
                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                  ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                 => ( ~ ( in @ X3 @ X2 )
                                                                   => ~ ( in @ X3 @ X1 ) ) )
                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                    ( ~ ( in @ X3 @ X1 )
                                                                   => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                      ( ( in @ X3 @ X2 )
                                                                     => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                 => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                   => ( ! [X1: $i,X2: $i] :
                                                                          ( ( ( setminus @ X1 @ X2 )
                                                                            = emptyset )
                                                                         => ( subset @ X1 @ X2 ) )
                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                            ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                           => ! [X4: $o] :
                                                                                ( ( ( in @ X3 @ X1 )
                                                                                 => ( ~ ( in @ X3 @ X2 )
                                                                                   => X4 ) )
                                                                               => ( ( ~ ( in @ X3 @ X1 )
                                                                                   => ( ( in @ X3 @ X2 )
                                                                                     => X4 ) )
                                                                                 => X4 ) ) )
                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                              ( ( in @ X3 @ X1 )
                                                                             => ( ~ ( in @ X3 @ X2 )
                                                                               => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                ( ~ ( in @ X3 @ X1 )
                                                                               => ( ( in @ X3 @ X2 )
                                                                                 => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                  ( ( in @ X3 @ X1 )
                                                                                 => ( ( in @ X3 @ X2 )
                                                                                   => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                    ( ~ ( in @ X3 @ X1 )
                                                                                   => ( ~ ( in @ X3 @ X2 )
                                                                                     => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                               => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                 => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                   => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                     => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                       => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                ( ( in @ X2 @ X1 )
                                                                                               => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                  ( ( in @ X2 @ X1 )
                                                                                                 => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                   => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                      ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                     => ( ( X3 != X1 )
                                                                                                       => ( X3 = X2 ) ) )
                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                       => ! [X4: $i] :
                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                           => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                         => ! [X4: $i] :
                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                             => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                           => ! [X4: $i] :
                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                               => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                             => ! [X4: $i] :
                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                 => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                               => ! [X4: $i] :
                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                   => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                 => ! [X4: $i] :
                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                     => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                    ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                   => ~ ! [X4: $i] :
                                                                                                                          ( ( in @ X4 @ X1 )
                                                                                                                         => ! [X5: $i] :
                                                                                                                              ( ( in @ X5 @ X2 )
                                                                                                                             => ( X3
                                                                                                                               != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                               => ( sP5
                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                        ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                       => ~ ! [X3: $i] :
                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                             => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                   => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                     => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                       => ( ! [X1: $i] :
                                                                                                                              ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                              = X1 )
                                                                                                                         => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                ( ! [X3: $i] :
                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                   => ! [X4: $i] :
                                                                                                                                        ( ( in @ X4 @ X1 )
                                                                                                                                       => ( ( X2 @ X3 )
                                                                                                                                         => ( ( X2 @ X4 )
                                                                                                                                           => ( X3 = X4 ) ) ) ) )
                                                                                                                               => ( ~ ! [X3: $i] :
                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                       => ~ ( X2 @ X3 ) )
                                                                                                                                 => ~ ! [X3: $i] :
                                                                                                                                        ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                       => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                         != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                           => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                  ( ~ ! [X3: $i] :
                                                                                                                                        ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                       => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                         != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                 => ~ ! [X3: $i] :
                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                       => ~ ( X2 @ X3 ) ) )
                                                                                                                             => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                   => ( ( X2 @ X3 )
                                                                                                                                     => ( ! [X4: $i] :
                                                                                                                                            ( ( in @ X4 @ X1 )
                                                                                                                                           => ( ( X2 @ X4 )
                                                                                                                                             => ( X4 = X3 ) ) )
                                                                                                                                       => ~ ! [X4: $i] :
                                                                                                                                              ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                             => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                               != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                               => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                      ( ! [X3: $i] :
                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                         => ! [X4: $i] :
                                                                                                                                              ( ( in @ X4 @ X1 )
                                                                                                                                             => ( ( X2 @ X3 )
                                                                                                                                               => ( ( X2 @ X4 )
                                                                                                                                                 => ( X3 = X4 ) ) ) ) )
                                                                                                                                     => ( ~ ! [X3: $i] :
                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                             => ~ ( X2 @ X3 ) )
                                                                                                                                       => ~ ! [X3: $i] :
                                                                                                                                              ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                             => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                               != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                        ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                          = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                       => ( X1 = X2 ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                          ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                         => ( X1 = X3 ) )
                                                                                                                                     => ( ! [X1: $i] :
                                                                                                                                            ( ( iskpair @ X1 )
                                                                                                                                           => ~ ! [X2: $i] :
                                                                                                                                                  ( ( in @ X2
                                                                                                                                                    @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                      @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                 => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                      @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                   != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                       => ( ! [X1: $i] :
                                                                                                                                              ( ~ ! [X2: $i] :
                                                                                                                                                    ( ( in @ X2 @ X1 )
                                                                                                                                                   => ( X1
                                                                                                                                                     != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                             => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                = X1 )
                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                  ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                 => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                    ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                      = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                   => ( X1 = X3 ) )
                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                      ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                        = ( kpair @ X3 @ X4 ) )
                                                                                                                                                     => ( X1 = X3 ) )
                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                        ( ( X1 = X2 )
                                                                                                                                                       => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                          = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                          ( ( X1 = X2 )
                                                                                                                                                         => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                            = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                            ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                              = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                           => ( ( X3 = X4 )
                                                                                                                                                             => ( X2 = X4 ) ) )
                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                              ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                             => ( X1 = X2 ) )
                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                  = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                               => ( X2 = X4 ) )
                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                  ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                    = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                 => ( X2 = X4 ) )
                                                                                                                                                             => ( ! [X1: $i] :
                                                                                                                                                                    ( ( iskpair @ X1 )
                                                                                                                                                                   => ~ ! [X2: $i] :
                                                                                                                                                                          ( ( in @ X2
                                                                                                                                                                            @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                              @ ^ [X3: $i] :
                                                                                                                                                                                  ( X1
                                                                                                                                                                                  = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                         => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                              @ ^ [X3: $i] :
                                                                                                                                                                                  ( X1
                                                                                                                                                                                  = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                           != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                      ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                      = X2 )
                                                                                                                                                                 => ( sP8
                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                         => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                            ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                           => ( in @ X3 @ X1 ) )
                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                              ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                             => ( in @ X4 @ X2 ) )
                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                                                                   => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                      = X3 ) ) )
                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                                                                     => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                        = X4 ) ) )
                                                                                                                                                                             => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                  ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                 => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                    = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h162,assumption,
    ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) ),
    introduced(assumption,[]) ).

thf(h163,assumption,
    ~ ( ! [X1: $i,X2: $i] :
          ( ( subset @ X1 @ X2 )
         => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
     => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
       => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
         => ( ! [X1: $i,X2: $i,X3: $i] :
                ( ( in @ X3 @ X1 )
               => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
           => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
             => ( ! [X1: $i,X2: $i,X3: $i] :
                    ( ( in @ X3 @ X2 )
                   => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
               => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                      ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                     => ( ( ( in @ X3 @ X1 )
                         => X4 )
                       => ( ( ( in @ X3 @ X2 )
                           => X4 )
                         => X4 ) ) )
                 => ( ! [X1: $i,X2: $i,X3: $i] :
                        ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                       => ( ~ ( in @ X3 @ X1 )
                         => ( in @ X3 @ X2 ) ) )
                   => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                     => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                       => ( ! [X1: $i,X2: $i,X3: $i] :
                              ( ( in @ X3 @ X1 )
                             => ( ( in @ X3 @ X2 )
                               => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                ( ( subset @ X3 @ X1 )
                               => ( ( subset @ X3 @ X2 )
                                 => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                  ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                 => ( in @ X3 @ X1 ) )
                             => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                               => ( ! [X1: $i,X2: $i] :
                                      ( ( subset @ X1 @ X2 )
                                     => ( ( binintersect @ X1 @ X2 )
                                        = X1 ) )
                                 => ( ! [X1: $i,X2: $i] :
                                        ( ( ( binintersect @ X1 @ X2 )
                                          = X2 )
                                       => ( subset @ X2 @ X1 ) )
                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                          ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                         => ( in @ X3 @ X2 ) )
                                     => ( ! [X1: $i,X2: $i] :
                                            ( ! [X3: $i] :
                                                ( ( in @ X3 @ X1 )
                                               => ~ ( in @ X3 @ X2 ) )
                                           => ( ( binintersect @ X1 @ X2 )
                                              = emptyset ) )
                                       => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                         => ( ! [X1: $i,X2: $i] :
                                                ( ( subset @ X2 @ X1 )
                                               => ( ( binintersect @ X1 @ X2 )
                                                  = X2 ) )
                                           => ( ! [X1: $i,X2: $i] :
                                                  ( ( ( binintersect @ X1 @ X2 )
                                                    = X1 )
                                                 => ( subset @ X1 @ X2 ) )
                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                    ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                    = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                      ( ( in @ X3 @ X1 )
                                                     => ( ~ ( in @ X3 @ X2 )
                                                       => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                        ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                       => ( in @ X3 @ X1 ) )
                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                          ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                         => ~ ( in @ X3 @ X2 ) )
                                                     => ( ! [X1: $i,X2: $i] :
                                                            ( ( subset @ X1 @ X2 )
                                                           => ( ( setminus @ X1 @ X2 )
                                                              = emptyset ) )
                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                              ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                             => ( ( in @ X3 @ X1 )
                                                               => ( in @ X3 @ X2 ) ) )
                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                               => ( ~ ( in @ X3 @ X2 )
                                                                 => ~ ( in @ X3 @ X1 ) ) )
                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                  ( ~ ( in @ X3 @ X1 )
                                                                 => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                    ( ( in @ X3 @ X2 )
                                                                   => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                               => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                 => ( ! [X1: $i,X2: $i] :
                                                                        ( ( ( setminus @ X1 @ X2 )
                                                                          = emptyset )
                                                                       => ( subset @ X1 @ X2 ) )
                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                          ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                         => ! [X4: $o] :
                                                                              ( ( ( in @ X3 @ X1 )
                                                                               => ( ~ ( in @ X3 @ X2 )
                                                                                 => X4 ) )
                                                                             => ( ( ~ ( in @ X3 @ X1 )
                                                                                 => ( ( in @ X3 @ X2 )
                                                                                   => X4 ) )
                                                                               => X4 ) ) )
                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                            ( ( in @ X3 @ X1 )
                                                                           => ( ~ ( in @ X3 @ X2 )
                                                                             => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                              ( ~ ( in @ X3 @ X1 )
                                                                             => ( ( in @ X3 @ X2 )
                                                                               => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                ( ( in @ X3 @ X1 )
                                                                               => ( ( in @ X3 @ X2 )
                                                                                 => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                  ( ~ ( in @ X3 @ X1 )
                                                                                 => ( ~ ( in @ X3 @ X2 )
                                                                                   => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                             => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                               => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                 => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                   => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                     => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                              ( ( in @ X2 @ X1 )
                                                                                             => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                ( ( in @ X2 @ X1 )
                                                                                               => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                 => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                    ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                   => ( ( X3 != X1 )
                                                                                                     => ( X3 = X2 ) ) )
                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                     => ! [X4: $i] :
                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                         => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                       => ! [X4: $i] :
                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                           => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                         => ! [X4: $i] :
                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                             => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                           => ! [X4: $i] :
                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                               => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                             => ! [X4: $i] :
                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                 => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                               => ! [X4: $i] :
                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                   => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                  ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                 => ~ ! [X4: $i] :
                                                                                                                        ( ( in @ X4 @ X1 )
                                                                                                                       => ! [X5: $i] :
                                                                                                                            ( ( in @ X5 @ X2 )
                                                                                                                           => ( X3
                                                                                                                             != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                             => ( sP5
                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                      ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                     => ~ ! [X3: $i] :
                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                           => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                 => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                   => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                     => ( ! [X1: $i] :
                                                                                                                            ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                            = X1 )
                                                                                                                       => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                              ( ! [X3: $i] :
                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                 => ! [X4: $i] :
                                                                                                                                      ( ( in @ X4 @ X1 )
                                                                                                                                     => ( ( X2 @ X3 )
                                                                                                                                       => ( ( X2 @ X4 )
                                                                                                                                         => ( X3 = X4 ) ) ) ) )
                                                                                                                             => ( ~ ! [X3: $i] :
                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                     => ~ ( X2 @ X3 ) )
                                                                                                                               => ~ ! [X3: $i] :
                                                                                                                                      ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                     => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                       != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                         => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                ( ~ ! [X3: $i] :
                                                                                                                                      ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                     => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                       != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                               => ~ ! [X3: $i] :
                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                     => ~ ( X2 @ X3 ) ) )
                                                                                                                           => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                 => ( ( X2 @ X3 )
                                                                                                                                   => ( ! [X4: $i] :
                                                                                                                                          ( ( in @ X4 @ X1 )
                                                                                                                                         => ( ( X2 @ X4 )
                                                                                                                                           => ( X4 = X3 ) ) )
                                                                                                                                     => ~ ! [X4: $i] :
                                                                                                                                            ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                           => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                             != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                             => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                    ( ! [X3: $i] :
                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                       => ! [X4: $i] :
                                                                                                                                            ( ( in @ X4 @ X1 )
                                                                                                                                           => ( ( X2 @ X3 )
                                                                                                                                             => ( ( X2 @ X4 )
                                                                                                                                               => ( X3 = X4 ) ) ) ) )
                                                                                                                                   => ( ~ ! [X3: $i] :
                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                           => ~ ( X2 @ X3 ) )
                                                                                                                                     => ~ ! [X3: $i] :
                                                                                                                                            ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                           => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                             != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                      ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                        = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                     => ( X1 = X2 ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                        ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                       => ( X1 = X3 ) )
                                                                                                                                   => ( ! [X1: $i] :
                                                                                                                                          ( ( iskpair @ X1 )
                                                                                                                                         => ~ ! [X2: $i] :
                                                                                                                                                ( ( in @ X2
                                                                                                                                                  @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                    @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                               => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                    @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                 != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                     => ( ! [X1: $i] :
                                                                                                                                            ( ~ ! [X2: $i] :
                                                                                                                                                  ( ( in @ X2 @ X1 )
                                                                                                                                                 => ( X1
                                                                                                                                                   != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                           => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                              ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                              = X1 )
                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                               => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                  ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                    = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                 => ( X1 = X3 ) )
                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                    ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                      = ( kpair @ X3 @ X4 ) )
                                                                                                                                                   => ( X1 = X3 ) )
                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                      ( ( X1 = X2 )
                                                                                                                                                     => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                        = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                        ( ( X1 = X2 )
                                                                                                                                                       => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                          = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                          ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                            = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                         => ( ( X3 = X4 )
                                                                                                                                                           => ( X2 = X4 ) ) )
                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                            ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                              = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                           => ( X1 = X2 ) )
                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                              ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                             => ( X2 = X4 ) )
                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                  = ( kpair @ X3 @ X4 ) )
                                                                                                                                                               => ( X2 = X4 ) )
                                                                                                                                                           => ( ! [X1: $i] :
                                                                                                                                                                  ( ( iskpair @ X1 )
                                                                                                                                                                 => ~ ! [X2: $i] :
                                                                                                                                                                        ( ( in @ X2
                                                                                                                                                                          @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                            @ ^ [X3: $i] :
                                                                                                                                                                                ( X1
                                                                                                                                                                                = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                       => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                            @ ^ [X3: $i] :
                                                                                                                                                                                ( X1
                                                                                                                                                                                = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                         != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                    ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                    = X2 )
                                                                                                                                                               => ( sP8
                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                       => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                          ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                         => ( in @ X3 @ X1 ) )
                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                            ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                           => ( in @ X4 @ X2 ) )
                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                                                                 => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                    = X3 ) ) )
                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                                                                   => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                      = X4 ) ) )
                                                                                                                                                                           => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                               => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                  = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h164,assumption,
    ! [X1: $i,X2: $i] :
      ( ( subset @ X1 @ X2 )
     => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) ),
    introduced(assumption,[]) ).

thf(h165,assumption,
    ~ ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
     => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
       => ( ! [X1: $i,X2: $i,X3: $i] :
              ( ( in @ X3 @ X1 )
             => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
         => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
           => ( ! [X1: $i,X2: $i,X3: $i] :
                  ( ( in @ X3 @ X2 )
                 => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
             => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                    ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                   => ( ( ( in @ X3 @ X1 )
                       => X4 )
                     => ( ( ( in @ X3 @ X2 )
                         => X4 )
                       => X4 ) ) )
               => ( ! [X1: $i,X2: $i,X3: $i] :
                      ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                     => ( ~ ( in @ X3 @ X1 )
                       => ( in @ X3 @ X2 ) ) )
                 => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                   => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                     => ( ! [X1: $i,X2: $i,X3: $i] :
                            ( ( in @ X3 @ X1 )
                           => ( ( in @ X3 @ X2 )
                             => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                       => ( ! [X1: $i,X2: $i,X3: $i] :
                              ( ( subset @ X3 @ X1 )
                             => ( ( subset @ X3 @ X2 )
                               => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                               => ( in @ X3 @ X1 ) )
                           => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                             => ( ! [X1: $i,X2: $i] :
                                    ( ( subset @ X1 @ X2 )
                                   => ( ( binintersect @ X1 @ X2 )
                                      = X1 ) )
                               => ( ! [X1: $i,X2: $i] :
                                      ( ( ( binintersect @ X1 @ X2 )
                                        = X2 )
                                     => ( subset @ X2 @ X1 ) )
                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                        ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                       => ( in @ X3 @ X2 ) )
                                   => ( ! [X1: $i,X2: $i] :
                                          ( ! [X3: $i] :
                                              ( ( in @ X3 @ X1 )
                                             => ~ ( in @ X3 @ X2 ) )
                                         => ( ( binintersect @ X1 @ X2 )
                                            = emptyset ) )
                                     => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                       => ( ! [X1: $i,X2: $i] :
                                              ( ( subset @ X2 @ X1 )
                                             => ( ( binintersect @ X1 @ X2 )
                                                = X2 ) )
                                         => ( ! [X1: $i,X2: $i] :
                                                ( ( ( binintersect @ X1 @ X2 )
                                                  = X1 )
                                               => ( subset @ X1 @ X2 ) )
                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                  ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                  = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                    ( ( in @ X3 @ X1 )
                                                   => ( ~ ( in @ X3 @ X2 )
                                                     => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                      ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                     => ( in @ X3 @ X1 ) )
                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                        ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                       => ~ ( in @ X3 @ X2 ) )
                                                   => ( ! [X1: $i,X2: $i] :
                                                          ( ( subset @ X1 @ X2 )
                                                         => ( ( setminus @ X1 @ X2 )
                                                            = emptyset ) )
                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                            ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                           => ( ( in @ X3 @ X1 )
                                                             => ( in @ X3 @ X2 ) ) )
                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                              ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                             => ( ~ ( in @ X3 @ X2 )
                                                               => ~ ( in @ X3 @ X1 ) ) )
                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                ( ~ ( in @ X3 @ X1 )
                                                               => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                  ( ( in @ X3 @ X2 )
                                                                 => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                             => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                               => ( ! [X1: $i,X2: $i] :
                                                                      ( ( ( setminus @ X1 @ X2 )
                                                                        = emptyset )
                                                                     => ( subset @ X1 @ X2 ) )
                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                        ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                       => ! [X4: $o] :
                                                                            ( ( ( in @ X3 @ X1 )
                                                                             => ( ~ ( in @ X3 @ X2 )
                                                                               => X4 ) )
                                                                           => ( ( ~ ( in @ X3 @ X1 )
                                                                               => ( ( in @ X3 @ X2 )
                                                                                 => X4 ) )
                                                                             => X4 ) ) )
                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                          ( ( in @ X3 @ X1 )
                                                                         => ( ~ ( in @ X3 @ X2 )
                                                                           => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                            ( ~ ( in @ X3 @ X1 )
                                                                           => ( ( in @ X3 @ X2 )
                                                                             => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                              ( ( in @ X3 @ X1 )
                                                                             => ( ( in @ X3 @ X2 )
                                                                               => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                ( ~ ( in @ X3 @ X1 )
                                                                               => ( ~ ( in @ X3 @ X2 )
                                                                                 => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                           => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                             => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                               => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                 => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                   => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                            ( ( in @ X2 @ X1 )
                                                                                           => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                              ( ( in @ X2 @ X1 )
                                                                                             => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                ( ( in @ X3 @ X1 )
                                                                                               => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                  ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                 => ( ( X3 != X1 )
                                                                                                   => ( X3 = X2 ) ) )
                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                   => ! [X4: $i] :
                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                       => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                     => ! [X4: $i] :
                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                         => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                       => ! [X4: $i] :
                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                           => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                         => ! [X4: $i] :
                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                             => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                           => ! [X4: $i] :
                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                               => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                             => ! [X4: $i] :
                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                 => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                               => ~ ! [X4: $i] :
                                                                                                                      ( ( in @ X4 @ X1 )
                                                                                                                     => ! [X5: $i] :
                                                                                                                          ( ( in @ X5 @ X2 )
                                                                                                                         => ( X3
                                                                                                                           != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                           => ( sP5
                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                    ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                   => ~ ! [X3: $i] :
                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                         => ~ ( in @ X2 @ X3 ) ) )
                                                                                                               => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                 => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                   => ( ! [X1: $i] :
                                                                                                                          ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                          = X1 )
                                                                                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                            ( ! [X3: $i] :
                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                               => ! [X4: $i] :
                                                                                                                                    ( ( in @ X4 @ X1 )
                                                                                                                                   => ( ( X2 @ X3 )
                                                                                                                                     => ( ( X2 @ X4 )
                                                                                                                                       => ( X3 = X4 ) ) ) ) )
                                                                                                                           => ( ~ ! [X3: $i] :
                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                   => ~ ( X2 @ X3 ) )
                                                                                                                             => ~ ! [X3: $i] :
                                                                                                                                    ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                   => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                     != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                       => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                              ( ~ ! [X3: $i] :
                                                                                                                                    ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                   => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                     != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                             => ~ ! [X3: $i] :
                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                   => ~ ( X2 @ X3 ) ) )
                                                                                                                         => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                               => ( ( X2 @ X3 )
                                                                                                                                 => ( ! [X4: $i] :
                                                                                                                                        ( ( in @ X4 @ X1 )
                                                                                                                                       => ( ( X2 @ X4 )
                                                                                                                                         => ( X4 = X3 ) ) )
                                                                                                                                   => ~ ! [X4: $i] :
                                                                                                                                          ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                         => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                           != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                           => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                  ( ! [X3: $i] :
                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                     => ! [X4: $i] :
                                                                                                                                          ( ( in @ X4 @ X1 )
                                                                                                                                         => ( ( X2 @ X3 )
                                                                                                                                           => ( ( X2 @ X4 )
                                                                                                                                             => ( X3 = X4 ) ) ) ) )
                                                                                                                                 => ( ~ ! [X3: $i] :
                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                         => ~ ( X2 @ X3 ) )
                                                                                                                                   => ~ ! [X3: $i] :
                                                                                                                                          ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                         => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                           != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                    ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                      = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                   => ( X1 = X2 ) )
                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                      ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                     => ( X1 = X3 ) )
                                                                                                                                 => ( ! [X1: $i] :
                                                                                                                                        ( ( iskpair @ X1 )
                                                                                                                                       => ~ ! [X2: $i] :
                                                                                                                                              ( ( in @ X2
                                                                                                                                                @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                  @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                             => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                  @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                               != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                   => ( ! [X1: $i] :
                                                                                                                                          ( ~ ! [X2: $i] :
                                                                                                                                                ( ( in @ X2 @ X1 )
                                                                                                                                               => ( X1
                                                                                                                                                 != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                         => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                            ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                            = X1 )
                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                              ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                             => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                  = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                               => ( X1 = X3 ) )
                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                  ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                    = ( kpair @ X3 @ X4 ) )
                                                                                                                                                 => ( X1 = X3 ) )
                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                    ( ( X1 = X2 )
                                                                                                                                                   => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                      = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                      ( ( X1 = X2 )
                                                                                                                                                     => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                        = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                        ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                          = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                       => ( ( X3 = X4 )
                                                                                                                                                         => ( X2 = X4 ) ) )
                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                          ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                            = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                         => ( X1 = X2 ) )
                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                            ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                              = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                           => ( X2 = X4 ) )
                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                              ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                = ( kpair @ X3 @ X4 ) )
                                                                                                                                                             => ( X2 = X4 ) )
                                                                                                                                                         => ( ! [X1: $i] :
                                                                                                                                                                ( ( iskpair @ X1 )
                                                                                                                                                               => ~ ! [X2: $i] :
                                                                                                                                                                      ( ( in @ X2
                                                                                                                                                                        @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                          @ ^ [X3: $i] :
                                                                                                                                                                              ( X1
                                                                                                                                                                              = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                     => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                          @ ^ [X3: $i] :
                                                                                                                                                                              ( X1
                                                                                                                                                                              = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                       != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                  ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                  = X2 )
                                                                                                                                                             => ( sP8
                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                      ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                     => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                        ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                       => ( in @ X3 @ X1 ) )
                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                          ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                         => ( in @ X4 @ X2 ) )
                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                                                                               => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                  = X3 ) ) )
                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                                                                 => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                    = X4 ) ) )
                                                                                                                                                                         => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                              ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                             => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h166,assumption,
    ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) ),
    introduced(assumption,[]) ).

thf(h167,assumption,
    ~ ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
     => ( ! [X1: $i,X2: $i,X3: $i] :
            ( ( in @ X3 @ X1 )
           => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
       => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
         => ( ! [X1: $i,X2: $i,X3: $i] :
                ( ( in @ X3 @ X2 )
               => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
           => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                  ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                 => ( ( ( in @ X3 @ X1 )
                     => X4 )
                   => ( ( ( in @ X3 @ X2 )
                       => X4 )
                     => X4 ) ) )
             => ( ! [X1: $i,X2: $i,X3: $i] :
                    ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                   => ( ~ ( in @ X3 @ X1 )
                     => ( in @ X3 @ X2 ) ) )
               => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                 => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                   => ( ! [X1: $i,X2: $i,X3: $i] :
                          ( ( in @ X3 @ X1 )
                         => ( ( in @ X3 @ X2 )
                           => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                     => ( ! [X1: $i,X2: $i,X3: $i] :
                            ( ( subset @ X3 @ X1 )
                           => ( ( subset @ X3 @ X2 )
                             => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                       => ( ! [X1: $i,X2: $i,X3: $i] :
                              ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                             => ( in @ X3 @ X1 ) )
                         => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                           => ( ! [X1: $i,X2: $i] :
                                  ( ( subset @ X1 @ X2 )
                                 => ( ( binintersect @ X1 @ X2 )
                                    = X1 ) )
                             => ( ! [X1: $i,X2: $i] :
                                    ( ( ( binintersect @ X1 @ X2 )
                                      = X2 )
                                   => ( subset @ X2 @ X1 ) )
                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                      ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                     => ( in @ X3 @ X2 ) )
                                 => ( ! [X1: $i,X2: $i] :
                                        ( ! [X3: $i] :
                                            ( ( in @ X3 @ X1 )
                                           => ~ ( in @ X3 @ X2 ) )
                                       => ( ( binintersect @ X1 @ X2 )
                                          = emptyset ) )
                                   => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                     => ( ! [X1: $i,X2: $i] :
                                            ( ( subset @ X2 @ X1 )
                                           => ( ( binintersect @ X1 @ X2 )
                                              = X2 ) )
                                       => ( ! [X1: $i,X2: $i] :
                                              ( ( ( binintersect @ X1 @ X2 )
                                                = X1 )
                                             => ( subset @ X1 @ X2 ) )
                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                  ( ( in @ X3 @ X1 )
                                                 => ( ~ ( in @ X3 @ X2 )
                                                   => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                    ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                   => ( in @ X3 @ X1 ) )
                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                      ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                     => ~ ( in @ X3 @ X2 ) )
                                                 => ( ! [X1: $i,X2: $i] :
                                                        ( ( subset @ X1 @ X2 )
                                                       => ( ( setminus @ X1 @ X2 )
                                                          = emptyset ) )
                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                          ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                         => ( ( in @ X3 @ X1 )
                                                           => ( in @ X3 @ X2 ) ) )
                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                            ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                           => ( ~ ( in @ X3 @ X2 )
                                                             => ~ ( in @ X3 @ X1 ) ) )
                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                              ( ~ ( in @ X3 @ X1 )
                                                             => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                ( ( in @ X3 @ X2 )
                                                               => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                           => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                             => ( ! [X1: $i,X2: $i] :
                                                                    ( ( ( setminus @ X1 @ X2 )
                                                                      = emptyset )
                                                                   => ( subset @ X1 @ X2 ) )
                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                      ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                     => ! [X4: $o] :
                                                                          ( ( ( in @ X3 @ X1 )
                                                                           => ( ~ ( in @ X3 @ X2 )
                                                                             => X4 ) )
                                                                         => ( ( ~ ( in @ X3 @ X1 )
                                                                             => ( ( in @ X3 @ X2 )
                                                                               => X4 ) )
                                                                           => X4 ) ) )
                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                        ( ( in @ X3 @ X1 )
                                                                       => ( ~ ( in @ X3 @ X2 )
                                                                         => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                          ( ~ ( in @ X3 @ X1 )
                                                                         => ( ( in @ X3 @ X2 )
                                                                           => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                            ( ( in @ X3 @ X1 )
                                                                           => ( ( in @ X3 @ X2 )
                                                                             => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                              ( ~ ( in @ X3 @ X1 )
                                                                             => ( ~ ( in @ X3 @ X2 )
                                                                               => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                         => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                           => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                             => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                               => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                 => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                          ( ( in @ X2 @ X1 )
                                                                                         => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                            ( ( in @ X2 @ X1 )
                                                                                           => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                              ( ( in @ X3 @ X1 )
                                                                                             => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                               => ( ( X3 != X1 )
                                                                                                 => ( X3 = X2 ) ) )
                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                 => ! [X4: $i] :
                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                     => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                   => ! [X4: $i] :
                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                       => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                     => ! [X4: $i] :
                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                         => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                       => ! [X4: $i] :
                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                           => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                         => ! [X4: $i] :
                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                             => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                           => ! [X4: $i] :
                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                               => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                              ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                             => ~ ! [X4: $i] :
                                                                                                                    ( ( in @ X4 @ X1 )
                                                                                                                   => ! [X5: $i] :
                                                                                                                        ( ( in @ X5 @ X2 )
                                                                                                                       => ( X3
                                                                                                                         != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                         => ( sP5
                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                  ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                 => ~ ! [X3: $i] :
                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                       => ~ ( in @ X2 @ X3 ) ) )
                                                                                                             => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                               => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                 => ( ! [X1: $i] :
                                                                                                                        ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                        = X1 )
                                                                                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                          ( ! [X3: $i] :
                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                             => ! [X4: $i] :
                                                                                                                                  ( ( in @ X4 @ X1 )
                                                                                                                                 => ( ( X2 @ X3 )
                                                                                                                                   => ( ( X2 @ X4 )
                                                                                                                                     => ( X3 = X4 ) ) ) ) )
                                                                                                                         => ( ~ ! [X3: $i] :
                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                 => ~ ( X2 @ X3 ) )
                                                                                                                           => ~ ! [X3: $i] :
                                                                                                                                  ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                 => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                   != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                            ( ~ ! [X3: $i] :
                                                                                                                                  ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                 => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                   != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                           => ~ ! [X3: $i] :
                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                 => ~ ( X2 @ X3 ) ) )
                                                                                                                       => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                             => ( ( X2 @ X3 )
                                                                                                                               => ( ! [X4: $i] :
                                                                                                                                      ( ( in @ X4 @ X1 )
                                                                                                                                     => ( ( X2 @ X4 )
                                                                                                                                       => ( X4 = X3 ) ) )
                                                                                                                                 => ~ ! [X4: $i] :
                                                                                                                                        ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                       => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                         != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                         => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                ( ! [X3: $i] :
                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                   => ! [X4: $i] :
                                                                                                                                        ( ( in @ X4 @ X1 )
                                                                                                                                       => ( ( X2 @ X3 )
                                                                                                                                         => ( ( X2 @ X4 )
                                                                                                                                           => ( X3 = X4 ) ) ) ) )
                                                                                                                               => ( ~ ! [X3: $i] :
                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                       => ~ ( X2 @ X3 ) )
                                                                                                                                 => ~ ! [X3: $i] :
                                                                                                                                        ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                       => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                         != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                  ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                    = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                 => ( X1 = X2 ) )
                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                    ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                   => ( X1 = X3 ) )
                                                                                                                               => ( ! [X1: $i] :
                                                                                                                                      ( ( iskpair @ X1 )
                                                                                                                                     => ~ ! [X2: $i] :
                                                                                                                                            ( ( in @ X2
                                                                                                                                              @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                           => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                             != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                 => ( ! [X1: $i] :
                                                                                                                                        ( ~ ! [X2: $i] :
                                                                                                                                              ( ( in @ X2 @ X1 )
                                                                                                                                             => ( X1
                                                                                                                                               != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                       => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                          ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                          = X1 )
                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                            ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                           => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                              ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                             => ( X1 = X3 ) )
                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                  = ( kpair @ X3 @ X4 ) )
                                                                                                                                               => ( X1 = X3 ) )
                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                  ( ( X1 = X2 )
                                                                                                                                                 => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                    = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                    ( ( X1 = X2 )
                                                                                                                                                   => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                      = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                      ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                        = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                     => ( ( X3 = X4 )
                                                                                                                                                       => ( X2 = X4 ) ) )
                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                        ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                          = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                       => ( X1 = X2 ) )
                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                          ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                            = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                         => ( X2 = X4 ) )
                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                            ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                              = ( kpair @ X3 @ X4 ) )
                                                                                                                                                           => ( X2 = X4 ) )
                                                                                                                                                       => ( ! [X1: $i] :
                                                                                                                                                              ( ( iskpair @ X1 )
                                                                                                                                                             => ~ ! [X2: $i] :
                                                                                                                                                                    ( ( in @ X2
                                                                                                                                                                      @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                        @ ^ [X3: $i] :
                                                                                                                                                                            ( X1
                                                                                                                                                                            = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                   => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                        @ ^ [X3: $i] :
                                                                                                                                                                            ( X1
                                                                                                                                                                            = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                     != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                = X2 )
                                                                                                                                                           => ( sP8
                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                    ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                   => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                      ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                     => ( in @ X3 @ X1 ) )
                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                        ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                       => ( in @ X4 @ X2 ) )
                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                                                                             => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                = X3 ) ) )
                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                                                                               => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                  = X4 ) ) )
                                                                                                                                                                       => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                            ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                           => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                              = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h168,assumption,
    ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 ),
    introduced(assumption,[]) ).

thf(h169,assumption,
    ~ ( ! [X1: $i,X2: $i,X3: $i] :
          ( ( in @ X3 @ X1 )
         => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
     => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
       => ( ! [X1: $i,X2: $i,X3: $i] :
              ( ( in @ X3 @ X2 )
             => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
         => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
               => ( ( ( in @ X3 @ X1 )
                   => X4 )
                 => ( ( ( in @ X3 @ X2 )
                     => X4 )
                   => X4 ) ) )
           => ( ! [X1: $i,X2: $i,X3: $i] :
                  ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                 => ( ~ ( in @ X3 @ X1 )
                   => ( in @ X3 @ X2 ) ) )
             => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
               => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                 => ( ! [X1: $i,X2: $i,X3: $i] :
                        ( ( in @ X3 @ X1 )
                       => ( ( in @ X3 @ X2 )
                         => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                   => ( ! [X1: $i,X2: $i,X3: $i] :
                          ( ( subset @ X3 @ X1 )
                         => ( ( subset @ X3 @ X2 )
                           => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                     => ( ! [X1: $i,X2: $i,X3: $i] :
                            ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                           => ( in @ X3 @ X1 ) )
                       => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                         => ( ! [X1: $i,X2: $i] :
                                ( ( subset @ X1 @ X2 )
                               => ( ( binintersect @ X1 @ X2 )
                                  = X1 ) )
                           => ( ! [X1: $i,X2: $i] :
                                  ( ( ( binintersect @ X1 @ X2 )
                                    = X2 )
                                 => ( subset @ X2 @ X1 ) )
                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                    ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                   => ( in @ X3 @ X2 ) )
                               => ( ! [X1: $i,X2: $i] :
                                      ( ! [X3: $i] :
                                          ( ( in @ X3 @ X1 )
                                         => ~ ( in @ X3 @ X2 ) )
                                     => ( ( binintersect @ X1 @ X2 )
                                        = emptyset ) )
                                 => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                   => ( ! [X1: $i,X2: $i] :
                                          ( ( subset @ X2 @ X1 )
                                         => ( ( binintersect @ X1 @ X2 )
                                            = X2 ) )
                                     => ( ! [X1: $i,X2: $i] :
                                            ( ( ( binintersect @ X1 @ X2 )
                                              = X1 )
                                           => ( subset @ X1 @ X2 ) )
                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                              ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                              = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                ( ( in @ X3 @ X1 )
                                               => ( ~ ( in @ X3 @ X2 )
                                                 => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                  ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                 => ( in @ X3 @ X1 ) )
                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                    ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                   => ~ ( in @ X3 @ X2 ) )
                                               => ( ! [X1: $i,X2: $i] :
                                                      ( ( subset @ X1 @ X2 )
                                                     => ( ( setminus @ X1 @ X2 )
                                                        = emptyset ) )
                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                        ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                       => ( ( in @ X3 @ X1 )
                                                         => ( in @ X3 @ X2 ) ) )
                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                          ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                         => ( ~ ( in @ X3 @ X2 )
                                                           => ~ ( in @ X3 @ X1 ) ) )
                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                            ( ~ ( in @ X3 @ X1 )
                                                           => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                              ( ( in @ X3 @ X2 )
                                                             => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                         => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                           => ( ! [X1: $i,X2: $i] :
                                                                  ( ( ( setminus @ X1 @ X2 )
                                                                    = emptyset )
                                                                 => ( subset @ X1 @ X2 ) )
                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                    ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                   => ! [X4: $o] :
                                                                        ( ( ( in @ X3 @ X1 )
                                                                         => ( ~ ( in @ X3 @ X2 )
                                                                           => X4 ) )
                                                                       => ( ( ~ ( in @ X3 @ X1 )
                                                                           => ( ( in @ X3 @ X2 )
                                                                             => X4 ) )
                                                                         => X4 ) ) )
                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                      ( ( in @ X3 @ X1 )
                                                                     => ( ~ ( in @ X3 @ X2 )
                                                                       => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                        ( ~ ( in @ X3 @ X1 )
                                                                       => ( ( in @ X3 @ X2 )
                                                                         => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                          ( ( in @ X3 @ X1 )
                                                                         => ( ( in @ X3 @ X2 )
                                                                           => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                            ( ~ ( in @ X3 @ X1 )
                                                                           => ( ~ ( in @ X3 @ X2 )
                                                                             => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                       => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                         => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                           => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                             => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                               => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                        ( ( in @ X2 @ X1 )
                                                                                       => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                          ( ( in @ X2 @ X1 )
                                                                                         => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                            ( ( in @ X3 @ X1 )
                                                                                           => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                              ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                             => ( ( X3 != X1 )
                                                                                               => ( X3 = X2 ) ) )
                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                ( ( in @ X3 @ X1 )
                                                                                               => ! [X4: $i] :
                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                   => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                 => ! [X4: $i] :
                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                     => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                   => ! [X4: $i] :
                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                       => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                     => ! [X4: $i] :
                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                         => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                       => ! [X4: $i] :
                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                           => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                         => ! [X4: $i] :
                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                             => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                            ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                           => ~ ! [X4: $i] :
                                                                                                                  ( ( in @ X4 @ X1 )
                                                                                                                 => ! [X5: $i] :
                                                                                                                      ( ( in @ X5 @ X2 )
                                                                                                                     => ( X3
                                                                                                                       != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                       => ( sP5
                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                               => ~ ! [X3: $i] :
                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                     => ~ ( in @ X2 @ X3 ) ) )
                                                                                                           => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                             => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                               => ( ! [X1: $i] :
                                                                                                                      ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                      = X1 )
                                                                                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                        ( ! [X3: $i] :
                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                           => ! [X4: $i] :
                                                                                                                                ( ( in @ X4 @ X1 )
                                                                                                                               => ( ( X2 @ X3 )
                                                                                                                                 => ( ( X2 @ X4 )
                                                                                                                                   => ( X3 = X4 ) ) ) ) )
                                                                                                                       => ( ~ ! [X3: $i] :
                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                               => ~ ( X2 @ X3 ) )
                                                                                                                         => ~ ! [X3: $i] :
                                                                                                                                ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                               => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                 != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                          ( ~ ! [X3: $i] :
                                                                                                                                ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                               => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                 != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                         => ~ ! [X3: $i] :
                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                               => ~ ( X2 @ X3 ) ) )
                                                                                                                     => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                           => ( ( X2 @ X3 )
                                                                                                                             => ( ! [X4: $i] :
                                                                                                                                    ( ( in @ X4 @ X1 )
                                                                                                                                   => ( ( X2 @ X4 )
                                                                                                                                     => ( X4 = X3 ) ) )
                                                                                                                               => ~ ! [X4: $i] :
                                                                                                                                      ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                     => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                       != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                       => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                              ( ! [X3: $i] :
                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                 => ! [X4: $i] :
                                                                                                                                      ( ( in @ X4 @ X1 )
                                                                                                                                     => ( ( X2 @ X3 )
                                                                                                                                       => ( ( X2 @ X4 )
                                                                                                                                         => ( X3 = X4 ) ) ) ) )
                                                                                                                             => ( ~ ! [X3: $i] :
                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                     => ~ ( X2 @ X3 ) )
                                                                                                                               => ~ ! [X3: $i] :
                                                                                                                                      ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                     => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                       != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                  = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                               => ( X1 = X2 ) )
                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                  ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                 => ( X1 = X3 ) )
                                                                                                                             => ( ! [X1: $i] :
                                                                                                                                    ( ( iskpair @ X1 )
                                                                                                                                   => ~ ! [X2: $i] :
                                                                                                                                          ( ( in @ X2
                                                                                                                                            @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                              @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                         => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                              @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                           != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                               => ( ! [X1: $i] :
                                                                                                                                      ( ~ ! [X2: $i] :
                                                                                                                                            ( ( in @ X2 @ X1 )
                                                                                                                                           => ( X1
                                                                                                                                             != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                     => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                        ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                        = X1 )
                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                         => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                            ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                              = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                           => ( X1 = X3 ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                              ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                = ( kpair @ X3 @ X4 ) )
                                                                                                                                             => ( X1 = X3 ) )
                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                ( ( X1 = X2 )
                                                                                                                                               => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                  = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                  ( ( X1 = X2 )
                                                                                                                                                 => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                    = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                    ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                      = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                   => ( ( X3 = X4 )
                                                                                                                                                     => ( X2 = X4 ) ) )
                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                      ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                        = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                     => ( X1 = X2 ) )
                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                        ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                          = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                       => ( X2 = X4 ) )
                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                          ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                            = ( kpair @ X3 @ X4 ) )
                                                                                                                                                         => ( X2 = X4 ) )
                                                                                                                                                     => ( ! [X1: $i] :
                                                                                                                                                            ( ( iskpair @ X1 )
                                                                                                                                                           => ~ ! [X2: $i] :
                                                                                                                                                                  ( ( in @ X2
                                                                                                                                                                    @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                      @ ^ [X3: $i] :
                                                                                                                                                                          ( X1
                                                                                                                                                                          = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                 => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                      @ ^ [X3: $i] :
                                                                                                                                                                          ( X1
                                                                                                                                                                          = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                   != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                              ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                              = X2 )
                                                                                                                                                         => ( sP8
                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                  ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                 => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                    ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                   => ( in @ X3 @ X1 ) )
                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                      ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                     => ( in @ X4 @ X2 ) )
                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                                                           => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                              = X3 ) ) )
                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                                                                             => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                = X4 ) ) )
                                                                                                                                                                     => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                         => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                            = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h170,assumption,
    ! [X1: $i,X2: $i,X3: $i] :
      ( ( in @ X3 @ X1 )
     => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) ),
    introduced(assumption,[]) ).

thf(h171,assumption,
    ~ ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
     => ( ! [X1: $i,X2: $i,X3: $i] :
            ( ( in @ X3 @ X2 )
           => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
       => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
              ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
             => ( ( ( in @ X3 @ X1 )
                 => X4 )
               => ( ( ( in @ X3 @ X2 )
                   => X4 )
                 => X4 ) ) )
         => ( ! [X1: $i,X2: $i,X3: $i] :
                ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
               => ( ~ ( in @ X3 @ X1 )
                 => ( in @ X3 @ X2 ) ) )
           => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
             => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
               => ( ! [X1: $i,X2: $i,X3: $i] :
                      ( ( in @ X3 @ X1 )
                     => ( ( in @ X3 @ X2 )
                       => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                 => ( ! [X1: $i,X2: $i,X3: $i] :
                        ( ( subset @ X3 @ X1 )
                       => ( ( subset @ X3 @ X2 )
                         => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                   => ( ! [X1: $i,X2: $i,X3: $i] :
                          ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                         => ( in @ X3 @ X1 ) )
                     => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                       => ( ! [X1: $i,X2: $i] :
                              ( ( subset @ X1 @ X2 )
                             => ( ( binintersect @ X1 @ X2 )
                                = X1 ) )
                         => ( ! [X1: $i,X2: $i] :
                                ( ( ( binintersect @ X1 @ X2 )
                                  = X2 )
                               => ( subset @ X2 @ X1 ) )
                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                  ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                 => ( in @ X3 @ X2 ) )
                             => ( ! [X1: $i,X2: $i] :
                                    ( ! [X3: $i] :
                                        ( ( in @ X3 @ X1 )
                                       => ~ ( in @ X3 @ X2 ) )
                                   => ( ( binintersect @ X1 @ X2 )
                                      = emptyset ) )
                               => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                 => ( ! [X1: $i,X2: $i] :
                                        ( ( subset @ X2 @ X1 )
                                       => ( ( binintersect @ X1 @ X2 )
                                          = X2 ) )
                                   => ( ! [X1: $i,X2: $i] :
                                          ( ( ( binintersect @ X1 @ X2 )
                                            = X1 )
                                         => ( subset @ X1 @ X2 ) )
                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                            ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                            = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                              ( ( in @ X3 @ X1 )
                                             => ( ~ ( in @ X3 @ X2 )
                                               => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                               => ( in @ X3 @ X1 ) )
                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                  ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                 => ~ ( in @ X3 @ X2 ) )
                                             => ( ! [X1: $i,X2: $i] :
                                                    ( ( subset @ X1 @ X2 )
                                                   => ( ( setminus @ X1 @ X2 )
                                                      = emptyset ) )
                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                      ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                     => ( ( in @ X3 @ X1 )
                                                       => ( in @ X3 @ X2 ) ) )
                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                        ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                       => ( ~ ( in @ X3 @ X2 )
                                                         => ~ ( in @ X3 @ X1 ) ) )
                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                          ( ~ ( in @ X3 @ X1 )
                                                         => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                            ( ( in @ X3 @ X2 )
                                                           => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                       => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                         => ( ! [X1: $i,X2: $i] :
                                                                ( ( ( setminus @ X1 @ X2 )
                                                                  = emptyset )
                                                               => ( subset @ X1 @ X2 ) )
                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                  ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                 => ! [X4: $o] :
                                                                      ( ( ( in @ X3 @ X1 )
                                                                       => ( ~ ( in @ X3 @ X2 )
                                                                         => X4 ) )
                                                                     => ( ( ~ ( in @ X3 @ X1 )
                                                                         => ( ( in @ X3 @ X2 )
                                                                           => X4 ) )
                                                                       => X4 ) ) )
                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                    ( ( in @ X3 @ X1 )
                                                                   => ( ~ ( in @ X3 @ X2 )
                                                                     => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                      ( ~ ( in @ X3 @ X1 )
                                                                     => ( ( in @ X3 @ X2 )
                                                                       => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                        ( ( in @ X3 @ X1 )
                                                                       => ( ( in @ X3 @ X2 )
                                                                         => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                          ( ~ ( in @ X3 @ X1 )
                                                                         => ( ~ ( in @ X3 @ X2 )
                                                                           => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                     => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                       => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                         => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                           => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                             => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                      ( ( in @ X2 @ X1 )
                                                                                     => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                        ( ( in @ X2 @ X1 )
                                                                                       => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                          ( ( in @ X3 @ X1 )
                                                                                         => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                            ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                           => ( ( X3 != X1 )
                                                                                             => ( X3 = X2 ) ) )
                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                              ( ( in @ X3 @ X1 )
                                                                                             => ! [X4: $i] :
                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                 => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                ( ( in @ X3 @ X1 )
                                                                                               => ! [X4: $i] :
                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                   => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                 => ! [X4: $i] :
                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                     => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                   => ! [X4: $i] :
                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                       => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                     => ! [X4: $i] :
                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                         => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                       => ! [X4: $i] :
                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                           => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                         => ~ ! [X4: $i] :
                                                                                                                ( ( in @ X4 @ X1 )
                                                                                                               => ! [X5: $i] :
                                                                                                                    ( ( in @ X5 @ X2 )
                                                                                                                   => ( X3
                                                                                                                     != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                     => ( sP5
                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                              ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                             => ~ ! [X3: $i] :
                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                   => ~ ( in @ X2 @ X3 ) ) )
                                                                                                         => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                           => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                             => ( ! [X1: $i] :
                                                                                                                    ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                    = X1 )
                                                                                                               => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                      ( ! [X3: $i] :
                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                         => ! [X4: $i] :
                                                                                                                              ( ( in @ X4 @ X1 )
                                                                                                                             => ( ( X2 @ X3 )
                                                                                                                               => ( ( X2 @ X4 )
                                                                                                                                 => ( X3 = X4 ) ) ) ) )
                                                                                                                     => ( ~ ! [X3: $i] :
                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                             => ~ ( X2 @ X3 ) )
                                                                                                                       => ~ ! [X3: $i] :
                                                                                                                              ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                             => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                               != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                        ( ~ ! [X3: $i] :
                                                                                                                              ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                             => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                               != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                       => ~ ! [X3: $i] :
                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                             => ~ ( X2 @ X3 ) ) )
                                                                                                                   => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                         => ( ( X2 @ X3 )
                                                                                                                           => ( ! [X4: $i] :
                                                                                                                                  ( ( in @ X4 @ X1 )
                                                                                                                                 => ( ( X2 @ X4 )
                                                                                                                                   => ( X4 = X3 ) ) )
                                                                                                                             => ~ ! [X4: $i] :
                                                                                                                                    ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                   => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                     != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                            ( ! [X3: $i] :
                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                               => ! [X4: $i] :
                                                                                                                                    ( ( in @ X4 @ X1 )
                                                                                                                                   => ( ( X2 @ X3 )
                                                                                                                                     => ( ( X2 @ X4 )
                                                                                                                                       => ( X3 = X4 ) ) ) ) )
                                                                                                                           => ( ~ ! [X3: $i] :
                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                   => ~ ( X2 @ X3 ) )
                                                                                                                             => ~ ! [X3: $i] :
                                                                                                                                    ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                   => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                     != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                              ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                             => ( X1 = X2 ) )
                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                               => ( X1 = X3 ) )
                                                                                                                           => ( ! [X1: $i] :
                                                                                                                                  ( ( iskpair @ X1 )
                                                                                                                                 => ~ ! [X2: $i] :
                                                                                                                                        ( ( in @ X2
                                                                                                                                          @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                            @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                       => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                            @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                         != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                             => ( ! [X1: $i] :
                                                                                                                                    ( ~ ! [X2: $i] :
                                                                                                                                          ( ( in @ X2 @ X1 )
                                                                                                                                         => ( X1
                                                                                                                                           != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                   => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                      ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                      = X1 )
                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                       => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                          ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                            = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                         => ( X1 = X3 ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                            ( ( ( kpair @ X1 @ X2 )
                                                                                                                                              = ( kpair @ X3 @ X4 ) )
                                                                                                                                           => ( X1 = X3 ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                              ( ( X1 = X2 )
                                                                                                                                             => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                ( ( X1 = X2 )
                                                                                                                                               => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                  = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                  ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                    = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                 => ( ( X3 = X4 )
                                                                                                                                                   => ( X2 = X4 ) ) )
                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                    ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                      = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                   => ( X1 = X2 ) )
                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                      ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                        = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                     => ( X2 = X4 ) )
                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                        ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                          = ( kpair @ X3 @ X4 ) )
                                                                                                                                                       => ( X2 = X4 ) )
                                                                                                                                                   => ( ! [X1: $i] :
                                                                                                                                                          ( ( iskpair @ X1 )
                                                                                                                                                         => ~ ! [X2: $i] :
                                                                                                                                                                ( ( in @ X2
                                                                                                                                                                  @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                    @ ^ [X3: $i] :
                                                                                                                                                                        ( X1
                                                                                                                                                                        = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                               => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                    @ ^ [X3: $i] :
                                                                                                                                                                        ( X1
                                                                                                                                                                        = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                 != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                            ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                            = X2 )
                                                                                                                                                       => ( sP8
                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                               => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                  ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                 => ( in @ X3 @ X1 ) )
                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                    ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                   => ( in @ X4 @ X2 ) )
                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                                                         => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                            = X3 ) ) )
                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                                                           => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                              = X4 ) ) )
                                                                                                                                                                   => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                       => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                          = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h172,assumption,
    ~ ( ! [X1: $i,X2: $i,X3: $i] :
          ( ( in @ X3 @ X2 )
         => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
     => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
            ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
           => ( ( ( in @ X3 @ X1 )
               => X4 )
             => ( ( ( in @ X3 @ X2 )
                 => X4 )
               => X4 ) ) )
       => ( ! [X1: $i,X2: $i,X3: $i] :
              ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
             => ( ~ ( in @ X3 @ X1 )
               => ( in @ X3 @ X2 ) ) )
         => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
           => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
             => ( ! [X1: $i,X2: $i,X3: $i] :
                    ( ( in @ X3 @ X1 )
                   => ( ( in @ X3 @ X2 )
                     => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
               => ( ! [X1: $i,X2: $i,X3: $i] :
                      ( ( subset @ X3 @ X1 )
                     => ( ( subset @ X3 @ X2 )
                       => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                 => ( ! [X1: $i,X2: $i,X3: $i] :
                        ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                       => ( in @ X3 @ X1 ) )
                   => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                     => ( ! [X1: $i,X2: $i] :
                            ( ( subset @ X1 @ X2 )
                           => ( ( binintersect @ X1 @ X2 )
                              = X1 ) )
                       => ( ! [X1: $i,X2: $i] :
                              ( ( ( binintersect @ X1 @ X2 )
                                = X2 )
                             => ( subset @ X2 @ X1 ) )
                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                               => ( in @ X3 @ X2 ) )
                           => ( ! [X1: $i,X2: $i] :
                                  ( ! [X3: $i] :
                                      ( ( in @ X3 @ X1 )
                                     => ~ ( in @ X3 @ X2 ) )
                                 => ( ( binintersect @ X1 @ X2 )
                                    = emptyset ) )
                             => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                               => ( ! [X1: $i,X2: $i] :
                                      ( ( subset @ X2 @ X1 )
                                     => ( ( binintersect @ X1 @ X2 )
                                        = X2 ) )
                                 => ( ! [X1: $i,X2: $i] :
                                        ( ( ( binintersect @ X1 @ X2 )
                                          = X1 )
                                       => ( subset @ X1 @ X2 ) )
                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                          ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                          = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                            ( ( in @ X3 @ X1 )
                                           => ( ~ ( in @ X3 @ X2 )
                                             => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                              ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                             => ( in @ X3 @ X1 ) )
                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                               => ~ ( in @ X3 @ X2 ) )
                                           => ( ! [X1: $i,X2: $i] :
                                                  ( ( subset @ X1 @ X2 )
                                                 => ( ( setminus @ X1 @ X2 )
                                                    = emptyset ) )
                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                    ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                   => ( ( in @ X3 @ X1 )
                                                     => ( in @ X3 @ X2 ) ) )
                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                      ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                     => ( ~ ( in @ X3 @ X2 )
                                                       => ~ ( in @ X3 @ X1 ) ) )
                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                        ( ~ ( in @ X3 @ X1 )
                                                       => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                          ( ( in @ X3 @ X2 )
                                                         => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                     => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                       => ( ! [X1: $i,X2: $i] :
                                                              ( ( ( setminus @ X1 @ X2 )
                                                                = emptyset )
                                                             => ( subset @ X1 @ X2 ) )
                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                               => ! [X4: $o] :
                                                                    ( ( ( in @ X3 @ X1 )
                                                                     => ( ~ ( in @ X3 @ X2 )
                                                                       => X4 ) )
                                                                   => ( ( ~ ( in @ X3 @ X1 )
                                                                       => ( ( in @ X3 @ X2 )
                                                                         => X4 ) )
                                                                     => X4 ) ) )
                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                  ( ( in @ X3 @ X1 )
                                                                 => ( ~ ( in @ X3 @ X2 )
                                                                   => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                    ( ~ ( in @ X3 @ X1 )
                                                                   => ( ( in @ X3 @ X2 )
                                                                     => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                      ( ( in @ X3 @ X1 )
                                                                     => ( ( in @ X3 @ X2 )
                                                                       => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                        ( ~ ( in @ X3 @ X1 )
                                                                       => ( ~ ( in @ X3 @ X2 )
                                                                         => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                   => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                     => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                       => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                         => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                           => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                    ( ( in @ X2 @ X1 )
                                                                                   => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                      ( ( in @ X2 @ X1 )
                                                                                     => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                        ( ( in @ X3 @ X1 )
                                                                                       => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                          ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                         => ( ( X3 != X1 )
                                                                                           => ( X3 = X2 ) ) )
                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                            ( ( in @ X3 @ X1 )
                                                                                           => ! [X4: $i] :
                                                                                                ( ( in @ X4 @ X2 )
                                                                                               => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                              ( ( in @ X3 @ X1 )
                                                                                             => ! [X4: $i] :
                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                 => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                ( ( in @ X3 @ X1 )
                                                                                               => ! [X4: $i] :
                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                   => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                 => ! [X4: $i] :
                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                     => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                   => ! [X4: $i] :
                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                       => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                     => ! [X4: $i] :
                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                         => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                       => ~ ! [X4: $i] :
                                                                                                              ( ( in @ X4 @ X1 )
                                                                                                             => ! [X5: $i] :
                                                                                                                  ( ( in @ X5 @ X2 )
                                                                                                                 => ( X3
                                                                                                                   != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                   => ( sP5
                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                            ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                           => ~ ! [X3: $i] :
                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                 => ~ ( in @ X2 @ X3 ) ) )
                                                                                                       => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                         => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                           => ( ! [X1: $i] :
                                                                                                                  ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                  = X1 )
                                                                                                             => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                    ( ! [X3: $i] :
                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                       => ! [X4: $i] :
                                                                                                                            ( ( in @ X4 @ X1 )
                                                                                                                           => ( ( X2 @ X3 )
                                                                                                                             => ( ( X2 @ X4 )
                                                                                                                               => ( X3 = X4 ) ) ) ) )
                                                                                                                   => ( ~ ! [X3: $i] :
                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                           => ~ ( X2 @ X3 ) )
                                                                                                                     => ~ ! [X3: $i] :
                                                                                                                            ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                           => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                             != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                               => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                      ( ~ ! [X3: $i] :
                                                                                                                            ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                           => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                             != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                     => ~ ! [X3: $i] :
                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                           => ~ ( X2 @ X3 ) ) )
                                                                                                                 => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                       => ( ( X2 @ X3 )
                                                                                                                         => ( ! [X4: $i] :
                                                                                                                                ( ( in @ X4 @ X1 )
                                                                                                                               => ( ( X2 @ X4 )
                                                                                                                                 => ( X4 = X3 ) ) )
                                                                                                                           => ~ ! [X4: $i] :
                                                                                                                                  ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                 => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                   != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                          ( ! [X3: $i] :
                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                             => ! [X4: $i] :
                                                                                                                                  ( ( in @ X4 @ X1 )
                                                                                                                                 => ( ( X2 @ X3 )
                                                                                                                                   => ( ( X2 @ X4 )
                                                                                                                                     => ( X3 = X4 ) ) ) ) )
                                                                                                                         => ( ~ ! [X3: $i] :
                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                 => ~ ( X2 @ X3 ) )
                                                                                                                           => ~ ! [X3: $i] :
                                                                                                                                  ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                 => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                   != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                            ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                              = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                           => ( X1 = X2 ) )
                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                              ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                             => ( X1 = X3 ) )
                                                                                                                         => ( ! [X1: $i] :
                                                                                                                                ( ( iskpair @ X1 )
                                                                                                                               => ~ ! [X2: $i] :
                                                                                                                                      ( ( in @ X2
                                                                                                                                        @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                          @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                     => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                          @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                       != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                           => ( ! [X1: $i] :
                                                                                                                                  ( ~ ! [X2: $i] :
                                                                                                                                        ( ( in @ X2 @ X1 )
                                                                                                                                       => ( X1
                                                                                                                                         != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                 => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                    ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                    = X1 )
                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                      ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                     => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                        ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                          = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                       => ( X1 = X3 ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                          ( ( ( kpair @ X1 @ X2 )
                                                                                                                                            = ( kpair @ X3 @ X4 ) )
                                                                                                                                         => ( X1 = X3 ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                            ( ( X1 = X2 )
                                                                                                                                           => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                              = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                              ( ( X1 = X2 )
                                                                                                                                             => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                  = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                               => ( ( X3 = X4 )
                                                                                                                                                 => ( X2 = X4 ) ) )
                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                  ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                    = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                 => ( X1 = X2 ) )
                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                    ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                      = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                   => ( X2 = X4 ) )
                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                      ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                        = ( kpair @ X3 @ X4 ) )
                                                                                                                                                     => ( X2 = X4 ) )
                                                                                                                                                 => ( ! [X1: $i] :
                                                                                                                                                        ( ( iskpair @ X1 )
                                                                                                                                                       => ~ ! [X2: $i] :
                                                                                                                                                              ( ( in @ X2
                                                                                                                                                                @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                  @ ^ [X3: $i] :
                                                                                                                                                                      ( X1
                                                                                                                                                                      = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                             => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                  @ ^ [X3: $i] :
                                                                                                                                                                      ( X1
                                                                                                                                                                      = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                               != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                          ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                          = X2 )
                                                                                                                                                     => ( sP8
                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                              ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                             => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                               => ( in @ X3 @ X1 ) )
                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                  ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                 => ( in @ X4 @ X2 ) )
                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                                                       => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                          = X3 ) ) )
                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                                                         => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                            = X4 ) ) )
                                                                                                                                                                 => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                      ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                     => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                        = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h173,assumption,
    ! [X1: $i,X2: $i,X3: $i] :
      ( ( in @ X3 @ X2 )
     => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) ),
    introduced(assumption,[]) ).

thf(h174,assumption,
    ~ ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
          ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
         => ( ( ( in @ X3 @ X1 )
             => X4 )
           => ( ( ( in @ X3 @ X2 )
               => X4 )
             => X4 ) ) )
     => ( ! [X1: $i,X2: $i,X3: $i] :
            ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
           => ( ~ ( in @ X3 @ X1 )
             => ( in @ X3 @ X2 ) ) )
       => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
         => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
           => ( ! [X1: $i,X2: $i,X3: $i] :
                  ( ( in @ X3 @ X1 )
                 => ( ( in @ X3 @ X2 )
                   => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
             => ( ! [X1: $i,X2: $i,X3: $i] :
                    ( ( subset @ X3 @ X1 )
                   => ( ( subset @ X3 @ X2 )
                     => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
               => ( ! [X1: $i,X2: $i,X3: $i] :
                      ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                     => ( in @ X3 @ X1 ) )
                 => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                   => ( ! [X1: $i,X2: $i] :
                          ( ( subset @ X1 @ X2 )
                         => ( ( binintersect @ X1 @ X2 )
                            = X1 ) )
                     => ( ! [X1: $i,X2: $i] :
                            ( ( ( binintersect @ X1 @ X2 )
                              = X2 )
                           => ( subset @ X2 @ X1 ) )
                       => ( ! [X1: $i,X2: $i,X3: $i] :
                              ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                             => ( in @ X3 @ X2 ) )
                         => ( ! [X1: $i,X2: $i] :
                                ( ! [X3: $i] :
                                    ( ( in @ X3 @ X1 )
                                   => ~ ( in @ X3 @ X2 ) )
                               => ( ( binintersect @ X1 @ X2 )
                                  = emptyset ) )
                           => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                             => ( ! [X1: $i,X2: $i] :
                                    ( ( subset @ X2 @ X1 )
                                   => ( ( binintersect @ X1 @ X2 )
                                      = X2 ) )
                               => ( ! [X1: $i,X2: $i] :
                                      ( ( ( binintersect @ X1 @ X2 )
                                        = X1 )
                                     => ( subset @ X1 @ X2 ) )
                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                        ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                        = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                          ( ( in @ X3 @ X1 )
                                         => ( ~ ( in @ X3 @ X2 )
                                           => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                            ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                           => ( in @ X3 @ X1 ) )
                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                              ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                             => ~ ( in @ X3 @ X2 ) )
                                         => ( ! [X1: $i,X2: $i] :
                                                ( ( subset @ X1 @ X2 )
                                               => ( ( setminus @ X1 @ X2 )
                                                  = emptyset ) )
                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                  ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                 => ( ( in @ X3 @ X1 )
                                                   => ( in @ X3 @ X2 ) ) )
                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                    ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                   => ( ~ ( in @ X3 @ X2 )
                                                     => ~ ( in @ X3 @ X1 ) ) )
                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                      ( ~ ( in @ X3 @ X1 )
                                                     => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                        ( ( in @ X3 @ X2 )
                                                       => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                   => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                     => ( ! [X1: $i,X2: $i] :
                                                            ( ( ( setminus @ X1 @ X2 )
                                                              = emptyset )
                                                           => ( subset @ X1 @ X2 ) )
                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                              ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                             => ! [X4: $o] :
                                                                  ( ( ( in @ X3 @ X1 )
                                                                   => ( ~ ( in @ X3 @ X2 )
                                                                     => X4 ) )
                                                                 => ( ( ~ ( in @ X3 @ X1 )
                                                                     => ( ( in @ X3 @ X2 )
                                                                       => X4 ) )
                                                                   => X4 ) ) )
                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                ( ( in @ X3 @ X1 )
                                                               => ( ~ ( in @ X3 @ X2 )
                                                                 => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                  ( ~ ( in @ X3 @ X1 )
                                                                 => ( ( in @ X3 @ X2 )
                                                                   => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                    ( ( in @ X3 @ X1 )
                                                                   => ( ( in @ X3 @ X2 )
                                                                     => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                      ( ~ ( in @ X3 @ X1 )
                                                                     => ( ~ ( in @ X3 @ X2 )
                                                                       => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                 => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                   => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                     => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                       => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                         => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                  ( ( in @ X2 @ X1 )
                                                                                 => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                    ( ( in @ X2 @ X1 )
                                                                                   => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                      ( ( in @ X3 @ X1 )
                                                                                     => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                        ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                       => ( ( X3 != X1 )
                                                                                         => ( X3 = X2 ) ) )
                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                          ( ( in @ X3 @ X1 )
                                                                                         => ! [X4: $i] :
                                                                                              ( ( in @ X4 @ X2 )
                                                                                             => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                            ( ( in @ X3 @ X1 )
                                                                                           => ! [X4: $i] :
                                                                                                ( ( in @ X4 @ X2 )
                                                                                               => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                              ( ( in @ X3 @ X1 )
                                                                                             => ! [X4: $i] :
                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                 => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                ( ( in @ X3 @ X1 )
                                                                                               => ! [X4: $i] :
                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                   => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                 => ! [X4: $i] :
                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                     => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                   => ! [X4: $i] :
                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                       => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                      ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                     => ~ ! [X4: $i] :
                                                                                                            ( ( in @ X4 @ X1 )
                                                                                                           => ! [X5: $i] :
                                                                                                                ( ( in @ X5 @ X2 )
                                                                                                               => ( X3
                                                                                                                 != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                 => ( sP5
                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                          ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                         => ~ ! [X3: $i] :
                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                               => ~ ( in @ X2 @ X3 ) ) )
                                                                                                     => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                       => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                         => ( ! [X1: $i] :
                                                                                                                ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                = X1 )
                                                                                                           => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                  ( ! [X3: $i] :
                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                     => ! [X4: $i] :
                                                                                                                          ( ( in @ X4 @ X1 )
                                                                                                                         => ( ( X2 @ X3 )
                                                                                                                           => ( ( X2 @ X4 )
                                                                                                                             => ( X3 = X4 ) ) ) ) )
                                                                                                                 => ( ~ ! [X3: $i] :
                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                         => ~ ( X2 @ X3 ) )
                                                                                                                   => ~ ! [X3: $i] :
                                                                                                                          ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                         => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                           != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                             => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                    ( ~ ! [X3: $i] :
                                                                                                                          ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                         => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                           != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                   => ~ ! [X3: $i] :
                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                         => ~ ( X2 @ X3 ) ) )
                                                                                                               => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                     => ( ( X2 @ X3 )
                                                                                                                       => ( ! [X4: $i] :
                                                                                                                              ( ( in @ X4 @ X1 )
                                                                                                                             => ( ( X2 @ X4 )
                                                                                                                               => ( X4 = X3 ) ) )
                                                                                                                         => ~ ! [X4: $i] :
                                                                                                                                ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                               => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                 != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                        ( ! [X3: $i] :
                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                           => ! [X4: $i] :
                                                                                                                                ( ( in @ X4 @ X1 )
                                                                                                                               => ( ( X2 @ X3 )
                                                                                                                                 => ( ( X2 @ X4 )
                                                                                                                                   => ( X3 = X4 ) ) ) ) )
                                                                                                                       => ( ~ ! [X3: $i] :
                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                               => ~ ( X2 @ X3 ) )
                                                                                                                         => ~ ! [X3: $i] :
                                                                                                                                ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                               => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                 != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                          ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                            = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                         => ( X1 = X2 ) )
                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                            ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                           => ( X1 = X3 ) )
                                                                                                                       => ( ! [X1: $i] :
                                                                                                                              ( ( iskpair @ X1 )
                                                                                                                             => ~ ! [X2: $i] :
                                                                                                                                    ( ( in @ X2
                                                                                                                                      @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                        @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                   => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                        @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                     != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                         => ( ! [X1: $i] :
                                                                                                                                ( ~ ! [X2: $i] :
                                                                                                                                      ( ( in @ X2 @ X1 )
                                                                                                                                     => ( X1
                                                                                                                                       != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                               => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                  ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                  = X1 )
                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                    ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                   => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                      ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                        = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                     => ( X1 = X3 ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                        ( ( ( kpair @ X1 @ X2 )
                                                                                                                                          = ( kpair @ X3 @ X4 ) )
                                                                                                                                       => ( X1 = X3 ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                          ( ( X1 = X2 )
                                                                                                                                         => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                            = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                            ( ( X1 = X2 )
                                                                                                                                           => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                              = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                              ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                             => ( ( X3 = X4 )
                                                                                                                                               => ( X2 = X4 ) ) )
                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                  = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                               => ( X1 = X2 ) )
                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                  ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                    = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                 => ( X2 = X4 ) )
                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                    ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                      = ( kpair @ X3 @ X4 ) )
                                                                                                                                                   => ( X2 = X4 ) )
                                                                                                                                               => ( ! [X1: $i] :
                                                                                                                                                      ( ( iskpair @ X1 )
                                                                                                                                                     => ~ ! [X2: $i] :
                                                                                                                                                            ( ( in @ X2
                                                                                                                                                              @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                @ ^ [X3: $i] :
                                                                                                                                                                    ( X1
                                                                                                                                                                    = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                           => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                @ ^ [X3: $i] :
                                                                                                                                                                    ( X1
                                                                                                                                                                    = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                             != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                        ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                        = X2 )
                                                                                                                                                   => ( sP8
                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                            ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                           => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                              ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                             => ( in @ X3 @ X1 ) )
                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                               => ( in @ X4 @ X2 ) )
                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                                                     => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                        = X3 ) ) )
                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                                                       => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                          = X4 ) ) )
                                                                                                                                                               => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                    ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                   => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                      = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h175,assumption,
    ! [X1: $i,X2: $i,X3: $i,X4: $o] :
      ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
     => ( ( ( in @ X3 @ X1 )
         => X4 )
       => ( ( ( in @ X3 @ X2 )
           => X4 )
         => X4 ) ) ),
    introduced(assumption,[]) ).

thf(h176,assumption,
    ~ ( ! [X1: $i,X2: $i,X3: $i] :
          ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
         => ( ~ ( in @ X3 @ X1 )
           => ( in @ X3 @ X2 ) ) )
     => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
       => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
         => ( ! [X1: $i,X2: $i,X3: $i] :
                ( ( in @ X3 @ X1 )
               => ( ( in @ X3 @ X2 )
                 => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
           => ( ! [X1: $i,X2: $i,X3: $i] :
                  ( ( subset @ X3 @ X1 )
                 => ( ( subset @ X3 @ X2 )
                   => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
             => ( ! [X1: $i,X2: $i,X3: $i] :
                    ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                   => ( in @ X3 @ X1 ) )
               => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                 => ( ! [X1: $i,X2: $i] :
                        ( ( subset @ X1 @ X2 )
                       => ( ( binintersect @ X1 @ X2 )
                          = X1 ) )
                   => ( ! [X1: $i,X2: $i] :
                          ( ( ( binintersect @ X1 @ X2 )
                            = X2 )
                         => ( subset @ X2 @ X1 ) )
                     => ( ! [X1: $i,X2: $i,X3: $i] :
                            ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                           => ( in @ X3 @ X2 ) )
                       => ( ! [X1: $i,X2: $i] :
                              ( ! [X3: $i] :
                                  ( ( in @ X3 @ X1 )
                                 => ~ ( in @ X3 @ X2 ) )
                             => ( ( binintersect @ X1 @ X2 )
                                = emptyset ) )
                         => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                           => ( ! [X1: $i,X2: $i] :
                                  ( ( subset @ X2 @ X1 )
                                 => ( ( binintersect @ X1 @ X2 )
                                    = X2 ) )
                             => ( ! [X1: $i,X2: $i] :
                                    ( ( ( binintersect @ X1 @ X2 )
                                      = X1 )
                                   => ( subset @ X1 @ X2 ) )
                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                      ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                      = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                        ( ( in @ X3 @ X1 )
                                       => ( ~ ( in @ X3 @ X2 )
                                         => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                          ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                         => ( in @ X3 @ X1 ) )
                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                            ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                           => ~ ( in @ X3 @ X2 ) )
                                       => ( ! [X1: $i,X2: $i] :
                                              ( ( subset @ X1 @ X2 )
                                             => ( ( setminus @ X1 @ X2 )
                                                = emptyset ) )
                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                               => ( ( in @ X3 @ X1 )
                                                 => ( in @ X3 @ X2 ) ) )
                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                  ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                 => ( ~ ( in @ X3 @ X2 )
                                                   => ~ ( in @ X3 @ X1 ) ) )
                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                    ( ~ ( in @ X3 @ X1 )
                                                   => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                      ( ( in @ X3 @ X2 )
                                                     => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                 => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                   => ( ! [X1: $i,X2: $i] :
                                                          ( ( ( setminus @ X1 @ X2 )
                                                            = emptyset )
                                                         => ( subset @ X1 @ X2 ) )
                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                            ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                           => ! [X4: $o] :
                                                                ( ( ( in @ X3 @ X1 )
                                                                 => ( ~ ( in @ X3 @ X2 )
                                                                   => X4 ) )
                                                               => ( ( ~ ( in @ X3 @ X1 )
                                                                   => ( ( in @ X3 @ X2 )
                                                                     => X4 ) )
                                                                 => X4 ) ) )
                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                              ( ( in @ X3 @ X1 )
                                                             => ( ~ ( in @ X3 @ X2 )
                                                               => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                ( ~ ( in @ X3 @ X1 )
                                                               => ( ( in @ X3 @ X2 )
                                                                 => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                  ( ( in @ X3 @ X1 )
                                                                 => ( ( in @ X3 @ X2 )
                                                                   => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                    ( ~ ( in @ X3 @ X1 )
                                                                   => ( ~ ( in @ X3 @ X2 )
                                                                     => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                               => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                 => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                   => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                     => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                       => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                ( ( in @ X2 @ X1 )
                                                                               => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                  ( ( in @ X2 @ X1 )
                                                                                 => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                    ( ( in @ X3 @ X1 )
                                                                                   => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                      ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                     => ( ( X3 != X1 )
                                                                                       => ( X3 = X2 ) ) )
                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                        ( ( in @ X3 @ X1 )
                                                                                       => ! [X4: $i] :
                                                                                            ( ( in @ X4 @ X2 )
                                                                                           => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                          ( ( in @ X3 @ X1 )
                                                                                         => ! [X4: $i] :
                                                                                              ( ( in @ X4 @ X2 )
                                                                                             => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                            ( ( in @ X3 @ X1 )
                                                                                           => ! [X4: $i] :
                                                                                                ( ( in @ X4 @ X2 )
                                                                                               => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                              ( ( in @ X3 @ X1 )
                                                                                             => ! [X4: $i] :
                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                 => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                ( ( in @ X3 @ X1 )
                                                                                               => ! [X4: $i] :
                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                   => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                 => ! [X4: $i] :
                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                     => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                    ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                   => ~ ! [X4: $i] :
                                                                                                          ( ( in @ X4 @ X1 )
                                                                                                         => ! [X5: $i] :
                                                                                                              ( ( in @ X5 @ X2 )
                                                                                                             => ( X3
                                                                                                               != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                               => ( sP5
                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                        ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                       => ~ ! [X3: $i] :
                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                             => ~ ( in @ X2 @ X3 ) ) )
                                                                                                   => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                     => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                       => ( ! [X1: $i] :
                                                                                                              ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                              = X1 )
                                                                                                         => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                ( ! [X3: $i] :
                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                   => ! [X4: $i] :
                                                                                                                        ( ( in @ X4 @ X1 )
                                                                                                                       => ( ( X2 @ X3 )
                                                                                                                         => ( ( X2 @ X4 )
                                                                                                                           => ( X3 = X4 ) ) ) ) )
                                                                                                               => ( ~ ! [X3: $i] :
                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                       => ~ ( X2 @ X3 ) )
                                                                                                                 => ~ ! [X3: $i] :
                                                                                                                        ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                       => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                         != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                           => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                  ( ~ ! [X3: $i] :
                                                                                                                        ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                       => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                         != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                 => ~ ! [X3: $i] :
                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                       => ~ ( X2 @ X3 ) ) )
                                                                                                             => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                   => ( ( X2 @ X3 )
                                                                                                                     => ( ! [X4: $i] :
                                                                                                                            ( ( in @ X4 @ X1 )
                                                                                                                           => ( ( X2 @ X4 )
                                                                                                                             => ( X4 = X3 ) ) )
                                                                                                                       => ~ ! [X4: $i] :
                                                                                                                              ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                             => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                               != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                               => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                      ( ! [X3: $i] :
                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                         => ! [X4: $i] :
                                                                                                                              ( ( in @ X4 @ X1 )
                                                                                                                             => ( ( X2 @ X3 )
                                                                                                                               => ( ( X2 @ X4 )
                                                                                                                                 => ( X3 = X4 ) ) ) ) )
                                                                                                                     => ( ~ ! [X3: $i] :
                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                             => ~ ( X2 @ X3 ) )
                                                                                                                       => ~ ! [X3: $i] :
                                                                                                                              ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                             => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                               != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                        ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                          = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                       => ( X1 = X2 ) )
                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                          ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                         => ( X1 = X3 ) )
                                                                                                                     => ( ! [X1: $i] :
                                                                                                                            ( ( iskpair @ X1 )
                                                                                                                           => ~ ! [X2: $i] :
                                                                                                                                  ( ( in @ X2
                                                                                                                                    @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                      @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                 => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                      @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                   != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                       => ( ! [X1: $i] :
                                                                                                                              ( ~ ! [X2: $i] :
                                                                                                                                    ( ( in @ X2 @ X1 )
                                                                                                                                   => ( X1
                                                                                                                                     != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                             => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                = X1 )
                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                  ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                 => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                    ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                      = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                   => ( X1 = X3 ) )
                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                      ( ( ( kpair @ X1 @ X2 )
                                                                                                                                        = ( kpair @ X3 @ X4 ) )
                                                                                                                                     => ( X1 = X3 ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                        ( ( X1 = X2 )
                                                                                                                                       => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                          = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                          ( ( X1 = X2 )
                                                                                                                                         => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                            = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                            ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                              = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                           => ( ( X3 = X4 )
                                                                                                                                             => ( X2 = X4 ) ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                              ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                             => ( X1 = X2 ) )
                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                  = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                               => ( X2 = X4 ) )
                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                  ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                    = ( kpair @ X3 @ X4 ) )
                                                                                                                                                 => ( X2 = X4 ) )
                                                                                                                                             => ( ! [X1: $i] :
                                                                                                                                                    ( ( iskpair @ X1 )
                                                                                                                                                   => ~ ! [X2: $i] :
                                                                                                                                                          ( ( in @ X2
                                                                                                                                                            @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                              @ ^ [X3: $i] :
                                                                                                                                                                  ( X1
                                                                                                                                                                  = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                         => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                              @ ^ [X3: $i] :
                                                                                                                                                                  ( X1
                                                                                                                                                                  = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                           != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                      ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                      = X2 )
                                                                                                                                                 => ( sP8
                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                         => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                            ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                           => ( in @ X3 @ X1 ) )
                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                              ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                             => ( in @ X4 @ X2 ) )
                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                                                   => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                      = X3 ) ) )
                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                                                     => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                        = X4 ) ) )
                                                                                                                                                             => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                  ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                 => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                    = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h177,assumption,
    ! [X1: $i,X2: $i,X3: $i] :
      ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
     => ( ~ ( in @ X3 @ X1 )
       => ( in @ X3 @ X2 ) ) ),
    introduced(assumption,[]) ).

thf(h178,assumption,
    ~ ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
     => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
       => ( ! [X1: $i,X2: $i,X3: $i] :
              ( ( in @ X3 @ X1 )
             => ( ( in @ X3 @ X2 )
               => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
         => ( ! [X1: $i,X2: $i,X3: $i] :
                ( ( subset @ X3 @ X1 )
               => ( ( subset @ X3 @ X2 )
                 => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
           => ( ! [X1: $i,X2: $i,X3: $i] :
                  ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                 => ( in @ X3 @ X1 ) )
             => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
               => ( ! [X1: $i,X2: $i] :
                      ( ( subset @ X1 @ X2 )
                     => ( ( binintersect @ X1 @ X2 )
                        = X1 ) )
                 => ( ! [X1: $i,X2: $i] :
                        ( ( ( binintersect @ X1 @ X2 )
                          = X2 )
                       => ( subset @ X2 @ X1 ) )
                   => ( ! [X1: $i,X2: $i,X3: $i] :
                          ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                         => ( in @ X3 @ X2 ) )
                     => ( ! [X1: $i,X2: $i] :
                            ( ! [X3: $i] :
                                ( ( in @ X3 @ X1 )
                               => ~ ( in @ X3 @ X2 ) )
                           => ( ( binintersect @ X1 @ X2 )
                              = emptyset ) )
                       => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                         => ( ! [X1: $i,X2: $i] :
                                ( ( subset @ X2 @ X1 )
                               => ( ( binintersect @ X1 @ X2 )
                                  = X2 ) )
                           => ( ! [X1: $i,X2: $i] :
                                  ( ( ( binintersect @ X1 @ X2 )
                                    = X1 )
                                 => ( subset @ X1 @ X2 ) )
                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                    ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                    = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                      ( ( in @ X3 @ X1 )
                                     => ( ~ ( in @ X3 @ X2 )
                                       => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                        ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                       => ( in @ X3 @ X1 ) )
                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                          ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                         => ~ ( in @ X3 @ X2 ) )
                                     => ( ! [X1: $i,X2: $i] :
                                            ( ( subset @ X1 @ X2 )
                                           => ( ( setminus @ X1 @ X2 )
                                              = emptyset ) )
                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                              ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                             => ( ( in @ X3 @ X1 )
                                               => ( in @ X3 @ X2 ) ) )
                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                               => ( ~ ( in @ X3 @ X2 )
                                                 => ~ ( in @ X3 @ X1 ) ) )
                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                  ( ~ ( in @ X3 @ X1 )
                                                 => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                    ( ( in @ X3 @ X2 )
                                                   => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                               => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                 => ( ! [X1: $i,X2: $i] :
                                                        ( ( ( setminus @ X1 @ X2 )
                                                          = emptyset )
                                                       => ( subset @ X1 @ X2 ) )
                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                          ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                         => ! [X4: $o] :
                                                              ( ( ( in @ X3 @ X1 )
                                                               => ( ~ ( in @ X3 @ X2 )
                                                                 => X4 ) )
                                                             => ( ( ~ ( in @ X3 @ X1 )
                                                                 => ( ( in @ X3 @ X2 )
                                                                   => X4 ) )
                                                               => X4 ) ) )
                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                            ( ( in @ X3 @ X1 )
                                                           => ( ~ ( in @ X3 @ X2 )
                                                             => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                              ( ~ ( in @ X3 @ X1 )
                                                             => ( ( in @ X3 @ X2 )
                                                               => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                ( ( in @ X3 @ X1 )
                                                               => ( ( in @ X3 @ X2 )
                                                                 => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                  ( ~ ( in @ X3 @ X1 )
                                                                 => ( ~ ( in @ X3 @ X2 )
                                                                   => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                             => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                               => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                 => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                   => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                     => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                       => ( ! [X1: $i,X2: $i] :
                                                                              ( ( in @ X2 @ X1 )
                                                                             => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                ( ( in @ X2 @ X1 )
                                                                               => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                  ( ( in @ X3 @ X1 )
                                                                                 => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                    ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                   => ( ( X3 != X1 )
                                                                                     => ( X3 = X2 ) ) )
                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                      ( ( in @ X3 @ X1 )
                                                                                     => ! [X4: $i] :
                                                                                          ( ( in @ X4 @ X2 )
                                                                                         => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                        ( ( in @ X3 @ X1 )
                                                                                       => ! [X4: $i] :
                                                                                            ( ( in @ X4 @ X2 )
                                                                                           => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                          ( ( in @ X3 @ X1 )
                                                                                         => ! [X4: $i] :
                                                                                              ( ( in @ X4 @ X2 )
                                                                                             => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                            ( ( in @ X3 @ X1 )
                                                                                           => ! [X4: $i] :
                                                                                                ( ( in @ X4 @ X2 )
                                                                                               => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                              ( ( in @ X3 @ X1 )
                                                                                             => ! [X4: $i] :
                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                 => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                ( ( in @ X3 @ X1 )
                                                                                               => ! [X4: $i] :
                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                   => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                  ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                 => ~ ! [X4: $i] :
                                                                                                        ( ( in @ X4 @ X1 )
                                                                                                       => ! [X5: $i] :
                                                                                                            ( ( in @ X5 @ X2 )
                                                                                                           => ( X3
                                                                                                             != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                             => ( sP5
                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                      ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                     => ~ ! [X3: $i] :
                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                           => ~ ( in @ X2 @ X3 ) ) )
                                                                                                 => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                   => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                     => ( ! [X1: $i] :
                                                                                                            ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                            = X1 )
                                                                                                       => ( ! [X1: $i,X2: $i > $o] :
                                                                                                              ( ! [X3: $i] :
                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                 => ! [X4: $i] :
                                                                                                                      ( ( in @ X4 @ X1 )
                                                                                                                     => ( ( X2 @ X3 )
                                                                                                                       => ( ( X2 @ X4 )
                                                                                                                         => ( X3 = X4 ) ) ) ) )
                                                                                                             => ( ~ ! [X3: $i] :
                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                     => ~ ( X2 @ X3 ) )
                                                                                                               => ~ ! [X3: $i] :
                                                                                                                      ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                     => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                       != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                         => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                ( ~ ! [X3: $i] :
                                                                                                                      ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                     => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                       != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                               => ~ ! [X3: $i] :
                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                     => ~ ( X2 @ X3 ) ) )
                                                                                                           => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                 => ( ( X2 @ X3 )
                                                                                                                   => ( ! [X4: $i] :
                                                                                                                          ( ( in @ X4 @ X1 )
                                                                                                                         => ( ( X2 @ X4 )
                                                                                                                           => ( X4 = X3 ) ) )
                                                                                                                     => ~ ! [X4: $i] :
                                                                                                                            ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                           => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                             != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                             => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                    ( ! [X3: $i] :
                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                       => ! [X4: $i] :
                                                                                                                            ( ( in @ X4 @ X1 )
                                                                                                                           => ( ( X2 @ X3 )
                                                                                                                             => ( ( X2 @ X4 )
                                                                                                                               => ( X3 = X4 ) ) ) ) )
                                                                                                                   => ( ~ ! [X3: $i] :
                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                           => ~ ( X2 @ X3 ) )
                                                                                                                     => ~ ! [X3: $i] :
                                                                                                                            ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                           => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                             != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                      ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                        = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                     => ( X1 = X2 ) )
                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                        ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                       => ( X1 = X3 ) )
                                                                                                                   => ( ! [X1: $i] :
                                                                                                                          ( ( iskpair @ X1 )
                                                                                                                         => ~ ! [X2: $i] :
                                                                                                                                ( ( in @ X2
                                                                                                                                  @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                    @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                               => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                    @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                 != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                     => ( ! [X1: $i] :
                                                                                                                            ( ~ ! [X2: $i] :
                                                                                                                                  ( ( in @ X2 @ X1 )
                                                                                                                                 => ( X1
                                                                                                                                   != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                           => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                              ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                              = X1 )
                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                               => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                  ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                    = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                 => ( X1 = X3 ) )
                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                    ( ( ( kpair @ X1 @ X2 )
                                                                                                                                      = ( kpair @ X3 @ X4 ) )
                                                                                                                                   => ( X1 = X3 ) )
                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                      ( ( X1 = X2 )
                                                                                                                                     => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                        = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                        ( ( X1 = X2 )
                                                                                                                                       => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                          = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                          ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                            = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                         => ( ( X3 = X4 )
                                                                                                                                           => ( X2 = X4 ) ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                            ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                              = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                           => ( X1 = X2 ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                              ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                             => ( X2 = X4 ) )
                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                  = ( kpair @ X3 @ X4 ) )
                                                                                                                                               => ( X2 = X4 ) )
                                                                                                                                           => ( ! [X1: $i] :
                                                                                                                                                  ( ( iskpair @ X1 )
                                                                                                                                                 => ~ ! [X2: $i] :
                                                                                                                                                        ( ( in @ X2
                                                                                                                                                          @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                            @ ^ [X3: $i] :
                                                                                                                                                                ( X1
                                                                                                                                                                = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                       => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                            @ ^ [X3: $i] :
                                                                                                                                                                ( X1
                                                                                                                                                                = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                         != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                    ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                    = X2 )
                                                                                                                                               => ( sP8
                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                       => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                          ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                         => ( in @ X3 @ X1 ) )
                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                            ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                           => ( in @ X4 @ X2 ) )
                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                                                 => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                    = X3 ) ) )
                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                                                   => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                      = X4 ) ) )
                                                                                                                                                           => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                               => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                  = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h179,assumption,
    ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) ),
    introduced(assumption,[]) ).

thf(h180,assumption,
    ~ ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
     => ( ! [X1: $i,X2: $i,X3: $i] :
            ( ( in @ X3 @ X1 )
           => ( ( in @ X3 @ X2 )
             => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
       => ( ! [X1: $i,X2: $i,X3: $i] :
              ( ( subset @ X3 @ X1 )
             => ( ( subset @ X3 @ X2 )
               => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
         => ( ! [X1: $i,X2: $i,X3: $i] :
                ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
               => ( in @ X3 @ X1 ) )
           => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
             => ( ! [X1: $i,X2: $i] :
                    ( ( subset @ X1 @ X2 )
                   => ( ( binintersect @ X1 @ X2 )
                      = X1 ) )
               => ( ! [X1: $i,X2: $i] :
                      ( ( ( binintersect @ X1 @ X2 )
                        = X2 )
                     => ( subset @ X2 @ X1 ) )
                 => ( ! [X1: $i,X2: $i,X3: $i] :
                        ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                       => ( in @ X3 @ X2 ) )
                   => ( ! [X1: $i,X2: $i] :
                          ( ! [X3: $i] :
                              ( ( in @ X3 @ X1 )
                             => ~ ( in @ X3 @ X2 ) )
                         => ( ( binintersect @ X1 @ X2 )
                            = emptyset ) )
                     => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                       => ( ! [X1: $i,X2: $i] :
                              ( ( subset @ X2 @ X1 )
                             => ( ( binintersect @ X1 @ X2 )
                                = X2 ) )
                         => ( ! [X1: $i,X2: $i] :
                                ( ( ( binintersect @ X1 @ X2 )
                                  = X1 )
                               => ( subset @ X1 @ X2 ) )
                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                  ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                  = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                    ( ( in @ X3 @ X1 )
                                   => ( ~ ( in @ X3 @ X2 )
                                     => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                      ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                     => ( in @ X3 @ X1 ) )
                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                        ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                       => ~ ( in @ X3 @ X2 ) )
                                   => ( ! [X1: $i,X2: $i] :
                                          ( ( subset @ X1 @ X2 )
                                         => ( ( setminus @ X1 @ X2 )
                                            = emptyset ) )
                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                            ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                           => ( ( in @ X3 @ X1 )
                                             => ( in @ X3 @ X2 ) ) )
                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                              ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                             => ( ~ ( in @ X3 @ X2 )
                                               => ~ ( in @ X3 @ X1 ) ) )
                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                ( ~ ( in @ X3 @ X1 )
                                               => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                  ( ( in @ X3 @ X2 )
                                                 => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                             => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                               => ( ! [X1: $i,X2: $i] :
                                                      ( ( ( setminus @ X1 @ X2 )
                                                        = emptyset )
                                                     => ( subset @ X1 @ X2 ) )
                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                        ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                       => ! [X4: $o] :
                                                            ( ( ( in @ X3 @ X1 )
                                                             => ( ~ ( in @ X3 @ X2 )
                                                               => X4 ) )
                                                           => ( ( ~ ( in @ X3 @ X1 )
                                                               => ( ( in @ X3 @ X2 )
                                                                 => X4 ) )
                                                             => X4 ) ) )
                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                          ( ( in @ X3 @ X1 )
                                                         => ( ~ ( in @ X3 @ X2 )
                                                           => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                            ( ~ ( in @ X3 @ X1 )
                                                           => ( ( in @ X3 @ X2 )
                                                             => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                              ( ( in @ X3 @ X1 )
                                                             => ( ( in @ X3 @ X2 )
                                                               => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                ( ~ ( in @ X3 @ X1 )
                                                               => ( ~ ( in @ X3 @ X2 )
                                                                 => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                           => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                             => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                               => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                 => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                   => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                     => ( ! [X1: $i,X2: $i] :
                                                                            ( ( in @ X2 @ X1 )
                                                                           => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                       => ( ! [X1: $i,X2: $i] :
                                                                              ( ( in @ X2 @ X1 )
                                                                             => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                ( ( in @ X3 @ X1 )
                                                                               => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                  ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                 => ( ( X3 != X1 )
                                                                                   => ( X3 = X2 ) ) )
                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                    ( ( in @ X3 @ X1 )
                                                                                   => ! [X4: $i] :
                                                                                        ( ( in @ X4 @ X2 )
                                                                                       => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                      ( ( in @ X3 @ X1 )
                                                                                     => ! [X4: $i] :
                                                                                          ( ( in @ X4 @ X2 )
                                                                                         => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                        ( ( in @ X3 @ X1 )
                                                                                       => ! [X4: $i] :
                                                                                            ( ( in @ X4 @ X2 )
                                                                                           => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                          ( ( in @ X3 @ X1 )
                                                                                         => ! [X4: $i] :
                                                                                              ( ( in @ X4 @ X2 )
                                                                                             => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                            ( ( in @ X3 @ X1 )
                                                                                           => ! [X4: $i] :
                                                                                                ( ( in @ X4 @ X2 )
                                                                                               => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                              ( ( in @ X3 @ X1 )
                                                                                             => ! [X4: $i] :
                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                 => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                               => ~ ! [X4: $i] :
                                                                                                      ( ( in @ X4 @ X1 )
                                                                                                     => ! [X5: $i] :
                                                                                                          ( ( in @ X5 @ X2 )
                                                                                                         => ( X3
                                                                                                           != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                           => ( sP5
                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                    ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                   => ~ ! [X3: $i] :
                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                         => ~ ( in @ X2 @ X3 ) ) )
                                                                                               => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                 => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                   => ( ! [X1: $i] :
                                                                                                          ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                          = X1 )
                                                                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                                                                            ( ! [X3: $i] :
                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                               => ! [X4: $i] :
                                                                                                                    ( ( in @ X4 @ X1 )
                                                                                                                   => ( ( X2 @ X3 )
                                                                                                                     => ( ( X2 @ X4 )
                                                                                                                       => ( X3 = X4 ) ) ) ) )
                                                                                                           => ( ~ ! [X3: $i] :
                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                   => ~ ( X2 @ X3 ) )
                                                                                                             => ~ ! [X3: $i] :
                                                                                                                    ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                   => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                     != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                       => ( ! [X1: $i,X2: $i > $o] :
                                                                                                              ( ~ ! [X3: $i] :
                                                                                                                    ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                   => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                     != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                             => ~ ! [X3: $i] :
                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                   => ~ ( X2 @ X3 ) ) )
                                                                                                         => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                               => ( ( X2 @ X3 )
                                                                                                                 => ( ! [X4: $i] :
                                                                                                                        ( ( in @ X4 @ X1 )
                                                                                                                       => ( ( X2 @ X4 )
                                                                                                                         => ( X4 = X3 ) ) )
                                                                                                                   => ~ ! [X4: $i] :
                                                                                                                          ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                         => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                           != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                           => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                  ( ! [X3: $i] :
                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                     => ! [X4: $i] :
                                                                                                                          ( ( in @ X4 @ X1 )
                                                                                                                         => ( ( X2 @ X3 )
                                                                                                                           => ( ( X2 @ X4 )
                                                                                                                             => ( X3 = X4 ) ) ) ) )
                                                                                                                 => ( ~ ! [X3: $i] :
                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                         => ~ ( X2 @ X3 ) )
                                                                                                                   => ~ ! [X3: $i] :
                                                                                                                          ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                         => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                           != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                    ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                      = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                   => ( X1 = X2 ) )
                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                      ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                     => ( X1 = X3 ) )
                                                                                                                 => ( ! [X1: $i] :
                                                                                                                        ( ( iskpair @ X1 )
                                                                                                                       => ~ ! [X2: $i] :
                                                                                                                              ( ( in @ X2
                                                                                                                                @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                  @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                             => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                  @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                               != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                   => ( ! [X1: $i] :
                                                                                                                          ( ~ ! [X2: $i] :
                                                                                                                                ( ( in @ X2 @ X1 )
                                                                                                                               => ( X1
                                                                                                                                 != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                         => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                            ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                            = X1 )
                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                              ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                             => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                  = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                               => ( X1 = X3 ) )
                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                  ( ( ( kpair @ X1 @ X2 )
                                                                                                                                    = ( kpair @ X3 @ X4 ) )
                                                                                                                                 => ( X1 = X3 ) )
                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                    ( ( X1 = X2 )
                                                                                                                                   => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                      = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                      ( ( X1 = X2 )
                                                                                                                                     => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                        = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                        ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                          = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                       => ( ( X3 = X4 )
                                                                                                                                         => ( X2 = X4 ) ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                          ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                            = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                         => ( X1 = X2 ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                            ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                              = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                           => ( X2 = X4 ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                              ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                = ( kpair @ X3 @ X4 ) )
                                                                                                                                             => ( X2 = X4 ) )
                                                                                                                                         => ( ! [X1: $i] :
                                                                                                                                                ( ( iskpair @ X1 )
                                                                                                                                               => ~ ! [X2: $i] :
                                                                                                                                                      ( ( in @ X2
                                                                                                                                                        @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                          @ ^ [X3: $i] :
                                                                                                                                                              ( X1
                                                                                                                                                              = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                     => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                          @ ^ [X3: $i] :
                                                                                                                                                              ( X1
                                                                                                                                                              = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                       != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                  ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                  = X2 )
                                                                                                                                             => ( sP8
                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                      ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                     => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                        ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                       => ( in @ X3 @ X1 ) )
                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                          ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                         => ( in @ X4 @ X2 ) )
                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                                                               => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                  = X3 ) ) )
                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                                                 => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                    = X4 ) ) )
                                                                                                                                                         => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                              ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                             => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h181,assumption,
    ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) ),
    introduced(assumption,[]) ).

thf(h182,assumption,
    ~ ( ! [X1: $i,X2: $i,X3: $i] :
          ( ( in @ X3 @ X1 )
         => ( ( in @ X3 @ X2 )
           => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
     => ( ! [X1: $i,X2: $i,X3: $i] :
            ( ( subset @ X3 @ X1 )
           => ( ( subset @ X3 @ X2 )
             => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
       => ( ! [X1: $i,X2: $i,X3: $i] :
              ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
             => ( in @ X3 @ X1 ) )
         => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
           => ( ! [X1: $i,X2: $i] :
                  ( ( subset @ X1 @ X2 )
                 => ( ( binintersect @ X1 @ X2 )
                    = X1 ) )
             => ( ! [X1: $i,X2: $i] :
                    ( ( ( binintersect @ X1 @ X2 )
                      = X2 )
                   => ( subset @ X2 @ X1 ) )
               => ( ! [X1: $i,X2: $i,X3: $i] :
                      ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                     => ( in @ X3 @ X2 ) )
                 => ( ! [X1: $i,X2: $i] :
                        ( ! [X3: $i] :
                            ( ( in @ X3 @ X1 )
                           => ~ ( in @ X3 @ X2 ) )
                       => ( ( binintersect @ X1 @ X2 )
                          = emptyset ) )
                   => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                     => ( ! [X1: $i,X2: $i] :
                            ( ( subset @ X2 @ X1 )
                           => ( ( binintersect @ X1 @ X2 )
                              = X2 ) )
                       => ( ! [X1: $i,X2: $i] :
                              ( ( ( binintersect @ X1 @ X2 )
                                = X1 )
                             => ( subset @ X1 @ X2 ) )
                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                  ( ( in @ X3 @ X1 )
                                 => ( ~ ( in @ X3 @ X2 )
                                   => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                    ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                   => ( in @ X3 @ X1 ) )
                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                      ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                     => ~ ( in @ X3 @ X2 ) )
                                 => ( ! [X1: $i,X2: $i] :
                                        ( ( subset @ X1 @ X2 )
                                       => ( ( setminus @ X1 @ X2 )
                                          = emptyset ) )
                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                          ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                         => ( ( in @ X3 @ X1 )
                                           => ( in @ X3 @ X2 ) ) )
                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                            ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                           => ( ~ ( in @ X3 @ X2 )
                                             => ~ ( in @ X3 @ X1 ) ) )
                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                              ( ~ ( in @ X3 @ X1 )
                                             => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                ( ( in @ X3 @ X2 )
                                               => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                           => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                             => ( ! [X1: $i,X2: $i] :
                                                    ( ( ( setminus @ X1 @ X2 )
                                                      = emptyset )
                                                   => ( subset @ X1 @ X2 ) )
                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                      ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                     => ! [X4: $o] :
                                                          ( ( ( in @ X3 @ X1 )
                                                           => ( ~ ( in @ X3 @ X2 )
                                                             => X4 ) )
                                                         => ( ( ~ ( in @ X3 @ X1 )
                                                             => ( ( in @ X3 @ X2 )
                                                               => X4 ) )
                                                           => X4 ) ) )
                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                        ( ( in @ X3 @ X1 )
                                                       => ( ~ ( in @ X3 @ X2 )
                                                         => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                          ( ~ ( in @ X3 @ X1 )
                                                         => ( ( in @ X3 @ X2 )
                                                           => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                            ( ( in @ X3 @ X1 )
                                                           => ( ( in @ X3 @ X2 )
                                                             => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                              ( ~ ( in @ X3 @ X1 )
                                                             => ( ~ ( in @ X3 @ X2 )
                                                               => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                         => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                           => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                             => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                               => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                 => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                   => ( ! [X1: $i,X2: $i] :
                                                                          ( ( in @ X2 @ X1 )
                                                                         => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                     => ( ! [X1: $i,X2: $i] :
                                                                            ( ( in @ X2 @ X1 )
                                                                           => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                              ( ( in @ X3 @ X1 )
                                                                             => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                               => ( ( X3 != X1 )
                                                                                 => ( X3 = X2 ) ) )
                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                  ( ( in @ X3 @ X1 )
                                                                                 => ! [X4: $i] :
                                                                                      ( ( in @ X4 @ X2 )
                                                                                     => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                    ( ( in @ X3 @ X1 )
                                                                                   => ! [X4: $i] :
                                                                                        ( ( in @ X4 @ X2 )
                                                                                       => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                      ( ( in @ X3 @ X1 )
                                                                                     => ! [X4: $i] :
                                                                                          ( ( in @ X4 @ X2 )
                                                                                         => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                        ( ( in @ X3 @ X1 )
                                                                                       => ! [X4: $i] :
                                                                                            ( ( in @ X4 @ X2 )
                                                                                           => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                          ( ( in @ X3 @ X1 )
                                                                                         => ! [X4: $i] :
                                                                                              ( ( in @ X4 @ X2 )
                                                                                             => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                            ( ( in @ X3 @ X1 )
                                                                                           => ! [X4: $i] :
                                                                                                ( ( in @ X4 @ X2 )
                                                                                               => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                              ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                             => ~ ! [X4: $i] :
                                                                                                    ( ( in @ X4 @ X1 )
                                                                                                   => ! [X5: $i] :
                                                                                                        ( ( in @ X5 @ X2 )
                                                                                                       => ( X3
                                                                                                         != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                         => ( sP5
                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                  ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                 => ~ ! [X3: $i] :
                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                       => ~ ( in @ X2 @ X3 ) ) )
                                                                                             => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                               => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                 => ( ! [X1: $i] :
                                                                                                        ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                        = X1 )
                                                                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                                                                          ( ! [X3: $i] :
                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                             => ! [X4: $i] :
                                                                                                                  ( ( in @ X4 @ X1 )
                                                                                                                 => ( ( X2 @ X3 )
                                                                                                                   => ( ( X2 @ X4 )
                                                                                                                     => ( X3 = X4 ) ) ) ) )
                                                                                                         => ( ~ ! [X3: $i] :
                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                 => ~ ( X2 @ X3 ) )
                                                                                                           => ~ ! [X3: $i] :
                                                                                                                  ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                 => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                   != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                                                                            ( ~ ! [X3: $i] :
                                                                                                                  ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                 => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                   != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                           => ~ ! [X3: $i] :
                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                 => ~ ( X2 @ X3 ) ) )
                                                                                                       => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                             => ( ( X2 @ X3 )
                                                                                                               => ( ! [X4: $i] :
                                                                                                                      ( ( in @ X4 @ X1 )
                                                                                                                     => ( ( X2 @ X4 )
                                                                                                                       => ( X4 = X3 ) ) )
                                                                                                                 => ~ ! [X4: $i] :
                                                                                                                        ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                       => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                         != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                         => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                ( ! [X3: $i] :
                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                   => ! [X4: $i] :
                                                                                                                        ( ( in @ X4 @ X1 )
                                                                                                                       => ( ( X2 @ X3 )
                                                                                                                         => ( ( X2 @ X4 )
                                                                                                                           => ( X3 = X4 ) ) ) ) )
                                                                                                               => ( ~ ! [X3: $i] :
                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                       => ~ ( X2 @ X3 ) )
                                                                                                                 => ~ ! [X3: $i] :
                                                                                                                        ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                       => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                         != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                  ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                    = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                 => ( X1 = X2 ) )
                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                    ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                   => ( X1 = X3 ) )
                                                                                                               => ( ! [X1: $i] :
                                                                                                                      ( ( iskpair @ X1 )
                                                                                                                     => ~ ! [X2: $i] :
                                                                                                                            ( ( in @ X2
                                                                                                                              @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                           => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                             != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                 => ( ! [X1: $i] :
                                                                                                                        ( ~ ! [X2: $i] :
                                                                                                                              ( ( in @ X2 @ X1 )
                                                                                                                             => ( X1
                                                                                                                               != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                       => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                          ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                          = X1 )
                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                            ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                           => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                              ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                             => ( X1 = X3 ) )
                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                ( ( ( kpair @ X1 @ X2 )
                                                                                                                                  = ( kpair @ X3 @ X4 ) )
                                                                                                                               => ( X1 = X3 ) )
                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                  ( ( X1 = X2 )
                                                                                                                                 => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                    = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                    ( ( X1 = X2 )
                                                                                                                                   => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                      = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                      ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                        = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                     => ( ( X3 = X4 )
                                                                                                                                       => ( X2 = X4 ) ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                        ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                          = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                       => ( X1 = X2 ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                          ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                            = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                         => ( X2 = X4 ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                            ( ( ( kpair @ X1 @ X2 )
                                                                                                                                              = ( kpair @ X3 @ X4 ) )
                                                                                                                                           => ( X2 = X4 ) )
                                                                                                                                       => ( ! [X1: $i] :
                                                                                                                                              ( ( iskpair @ X1 )
                                                                                                                                             => ~ ! [X2: $i] :
                                                                                                                                                    ( ( in @ X2
                                                                                                                                                      @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                        @ ^ [X3: $i] :
                                                                                                                                                            ( X1
                                                                                                                                                            = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                   => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                        @ ^ [X3: $i] :
                                                                                                                                                            ( X1
                                                                                                                                                            = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                     != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                = X2 )
                                                                                                                                           => ( sP8
                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                    ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                   => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                      ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                     => ( in @ X3 @ X1 ) )
                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                        ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                       => ( in @ X4 @ X2 ) )
                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                                                             => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                = X3 ) ) )
                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                                                               => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                  = X4 ) ) )
                                                                                                                                                       => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                            ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                           => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                              = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h183,assumption,
    ! [X1: $i,X2: $i,X3: $i] :
      ( ( in @ X3 @ X1 )
     => ( ( in @ X3 @ X2 )
       => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) ),
    introduced(assumption,[]) ).

thf(h184,assumption,
    ~ ( ! [X1: $i,X2: $i,X3: $i] :
          ( ( subset @ X3 @ X1 )
         => ( ( subset @ X3 @ X2 )
           => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
     => ( ! [X1: $i,X2: $i,X3: $i] :
            ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
           => ( in @ X3 @ X1 ) )
       => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
         => ( ! [X1: $i,X2: $i] :
                ( ( subset @ X1 @ X2 )
               => ( ( binintersect @ X1 @ X2 )
                  = X1 ) )
           => ( ! [X1: $i,X2: $i] :
                  ( ( ( binintersect @ X1 @ X2 )
                    = X2 )
                 => ( subset @ X2 @ X1 ) )
             => ( ! [X1: $i,X2: $i,X3: $i] :
                    ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                   => ( in @ X3 @ X2 ) )
               => ( ! [X1: $i,X2: $i] :
                      ( ! [X3: $i] :
                          ( ( in @ X3 @ X1 )
                         => ~ ( in @ X3 @ X2 ) )
                     => ( ( binintersect @ X1 @ X2 )
                        = emptyset ) )
                 => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                   => ( ! [X1: $i,X2: $i] :
                          ( ( subset @ X2 @ X1 )
                         => ( ( binintersect @ X1 @ X2 )
                            = X2 ) )
                     => ( ! [X1: $i,X2: $i] :
                            ( ( ( binintersect @ X1 @ X2 )
                              = X1 )
                           => ( subset @ X1 @ X2 ) )
                       => ( ! [X1: $i,X2: $i,X3: $i] :
                              ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                              = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                ( ( in @ X3 @ X1 )
                               => ( ~ ( in @ X3 @ X2 )
                                 => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                  ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                 => ( in @ X3 @ X1 ) )
                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                    ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                   => ~ ( in @ X3 @ X2 ) )
                               => ( ! [X1: $i,X2: $i] :
                                      ( ( subset @ X1 @ X2 )
                                     => ( ( setminus @ X1 @ X2 )
                                        = emptyset ) )
                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                        ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                       => ( ( in @ X3 @ X1 )
                                         => ( in @ X3 @ X2 ) ) )
                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                          ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                         => ( ~ ( in @ X3 @ X2 )
                                           => ~ ( in @ X3 @ X1 ) ) )
                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                            ( ~ ( in @ X3 @ X1 )
                                           => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                              ( ( in @ X3 @ X2 )
                                             => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                         => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                           => ( ! [X1: $i,X2: $i] :
                                                  ( ( ( setminus @ X1 @ X2 )
                                                    = emptyset )
                                                 => ( subset @ X1 @ X2 ) )
                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                    ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                   => ! [X4: $o] :
                                                        ( ( ( in @ X3 @ X1 )
                                                         => ( ~ ( in @ X3 @ X2 )
                                                           => X4 ) )
                                                       => ( ( ~ ( in @ X3 @ X1 )
                                                           => ( ( in @ X3 @ X2 )
                                                             => X4 ) )
                                                         => X4 ) ) )
                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                      ( ( in @ X3 @ X1 )
                                                     => ( ~ ( in @ X3 @ X2 )
                                                       => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                        ( ~ ( in @ X3 @ X1 )
                                                       => ( ( in @ X3 @ X2 )
                                                         => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                          ( ( in @ X3 @ X1 )
                                                         => ( ( in @ X3 @ X2 )
                                                           => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                            ( ~ ( in @ X3 @ X1 )
                                                           => ( ~ ( in @ X3 @ X2 )
                                                             => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                       => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                         => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                           => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                             => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                               => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                 => ( ! [X1: $i,X2: $i] :
                                                                        ( ( in @ X2 @ X1 )
                                                                       => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                   => ( ! [X1: $i,X2: $i] :
                                                                          ( ( in @ X2 @ X1 )
                                                                         => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                            ( ( in @ X3 @ X1 )
                                                                           => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                              ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                             => ( ( X3 != X1 )
                                                                               => ( X3 = X2 ) ) )
                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                ( ( in @ X3 @ X1 )
                                                                               => ! [X4: $i] :
                                                                                    ( ( in @ X4 @ X2 )
                                                                                   => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                  ( ( in @ X3 @ X1 )
                                                                                 => ! [X4: $i] :
                                                                                      ( ( in @ X4 @ X2 )
                                                                                     => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                    ( ( in @ X3 @ X1 )
                                                                                   => ! [X4: $i] :
                                                                                        ( ( in @ X4 @ X2 )
                                                                                       => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                      ( ( in @ X3 @ X1 )
                                                                                     => ! [X4: $i] :
                                                                                          ( ( in @ X4 @ X2 )
                                                                                         => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                        ( ( in @ X3 @ X1 )
                                                                                       => ! [X4: $i] :
                                                                                            ( ( in @ X4 @ X2 )
                                                                                           => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                          ( ( in @ X3 @ X1 )
                                                                                         => ! [X4: $i] :
                                                                                              ( ( in @ X4 @ X2 )
                                                                                             => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                            ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                           => ~ ! [X4: $i] :
                                                                                                  ( ( in @ X4 @ X1 )
                                                                                                 => ! [X5: $i] :
                                                                                                      ( ( in @ X5 @ X2 )
                                                                                                     => ( X3
                                                                                                       != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                       => ( sP5
                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                               => ~ ! [X3: $i] :
                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                     => ~ ( in @ X2 @ X3 ) ) )
                                                                                           => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                             => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                               => ( ! [X1: $i] :
                                                                                                      ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                      = X1 )
                                                                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                                                                        ( ! [X3: $i] :
                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                           => ! [X4: $i] :
                                                                                                                ( ( in @ X4 @ X1 )
                                                                                                               => ( ( X2 @ X3 )
                                                                                                                 => ( ( X2 @ X4 )
                                                                                                                   => ( X3 = X4 ) ) ) ) )
                                                                                                       => ( ~ ! [X3: $i] :
                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                               => ~ ( X2 @ X3 ) )
                                                                                                         => ~ ! [X3: $i] :
                                                                                                                ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                               => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                 != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                                                                          ( ~ ! [X3: $i] :
                                                                                                                ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                               => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                 != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                         => ~ ! [X3: $i] :
                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                               => ~ ( X2 @ X3 ) ) )
                                                                                                     => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                           => ( ( X2 @ X3 )
                                                                                                             => ( ! [X4: $i] :
                                                                                                                    ( ( in @ X4 @ X1 )
                                                                                                                   => ( ( X2 @ X4 )
                                                                                                                     => ( X4 = X3 ) ) )
                                                                                                               => ~ ! [X4: $i] :
                                                                                                                      ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                     => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                       != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                       => ( ! [X1: $i,X2: $i > $o] :
                                                                                                              ( ! [X3: $i] :
                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                 => ! [X4: $i] :
                                                                                                                      ( ( in @ X4 @ X1 )
                                                                                                                     => ( ( X2 @ X3 )
                                                                                                                       => ( ( X2 @ X4 )
                                                                                                                         => ( X3 = X4 ) ) ) ) )
                                                                                                             => ( ~ ! [X3: $i] :
                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                     => ~ ( X2 @ X3 ) )
                                                                                                               => ~ ! [X3: $i] :
                                                                                                                      ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                     => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                       != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                  = ( setadjoin @ X2 @ emptyset ) )
                                                                                                               => ( X1 = X2 ) )
                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                  ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                 => ( X1 = X3 ) )
                                                                                                             => ( ! [X1: $i] :
                                                                                                                    ( ( iskpair @ X1 )
                                                                                                                   => ~ ! [X2: $i] :
                                                                                                                          ( ( in @ X2
                                                                                                                            @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                              @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                         => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                              @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                           != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                               => ( ! [X1: $i] :
                                                                                                                      ( ~ ! [X2: $i] :
                                                                                                                            ( ( in @ X2 @ X1 )
                                                                                                                           => ( X1
                                                                                                                             != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                     => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                        ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                        = X1 )
                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                         => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                            ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                              = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                           => ( X1 = X3 ) )
                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                              ( ( ( kpair @ X1 @ X2 )
                                                                                                                                = ( kpair @ X3 @ X4 ) )
                                                                                                                             => ( X1 = X3 ) )
                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                ( ( X1 = X2 )
                                                                                                                               => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                  = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                  ( ( X1 = X2 )
                                                                                                                                 => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                    = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                    ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                      = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                   => ( ( X3 = X4 )
                                                                                                                                     => ( X2 = X4 ) ) )
                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                      ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                        = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                     => ( X1 = X2 ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                        ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                          = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                       => ( X2 = X4 ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                          ( ( ( kpair @ X1 @ X2 )
                                                                                                                                            = ( kpair @ X3 @ X4 ) )
                                                                                                                                         => ( X2 = X4 ) )
                                                                                                                                     => ( ! [X1: $i] :
                                                                                                                                            ( ( iskpair @ X1 )
                                                                                                                                           => ~ ! [X2: $i] :
                                                                                                                                                  ( ( in @ X2
                                                                                                                                                    @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                      @ ^ [X3: $i] :
                                                                                                                                                          ( X1
                                                                                                                                                          = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                 => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                      @ ^ [X3: $i] :
                                                                                                                                                          ( X1
                                                                                                                                                          = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                   != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                              ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                              = X2 )
                                                                                                                                         => ( sP8
                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                  ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                 => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                    ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                   => ( in @ X3 @ X1 ) )
                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                      ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                     => ( in @ X4 @ X2 ) )
                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                                           => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                              = X3 ) ) )
                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                                                             => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                = X4 ) ) )
                                                                                                                                                     => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                         => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                            = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h185,assumption,
    ! [X1: $i,X2: $i,X3: $i] :
      ( ( subset @ X3 @ X1 )
     => ( ( subset @ X3 @ X2 )
       => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) ),
    introduced(assumption,[]) ).

thf(h186,assumption,
    ~ ( ! [X1: $i,X2: $i,X3: $i] :
          ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
         => ( in @ X3 @ X1 ) )
     => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
       => ( ! [X1: $i,X2: $i] :
              ( ( subset @ X1 @ X2 )
             => ( ( binintersect @ X1 @ X2 )
                = X1 ) )
         => ( ! [X1: $i,X2: $i] :
                ( ( ( binintersect @ X1 @ X2 )
                  = X2 )
               => ( subset @ X2 @ X1 ) )
           => ( ! [X1: $i,X2: $i,X3: $i] :
                  ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                 => ( in @ X3 @ X2 ) )
             => ( ! [X1: $i,X2: $i] :
                    ( ! [X3: $i] :
                        ( ( in @ X3 @ X1 )
                       => ~ ( in @ X3 @ X2 ) )
                   => ( ( binintersect @ X1 @ X2 )
                      = emptyset ) )
               => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                 => ( ! [X1: $i,X2: $i] :
                        ( ( subset @ X2 @ X1 )
                       => ( ( binintersect @ X1 @ X2 )
                          = X2 ) )
                   => ( ! [X1: $i,X2: $i] :
                          ( ( ( binintersect @ X1 @ X2 )
                            = X1 )
                         => ( subset @ X1 @ X2 ) )
                     => ( ! [X1: $i,X2: $i,X3: $i] :
                            ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                            = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                       => ( ! [X1: $i,X2: $i,X3: $i] :
                              ( ( in @ X3 @ X1 )
                             => ( ~ ( in @ X3 @ X2 )
                               => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                               => ( in @ X3 @ X1 ) )
                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                  ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                 => ~ ( in @ X3 @ X2 ) )
                             => ( ! [X1: $i,X2: $i] :
                                    ( ( subset @ X1 @ X2 )
                                   => ( ( setminus @ X1 @ X2 )
                                      = emptyset ) )
                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                      ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                     => ( ( in @ X3 @ X1 )
                                       => ( in @ X3 @ X2 ) ) )
                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                        ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                       => ( ~ ( in @ X3 @ X2 )
                                         => ~ ( in @ X3 @ X1 ) ) )
                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                          ( ~ ( in @ X3 @ X1 )
                                         => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                            ( ( in @ X3 @ X2 )
                                           => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                       => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                         => ( ! [X1: $i,X2: $i] :
                                                ( ( ( setminus @ X1 @ X2 )
                                                  = emptyset )
                                               => ( subset @ X1 @ X2 ) )
                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                  ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                 => ! [X4: $o] :
                                                      ( ( ( in @ X3 @ X1 )
                                                       => ( ~ ( in @ X3 @ X2 )
                                                         => X4 ) )
                                                     => ( ( ~ ( in @ X3 @ X1 )
                                                         => ( ( in @ X3 @ X2 )
                                                           => X4 ) )
                                                       => X4 ) ) )
                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                    ( ( in @ X3 @ X1 )
                                                   => ( ~ ( in @ X3 @ X2 )
                                                     => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                      ( ~ ( in @ X3 @ X1 )
                                                     => ( ( in @ X3 @ X2 )
                                                       => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                        ( ( in @ X3 @ X1 )
                                                       => ( ( in @ X3 @ X2 )
                                                         => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                          ( ~ ( in @ X3 @ X1 )
                                                         => ( ~ ( in @ X3 @ X2 )
                                                           => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                     => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                       => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                         => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                           => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                             => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                               => ( ! [X1: $i,X2: $i] :
                                                                      ( ( in @ X2 @ X1 )
                                                                     => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                 => ( ! [X1: $i,X2: $i] :
                                                                        ( ( in @ X2 @ X1 )
                                                                       => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                          ( ( in @ X3 @ X1 )
                                                                         => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                            ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                           => ( ( X3 != X1 )
                                                                             => ( X3 = X2 ) ) )
                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                              ( ( in @ X3 @ X1 )
                                                                             => ! [X4: $i] :
                                                                                  ( ( in @ X4 @ X2 )
                                                                                 => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                ( ( in @ X3 @ X1 )
                                                                               => ! [X4: $i] :
                                                                                    ( ( in @ X4 @ X2 )
                                                                                   => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                  ( ( in @ X3 @ X1 )
                                                                                 => ! [X4: $i] :
                                                                                      ( ( in @ X4 @ X2 )
                                                                                     => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                    ( ( in @ X3 @ X1 )
                                                                                   => ! [X4: $i] :
                                                                                        ( ( in @ X4 @ X2 )
                                                                                       => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                      ( ( in @ X3 @ X1 )
                                                                                     => ! [X4: $i] :
                                                                                          ( ( in @ X4 @ X2 )
                                                                                         => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                        ( ( in @ X3 @ X1 )
                                                                                       => ! [X4: $i] :
                                                                                            ( ( in @ X4 @ X2 )
                                                                                           => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                         => ~ ! [X4: $i] :
                                                                                                ( ( in @ X4 @ X1 )
                                                                                               => ! [X5: $i] :
                                                                                                    ( ( in @ X5 @ X2 )
                                                                                                   => ( X3
                                                                                                     != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                     => ( sP5
                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                              ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                             => ~ ! [X3: $i] :
                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                   => ~ ( in @ X2 @ X3 ) ) )
                                                                                         => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                           => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                             => ( ! [X1: $i] :
                                                                                                    ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                    = X1 )
                                                                                               => ( ! [X1: $i,X2: $i > $o] :
                                                                                                      ( ! [X3: $i] :
                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                         => ! [X4: $i] :
                                                                                                              ( ( in @ X4 @ X1 )
                                                                                                             => ( ( X2 @ X3 )
                                                                                                               => ( ( X2 @ X4 )
                                                                                                                 => ( X3 = X4 ) ) ) ) )
                                                                                                     => ( ~ ! [X3: $i] :
                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                             => ~ ( X2 @ X3 ) )
                                                                                                       => ~ ! [X3: $i] :
                                                                                                              ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                             => ( ( dsetconstr @ X1 @ X2 )
                                                                                                               != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                                                                        ( ~ ! [X3: $i] :
                                                                                                              ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                             => ( ( dsetconstr @ X1 @ X2 )
                                                                                                               != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                       => ~ ! [X3: $i] :
                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                             => ~ ( X2 @ X3 ) ) )
                                                                                                   => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                         => ( ( X2 @ X3 )
                                                                                                           => ( ! [X4: $i] :
                                                                                                                  ( ( in @ X4 @ X1 )
                                                                                                                 => ( ( X2 @ X4 )
                                                                                                                   => ( X4 = X3 ) ) )
                                                                                                             => ~ ! [X4: $i] :
                                                                                                                    ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                   => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                     != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                                                                            ( ! [X3: $i] :
                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                               => ! [X4: $i] :
                                                                                                                    ( ( in @ X4 @ X1 )
                                                                                                                   => ( ( X2 @ X3 )
                                                                                                                     => ( ( X2 @ X4 )
                                                                                                                       => ( X3 = X4 ) ) ) ) )
                                                                                                           => ( ~ ! [X3: $i] :
                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                   => ~ ( X2 @ X3 ) )
                                                                                                             => ~ ! [X3: $i] :
                                                                                                                    ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                   => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                     != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                              ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                = ( setadjoin @ X2 @ emptyset ) )
                                                                                                             => ( X1 = X2 ) )
                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                               => ( X1 = X3 ) )
                                                                                                           => ( ! [X1: $i] :
                                                                                                                  ( ( iskpair @ X1 )
                                                                                                                 => ~ ! [X2: $i] :
                                                                                                                        ( ( in @ X2
                                                                                                                          @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                            @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                       => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                            @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                         != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                             => ( ! [X1: $i] :
                                                                                                                    ( ~ ! [X2: $i] :
                                                                                                                          ( ( in @ X2 @ X1 )
                                                                                                                         => ( X1
                                                                                                                           != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                   => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                      ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                      = X1 )
                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                       => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                          ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                            = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                         => ( X1 = X3 ) )
                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                            ( ( ( kpair @ X1 @ X2 )
                                                                                                                              = ( kpair @ X3 @ X4 ) )
                                                                                                                           => ( X1 = X3 ) )
                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                              ( ( X1 = X2 )
                                                                                                                             => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                ( ( X1 = X2 )
                                                                                                                               => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                  = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                  ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                    = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                 => ( ( X3 = X4 )
                                                                                                                                   => ( X2 = X4 ) ) )
                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                    ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                      = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                   => ( X1 = X2 ) )
                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                      ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                        = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                     => ( X2 = X4 ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                        ( ( ( kpair @ X1 @ X2 )
                                                                                                                                          = ( kpair @ X3 @ X4 ) )
                                                                                                                                       => ( X2 = X4 ) )
                                                                                                                                   => ( ! [X1: $i] :
                                                                                                                                          ( ( iskpair @ X1 )
                                                                                                                                         => ~ ! [X2: $i] :
                                                                                                                                                ( ( in @ X2
                                                                                                                                                  @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                    @ ^ [X3: $i] :
                                                                                                                                                        ( X1
                                                                                                                                                        = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                               => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                    @ ^ [X3: $i] :
                                                                                                                                                        ( X1
                                                                                                                                                        = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                 != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                            ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                            = X2 )
                                                                                                                                       => ( sP8
                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                               => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                  ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                 => ( in @ X3 @ X1 ) )
                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                    ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                   => ( in @ X4 @ X2 ) )
                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                                         => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                            = X3 ) ) )
                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                                           => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                              = X4 ) ) )
                                                                                                                                                   => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                       => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                          = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h187,assumption,
    ! [X1: $i,X2: $i,X3: $i] :
      ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
     => ( in @ X3 @ X1 ) ),
    introduced(assumption,[]) ).

thf(h188,assumption,
    ~ ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
     => ( ! [X1: $i,X2: $i] :
            ( ( subset @ X1 @ X2 )
           => ( ( binintersect @ X1 @ X2 )
              = X1 ) )
       => ( ! [X1: $i,X2: $i] :
              ( ( ( binintersect @ X1 @ X2 )
                = X2 )
             => ( subset @ X2 @ X1 ) )
         => ( ! [X1: $i,X2: $i,X3: $i] :
                ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
               => ( in @ X3 @ X2 ) )
           => ( ! [X1: $i,X2: $i] :
                  ( ! [X3: $i] :
                      ( ( in @ X3 @ X1 )
                     => ~ ( in @ X3 @ X2 ) )
                 => ( ( binintersect @ X1 @ X2 )
                    = emptyset ) )
             => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
               => ( ! [X1: $i,X2: $i] :
                      ( ( subset @ X2 @ X1 )
                     => ( ( binintersect @ X1 @ X2 )
                        = X2 ) )
                 => ( ! [X1: $i,X2: $i] :
                        ( ( ( binintersect @ X1 @ X2 )
                          = X1 )
                       => ( subset @ X1 @ X2 ) )
                   => ( ! [X1: $i,X2: $i,X3: $i] :
                          ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                          = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                     => ( ! [X1: $i,X2: $i,X3: $i] :
                            ( ( in @ X3 @ X1 )
                           => ( ~ ( in @ X3 @ X2 )
                             => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                       => ( ! [X1: $i,X2: $i,X3: $i] :
                              ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                             => ( in @ X3 @ X1 ) )
                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                               => ~ ( in @ X3 @ X2 ) )
                           => ( ! [X1: $i,X2: $i] :
                                  ( ( subset @ X1 @ X2 )
                                 => ( ( setminus @ X1 @ X2 )
                                    = emptyset ) )
                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                    ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                   => ( ( in @ X3 @ X1 )
                                     => ( in @ X3 @ X2 ) ) )
                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                      ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                     => ( ~ ( in @ X3 @ X2 )
                                       => ~ ( in @ X3 @ X1 ) ) )
                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                        ( ~ ( in @ X3 @ X1 )
                                       => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                          ( ( in @ X3 @ X2 )
                                         => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                     => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                       => ( ! [X1: $i,X2: $i] :
                                              ( ( ( setminus @ X1 @ X2 )
                                                = emptyset )
                                             => ( subset @ X1 @ X2 ) )
                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                               => ! [X4: $o] :
                                                    ( ( ( in @ X3 @ X1 )
                                                     => ( ~ ( in @ X3 @ X2 )
                                                       => X4 ) )
                                                   => ( ( ~ ( in @ X3 @ X1 )
                                                       => ( ( in @ X3 @ X2 )
                                                         => X4 ) )
                                                     => X4 ) ) )
                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                  ( ( in @ X3 @ X1 )
                                                 => ( ~ ( in @ X3 @ X2 )
                                                   => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                    ( ~ ( in @ X3 @ X1 )
                                                   => ( ( in @ X3 @ X2 )
                                                     => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                      ( ( in @ X3 @ X1 )
                                                     => ( ( in @ X3 @ X2 )
                                                       => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                        ( ~ ( in @ X3 @ X1 )
                                                       => ( ~ ( in @ X3 @ X2 )
                                                         => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                   => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                     => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                       => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                         => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                           => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                             => ( ! [X1: $i,X2: $i] :
                                                                    ( ( in @ X2 @ X1 )
                                                                   => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                               => ( ! [X1: $i,X2: $i] :
                                                                      ( ( in @ X2 @ X1 )
                                                                     => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                        ( ( in @ X3 @ X1 )
                                                                       => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                          ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                         => ( ( X3 != X1 )
                                                                           => ( X3 = X2 ) ) )
                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                            ( ( in @ X3 @ X1 )
                                                                           => ! [X4: $i] :
                                                                                ( ( in @ X4 @ X2 )
                                                                               => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                              ( ( in @ X3 @ X1 )
                                                                             => ! [X4: $i] :
                                                                                  ( ( in @ X4 @ X2 )
                                                                                 => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                ( ( in @ X3 @ X1 )
                                                                               => ! [X4: $i] :
                                                                                    ( ( in @ X4 @ X2 )
                                                                                   => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                  ( ( in @ X3 @ X1 )
                                                                                 => ! [X4: $i] :
                                                                                      ( ( in @ X4 @ X2 )
                                                                                     => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                    ( ( in @ X3 @ X1 )
                                                                                   => ! [X4: $i] :
                                                                                        ( ( in @ X4 @ X2 )
                                                                                       => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                      ( ( in @ X3 @ X1 )
                                                                                     => ! [X4: $i] :
                                                                                          ( ( in @ X4 @ X2 )
                                                                                         => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                       => ~ ! [X4: $i] :
                                                                                              ( ( in @ X4 @ X1 )
                                                                                             => ! [X5: $i] :
                                                                                                  ( ( in @ X5 @ X2 )
                                                                                                 => ( X3
                                                                                                   != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                   => ( sP5
                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                            ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                           => ~ ! [X3: $i] :
                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                 => ~ ( in @ X2 @ X3 ) ) )
                                                                                       => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                         => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                           => ( ! [X1: $i] :
                                                                                                  ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                  = X1 )
                                                                                             => ( ! [X1: $i,X2: $i > $o] :
                                                                                                    ( ! [X3: $i] :
                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                       => ! [X4: $i] :
                                                                                                            ( ( in @ X4 @ X1 )
                                                                                                           => ( ( X2 @ X3 )
                                                                                                             => ( ( X2 @ X4 )
                                                                                                               => ( X3 = X4 ) ) ) ) )
                                                                                                   => ( ~ ! [X3: $i] :
                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                           => ~ ( X2 @ X3 ) )
                                                                                                     => ~ ! [X3: $i] :
                                                                                                            ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                           => ( ( dsetconstr @ X1 @ X2 )
                                                                                                             != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                               => ( ! [X1: $i,X2: $i > $o] :
                                                                                                      ( ~ ! [X3: $i] :
                                                                                                            ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                           => ( ( dsetconstr @ X1 @ X2 )
                                                                                                             != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                     => ~ ! [X3: $i] :
                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                           => ~ ( X2 @ X3 ) ) )
                                                                                                 => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                       => ( ( X2 @ X3 )
                                                                                                         => ( ! [X4: $i] :
                                                                                                                ( ( in @ X4 @ X1 )
                                                                                                               => ( ( X2 @ X4 )
                                                                                                                 => ( X4 = X3 ) ) )
                                                                                                           => ~ ! [X4: $i] :
                                                                                                                  ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                 => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                   != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                                                                          ( ! [X3: $i] :
                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                             => ! [X4: $i] :
                                                                                                                  ( ( in @ X4 @ X1 )
                                                                                                                 => ( ( X2 @ X3 )
                                                                                                                   => ( ( X2 @ X4 )
                                                                                                                     => ( X3 = X4 ) ) ) ) )
                                                                                                         => ( ~ ! [X3: $i] :
                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                 => ~ ( X2 @ X3 ) )
                                                                                                           => ~ ! [X3: $i] :
                                                                                                                  ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                 => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                   != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                            ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                              = ( setadjoin @ X2 @ emptyset ) )
                                                                                                           => ( X1 = X2 ) )
                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                              ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                             => ( X1 = X3 ) )
                                                                                                         => ( ! [X1: $i] :
                                                                                                                ( ( iskpair @ X1 )
                                                                                                               => ~ ! [X2: $i] :
                                                                                                                      ( ( in @ X2
                                                                                                                        @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                          @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                     => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                          @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                       != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                           => ( ! [X1: $i] :
                                                                                                                  ( ~ ! [X2: $i] :
                                                                                                                        ( ( in @ X2 @ X1 )
                                                                                                                       => ( X1
                                                                                                                         != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                 => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                    ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                    = X1 )
                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                      ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                     => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                        ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                          = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                       => ( X1 = X3 ) )
                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                          ( ( ( kpair @ X1 @ X2 )
                                                                                                                            = ( kpair @ X3 @ X4 ) )
                                                                                                                         => ( X1 = X3 ) )
                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                            ( ( X1 = X2 )
                                                                                                                           => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                              = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                              ( ( X1 = X2 )
                                                                                                                             => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                  = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                               => ( ( X3 = X4 )
                                                                                                                                 => ( X2 = X4 ) ) )
                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                  ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                    = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                 => ( X1 = X2 ) )
                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                    ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                      = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                   => ( X2 = X4 ) )
                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                      ( ( ( kpair @ X1 @ X2 )
                                                                                                                                        = ( kpair @ X3 @ X4 ) )
                                                                                                                                     => ( X2 = X4 ) )
                                                                                                                                 => ( ! [X1: $i] :
                                                                                                                                        ( ( iskpair @ X1 )
                                                                                                                                       => ~ ! [X2: $i] :
                                                                                                                                              ( ( in @ X2
                                                                                                                                                @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                  @ ^ [X3: $i] :
                                                                                                                                                      ( X1
                                                                                                                                                      = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                             => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                  @ ^ [X3: $i] :
                                                                                                                                                      ( X1
                                                                                                                                                      = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                               != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                          ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                          = X2 )
                                                                                                                                     => ( sP8
                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                              ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                             => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                               => ( in @ X3 @ X1 ) )
                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                  ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                 => ( in @ X4 @ X2 ) )
                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                                       => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                          = X3 ) ) )
                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                                         => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                            = X4 ) ) )
                                                                                                                                                 => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                      ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                     => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                        = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h189,assumption,
    ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 ),
    introduced(assumption,[]) ).

thf(h190,assumption,
    ~ ( ! [X1: $i,X2: $i] :
          ( ( subset @ X1 @ X2 )
         => ( ( binintersect @ X1 @ X2 )
            = X1 ) )
     => ( ! [X1: $i,X2: $i] :
            ( ( ( binintersect @ X1 @ X2 )
              = X2 )
           => ( subset @ X2 @ X1 ) )
       => ( ! [X1: $i,X2: $i,X3: $i] :
              ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
             => ( in @ X3 @ X2 ) )
         => ( ! [X1: $i,X2: $i] :
                ( ! [X3: $i] :
                    ( ( in @ X3 @ X1 )
                   => ~ ( in @ X3 @ X2 ) )
               => ( ( binintersect @ X1 @ X2 )
                  = emptyset ) )
           => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
             => ( ! [X1: $i,X2: $i] :
                    ( ( subset @ X2 @ X1 )
                   => ( ( binintersect @ X1 @ X2 )
                      = X2 ) )
               => ( ! [X1: $i,X2: $i] :
                      ( ( ( binintersect @ X1 @ X2 )
                        = X1 )
                     => ( subset @ X1 @ X2 ) )
                 => ( ! [X1: $i,X2: $i,X3: $i] :
                        ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                        = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                   => ( ! [X1: $i,X2: $i,X3: $i] :
                          ( ( in @ X3 @ X1 )
                         => ( ~ ( in @ X3 @ X2 )
                           => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                     => ( ! [X1: $i,X2: $i,X3: $i] :
                            ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                           => ( in @ X3 @ X1 ) )
                       => ( ! [X1: $i,X2: $i,X3: $i] :
                              ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                             => ~ ( in @ X3 @ X2 ) )
                         => ( ! [X1: $i,X2: $i] :
                                ( ( subset @ X1 @ X2 )
                               => ( ( setminus @ X1 @ X2 )
                                  = emptyset ) )
                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                  ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                 => ( ( in @ X3 @ X1 )
                                   => ( in @ X3 @ X2 ) ) )
                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                    ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                   => ( ~ ( in @ X3 @ X2 )
                                     => ~ ( in @ X3 @ X1 ) ) )
                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                      ( ~ ( in @ X3 @ X1 )
                                     => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                        ( ( in @ X3 @ X2 )
                                       => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                   => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                     => ( ! [X1: $i,X2: $i] :
                                            ( ( ( setminus @ X1 @ X2 )
                                              = emptyset )
                                           => ( subset @ X1 @ X2 ) )
                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                              ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                             => ! [X4: $o] :
                                                  ( ( ( in @ X3 @ X1 )
                                                   => ( ~ ( in @ X3 @ X2 )
                                                     => X4 ) )
                                                 => ( ( ~ ( in @ X3 @ X1 )
                                                     => ( ( in @ X3 @ X2 )
                                                       => X4 ) )
                                                   => X4 ) ) )
                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                ( ( in @ X3 @ X1 )
                                               => ( ~ ( in @ X3 @ X2 )
                                                 => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                  ( ~ ( in @ X3 @ X1 )
                                                 => ( ( in @ X3 @ X2 )
                                                   => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                    ( ( in @ X3 @ X1 )
                                                   => ( ( in @ X3 @ X2 )
                                                     => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                      ( ~ ( in @ X3 @ X1 )
                                                     => ( ~ ( in @ X3 @ X2 )
                                                       => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                 => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                   => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                     => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                       => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                         => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                           => ( ! [X1: $i,X2: $i] :
                                                                  ( ( in @ X2 @ X1 )
                                                                 => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                             => ( ! [X1: $i,X2: $i] :
                                                                    ( ( in @ X2 @ X1 )
                                                                   => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                      ( ( in @ X3 @ X1 )
                                                                     => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                        ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                       => ( ( X3 != X1 )
                                                                         => ( X3 = X2 ) ) )
                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                          ( ( in @ X3 @ X1 )
                                                                         => ! [X4: $i] :
                                                                              ( ( in @ X4 @ X2 )
                                                                             => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                            ( ( in @ X3 @ X1 )
                                                                           => ! [X4: $i] :
                                                                                ( ( in @ X4 @ X2 )
                                                                               => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                              ( ( in @ X3 @ X1 )
                                                                             => ! [X4: $i] :
                                                                                  ( ( in @ X4 @ X2 )
                                                                                 => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                ( ( in @ X3 @ X1 )
                                                                               => ! [X4: $i] :
                                                                                    ( ( in @ X4 @ X2 )
                                                                                   => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                  ( ( in @ X3 @ X1 )
                                                                                 => ! [X4: $i] :
                                                                                      ( ( in @ X4 @ X2 )
                                                                                     => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                    ( ( in @ X3 @ X1 )
                                                                                   => ! [X4: $i] :
                                                                                        ( ( in @ X4 @ X2 )
                                                                                       => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                      ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                     => ~ ! [X4: $i] :
                                                                                            ( ( in @ X4 @ X1 )
                                                                                           => ! [X5: $i] :
                                                                                                ( ( in @ X5 @ X2 )
                                                                                               => ( X3
                                                                                                 != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                 => ( sP5
                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                          ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                         => ~ ! [X3: $i] :
                                                                                                ( ( in @ X3 @ X1 )
                                                                                               => ~ ( in @ X2 @ X3 ) ) )
                                                                                     => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                       => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                         => ( ! [X1: $i] :
                                                                                                ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                = X1 )
                                                                                           => ( ! [X1: $i,X2: $i > $o] :
                                                                                                  ( ! [X3: $i] :
                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                     => ! [X4: $i] :
                                                                                                          ( ( in @ X4 @ X1 )
                                                                                                         => ( ( X2 @ X3 )
                                                                                                           => ( ( X2 @ X4 )
                                                                                                             => ( X3 = X4 ) ) ) ) )
                                                                                                 => ( ~ ! [X3: $i] :
                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                         => ~ ( X2 @ X3 ) )
                                                                                                   => ~ ! [X3: $i] :
                                                                                                          ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                         => ( ( dsetconstr @ X1 @ X2 )
                                                                                                           != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                             => ( ! [X1: $i,X2: $i > $o] :
                                                                                                    ( ~ ! [X3: $i] :
                                                                                                          ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                         => ( ( dsetconstr @ X1 @ X2 )
                                                                                                           != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                   => ~ ! [X3: $i] :
                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                         => ~ ( X2 @ X3 ) ) )
                                                                                               => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                     => ( ( X2 @ X3 )
                                                                                                       => ( ! [X4: $i] :
                                                                                                              ( ( in @ X4 @ X1 )
                                                                                                             => ( ( X2 @ X4 )
                                                                                                               => ( X4 = X3 ) ) )
                                                                                                         => ~ ! [X4: $i] :
                                                                                                                ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                               => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                 != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                                                                        ( ! [X3: $i] :
                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                           => ! [X4: $i] :
                                                                                                                ( ( in @ X4 @ X1 )
                                                                                                               => ( ( X2 @ X3 )
                                                                                                                 => ( ( X2 @ X4 )
                                                                                                                   => ( X3 = X4 ) ) ) ) )
                                                                                                       => ( ~ ! [X3: $i] :
                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                               => ~ ( X2 @ X3 ) )
                                                                                                         => ~ ! [X3: $i] :
                                                                                                                ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                               => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                 != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                          ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                            = ( setadjoin @ X2 @ emptyset ) )
                                                                                                         => ( X1 = X2 ) )
                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                            ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                           => ( X1 = X3 ) )
                                                                                                       => ( ! [X1: $i] :
                                                                                                              ( ( iskpair @ X1 )
                                                                                                             => ~ ! [X2: $i] :
                                                                                                                    ( ( in @ X2
                                                                                                                      @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                        @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                   => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                        @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                     != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                         => ( ! [X1: $i] :
                                                                                                                ( ~ ! [X2: $i] :
                                                                                                                      ( ( in @ X2 @ X1 )
                                                                                                                     => ( X1
                                                                                                                       != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                               => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                  ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                  = X1 )
                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                    ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                   => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                      ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                        = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                     => ( X1 = X3 ) )
                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                        ( ( ( kpair @ X1 @ X2 )
                                                                                                                          = ( kpair @ X3 @ X4 ) )
                                                                                                                       => ( X1 = X3 ) )
                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                          ( ( X1 = X2 )
                                                                                                                         => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                            = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                            ( ( X1 = X2 )
                                                                                                                           => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                              = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                              ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                             => ( ( X3 = X4 )
                                                                                                                               => ( X2 = X4 ) ) )
                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                  = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                               => ( X1 = X2 ) )
                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                  ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                    = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                 => ( X2 = X4 ) )
                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                    ( ( ( kpair @ X1 @ X2 )
                                                                                                                                      = ( kpair @ X3 @ X4 ) )
                                                                                                                                   => ( X2 = X4 ) )
                                                                                                                               => ( ! [X1: $i] :
                                                                                                                                      ( ( iskpair @ X1 )
                                                                                                                                     => ~ ! [X2: $i] :
                                                                                                                                            ( ( in @ X2
                                                                                                                                              @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                @ ^ [X3: $i] :
                                                                                                                                                    ( X1
                                                                                                                                                    = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                           => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                @ ^ [X3: $i] :
                                                                                                                                                    ( X1
                                                                                                                                                    = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                             != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                        ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                        = X2 )
                                                                                                                                   => ( sP8
                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                            ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                           => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                              ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                             => ( in @ X3 @ X1 ) )
                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                               => ( in @ X4 @ X2 ) )
                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                                     => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                        = X3 ) ) )
                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                                       => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                          = X4 ) ) )
                                                                                                                                               => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                    ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                   => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                      = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h191,assumption,
    ! [X1: $i,X2: $i] :
      ( ( subset @ X1 @ X2 )
     => ( ( binintersect @ X1 @ X2 )
        = X1 ) ),
    introduced(assumption,[]) ).

thf(h192,assumption,
    ~ ( ! [X1: $i,X2: $i] :
          ( ( ( binintersect @ X1 @ X2 )
            = X2 )
         => ( subset @ X2 @ X1 ) )
     => ( ! [X1: $i,X2: $i,X3: $i] :
            ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
           => ( in @ X3 @ X2 ) )
       => ( ! [X1: $i,X2: $i] :
              ( ! [X3: $i] :
                  ( ( in @ X3 @ X1 )
                 => ~ ( in @ X3 @ X2 ) )
             => ( ( binintersect @ X1 @ X2 )
                = emptyset ) )
         => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
           => ( ! [X1: $i,X2: $i] :
                  ( ( subset @ X2 @ X1 )
                 => ( ( binintersect @ X1 @ X2 )
                    = X2 ) )
             => ( ! [X1: $i,X2: $i] :
                    ( ( ( binintersect @ X1 @ X2 )
                      = X1 )
                   => ( subset @ X1 @ X2 ) )
               => ( ! [X1: $i,X2: $i,X3: $i] :
                      ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                      = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                 => ( ! [X1: $i,X2: $i,X3: $i] :
                        ( ( in @ X3 @ X1 )
                       => ( ~ ( in @ X3 @ X2 )
                         => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                   => ( ! [X1: $i,X2: $i,X3: $i] :
                          ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                         => ( in @ X3 @ X1 ) )
                     => ( ! [X1: $i,X2: $i,X3: $i] :
                            ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                           => ~ ( in @ X3 @ X2 ) )
                       => ( ! [X1: $i,X2: $i] :
                              ( ( subset @ X1 @ X2 )
                             => ( ( setminus @ X1 @ X2 )
                                = emptyset ) )
                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                               => ( ( in @ X3 @ X1 )
                                 => ( in @ X3 @ X2 ) ) )
                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                  ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                 => ( ~ ( in @ X3 @ X2 )
                                   => ~ ( in @ X3 @ X1 ) ) )
                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                    ( ~ ( in @ X3 @ X1 )
                                   => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                      ( ( in @ X3 @ X2 )
                                     => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                 => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                   => ( ! [X1: $i,X2: $i] :
                                          ( ( ( setminus @ X1 @ X2 )
                                            = emptyset )
                                         => ( subset @ X1 @ X2 ) )
                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                            ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                           => ! [X4: $o] :
                                                ( ( ( in @ X3 @ X1 )
                                                 => ( ~ ( in @ X3 @ X2 )
                                                   => X4 ) )
                                               => ( ( ~ ( in @ X3 @ X1 )
                                                   => ( ( in @ X3 @ X2 )
                                                     => X4 ) )
                                                 => X4 ) ) )
                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                              ( ( in @ X3 @ X1 )
                                             => ( ~ ( in @ X3 @ X2 )
                                               => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                ( ~ ( in @ X3 @ X1 )
                                               => ( ( in @ X3 @ X2 )
                                                 => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                  ( ( in @ X3 @ X1 )
                                                 => ( ( in @ X3 @ X2 )
                                                   => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                    ( ~ ( in @ X3 @ X1 )
                                                   => ( ~ ( in @ X3 @ X2 )
                                                     => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                               => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                 => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                   => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                     => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                       => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                         => ( ! [X1: $i,X2: $i] :
                                                                ( ( in @ X2 @ X1 )
                                                               => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                           => ( ! [X1: $i,X2: $i] :
                                                                  ( ( in @ X2 @ X1 )
                                                                 => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                    ( ( in @ X3 @ X1 )
                                                                   => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                      ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                     => ( ( X3 != X1 )
                                                                       => ( X3 = X2 ) ) )
                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                        ( ( in @ X3 @ X1 )
                                                                       => ! [X4: $i] :
                                                                            ( ( in @ X4 @ X2 )
                                                                           => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                          ( ( in @ X3 @ X1 )
                                                                         => ! [X4: $i] :
                                                                              ( ( in @ X4 @ X2 )
                                                                             => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                            ( ( in @ X3 @ X1 )
                                                                           => ! [X4: $i] :
                                                                                ( ( in @ X4 @ X2 )
                                                                               => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                              ( ( in @ X3 @ X1 )
                                                                             => ! [X4: $i] :
                                                                                  ( ( in @ X4 @ X2 )
                                                                                 => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                ( ( in @ X3 @ X1 )
                                                                               => ! [X4: $i] :
                                                                                    ( ( in @ X4 @ X2 )
                                                                                   => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                  ( ( in @ X3 @ X1 )
                                                                                 => ! [X4: $i] :
                                                                                      ( ( in @ X4 @ X2 )
                                                                                     => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                    ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                   => ~ ! [X4: $i] :
                                                                                          ( ( in @ X4 @ X1 )
                                                                                         => ! [X5: $i] :
                                                                                              ( ( in @ X5 @ X2 )
                                                                                             => ( X3
                                                                                               != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                               => ( sP5
                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                        ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                       => ~ ! [X3: $i] :
                                                                                              ( ( in @ X3 @ X1 )
                                                                                             => ~ ( in @ X2 @ X3 ) ) )
                                                                                   => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                     => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                       => ( ! [X1: $i] :
                                                                                              ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                              = X1 )
                                                                                         => ( ! [X1: $i,X2: $i > $o] :
                                                                                                ( ! [X3: $i] :
                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                   => ! [X4: $i] :
                                                                                                        ( ( in @ X4 @ X1 )
                                                                                                       => ( ( X2 @ X3 )
                                                                                                         => ( ( X2 @ X4 )
                                                                                                           => ( X3 = X4 ) ) ) ) )
                                                                                               => ( ~ ! [X3: $i] :
                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                       => ~ ( X2 @ X3 ) )
                                                                                                 => ~ ! [X3: $i] :
                                                                                                        ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                       => ( ( dsetconstr @ X1 @ X2 )
                                                                                                         != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                           => ( ! [X1: $i,X2: $i > $o] :
                                                                                                  ( ~ ! [X3: $i] :
                                                                                                        ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                       => ( ( dsetconstr @ X1 @ X2 )
                                                                                                         != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                 => ~ ! [X3: $i] :
                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                       => ~ ( X2 @ X3 ) ) )
                                                                                             => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                   => ( ( X2 @ X3 )
                                                                                                     => ( ! [X4: $i] :
                                                                                                            ( ( in @ X4 @ X1 )
                                                                                                           => ( ( X2 @ X4 )
                                                                                                             => ( X4 = X3 ) ) )
                                                                                                       => ~ ! [X4: $i] :
                                                                                                              ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                             => ( ( dsetconstr @ X1 @ X2 )
                                                                                                               != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                               => ( ! [X1: $i,X2: $i > $o] :
                                                                                                      ( ! [X3: $i] :
                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                         => ! [X4: $i] :
                                                                                                              ( ( in @ X4 @ X1 )
                                                                                                             => ( ( X2 @ X3 )
                                                                                                               => ( ( X2 @ X4 )
                                                                                                                 => ( X3 = X4 ) ) ) ) )
                                                                                                     => ( ~ ! [X3: $i] :
                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                             => ~ ( X2 @ X3 ) )
                                                                                                       => ~ ! [X3: $i] :
                                                                                                              ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                             => ( ( dsetconstr @ X1 @ X2 )
                                                                                                               != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                        ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                          = ( setadjoin @ X2 @ emptyset ) )
                                                                                                       => ( X1 = X2 ) )
                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                          ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                         => ( X1 = X3 ) )
                                                                                                     => ( ! [X1: $i] :
                                                                                                            ( ( iskpair @ X1 )
                                                                                                           => ~ ! [X2: $i] :
                                                                                                                  ( ( in @ X2
                                                                                                                    @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                      @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                 => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                      @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                   != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                       => ( ! [X1: $i] :
                                                                                                              ( ~ ! [X2: $i] :
                                                                                                                    ( ( in @ X2 @ X1 )
                                                                                                                   => ( X1
                                                                                                                     != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                             => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                = X1 )
                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                  ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                 => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                    ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                      = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                   => ( X1 = X3 ) )
                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                      ( ( ( kpair @ X1 @ X2 )
                                                                                                                        = ( kpair @ X3 @ X4 ) )
                                                                                                                     => ( X1 = X3 ) )
                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                        ( ( X1 = X2 )
                                                                                                                       => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                          = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                          ( ( X1 = X2 )
                                                                                                                         => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                            = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                            ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                              = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                           => ( ( X3 = X4 )
                                                                                                                             => ( X2 = X4 ) ) )
                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                              ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                             => ( X1 = X2 ) )
                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                  = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                               => ( X2 = X4 ) )
                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                  ( ( ( kpair @ X1 @ X2 )
                                                                                                                                    = ( kpair @ X3 @ X4 ) )
                                                                                                                                 => ( X2 = X4 ) )
                                                                                                                             => ( ! [X1: $i] :
                                                                                                                                    ( ( iskpair @ X1 )
                                                                                                                                   => ~ ! [X2: $i] :
                                                                                                                                          ( ( in @ X2
                                                                                                                                            @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                              @ ^ [X3: $i] :
                                                                                                                                                  ( X1
                                                                                                                                                  = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                         => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                              @ ^ [X3: $i] :
                                                                                                                                                  ( X1
                                                                                                                                                  = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                           != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                      ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                      = X2 )
                                                                                                                                 => ( sP8
                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                         => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                            ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                           => ( in @ X3 @ X1 ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                              ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                             => ( in @ X4 @ X2 ) )
                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                                   => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                      = X3 ) ) )
                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                                     => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                        = X4 ) ) )
                                                                                                                                             => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                  ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                 => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                    = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h193,assumption,
    ! [X1: $i,X2: $i] :
      ( ( ( binintersect @ X1 @ X2 )
        = X2 )
     => ( subset @ X2 @ X1 ) ),
    introduced(assumption,[]) ).

thf(h194,assumption,
    ~ ( ! [X1: $i,X2: $i,X3: $i] :
          ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
         => ( in @ X3 @ X2 ) )
     => ( ! [X1: $i,X2: $i] :
            ( ! [X3: $i] :
                ( ( in @ X3 @ X1 )
               => ~ ( in @ X3 @ X2 ) )
           => ( ( binintersect @ X1 @ X2 )
              = emptyset ) )
       => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
         => ( ! [X1: $i,X2: $i] :
                ( ( subset @ X2 @ X1 )
               => ( ( binintersect @ X1 @ X2 )
                  = X2 ) )
           => ( ! [X1: $i,X2: $i] :
                  ( ( ( binintersect @ X1 @ X2 )
                    = X1 )
                 => ( subset @ X1 @ X2 ) )
             => ( ! [X1: $i,X2: $i,X3: $i] :
                    ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                    = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
               => ( ! [X1: $i,X2: $i,X3: $i] :
                      ( ( in @ X3 @ X1 )
                     => ( ~ ( in @ X3 @ X2 )
                       => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                 => ( ! [X1: $i,X2: $i,X3: $i] :
                        ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                       => ( in @ X3 @ X1 ) )
                   => ( ! [X1: $i,X2: $i,X3: $i] :
                          ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                         => ~ ( in @ X3 @ X2 ) )
                     => ( ! [X1: $i,X2: $i] :
                            ( ( subset @ X1 @ X2 )
                           => ( ( setminus @ X1 @ X2 )
                              = emptyset ) )
                       => ( ! [X1: $i,X2: $i,X3: $i] :
                              ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                             => ( ( in @ X3 @ X1 )
                               => ( in @ X3 @ X2 ) ) )
                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                               => ( ~ ( in @ X3 @ X2 )
                                 => ~ ( in @ X3 @ X1 ) ) )
                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                  ( ~ ( in @ X3 @ X1 )
                                 => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                    ( ( in @ X3 @ X2 )
                                   => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                               => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                 => ( ! [X1: $i,X2: $i] :
                                        ( ( ( setminus @ X1 @ X2 )
                                          = emptyset )
                                       => ( subset @ X1 @ X2 ) )
                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                          ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                         => ! [X4: $o] :
                                              ( ( ( in @ X3 @ X1 )
                                               => ( ~ ( in @ X3 @ X2 )
                                                 => X4 ) )
                                             => ( ( ~ ( in @ X3 @ X1 )
                                                 => ( ( in @ X3 @ X2 )
                                                   => X4 ) )
                                               => X4 ) ) )
                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                            ( ( in @ X3 @ X1 )
                                           => ( ~ ( in @ X3 @ X2 )
                                             => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                              ( ~ ( in @ X3 @ X1 )
                                             => ( ( in @ X3 @ X2 )
                                               => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                ( ( in @ X3 @ X1 )
                                               => ( ( in @ X3 @ X2 )
                                                 => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                  ( ~ ( in @ X3 @ X1 )
                                                 => ( ~ ( in @ X3 @ X2 )
                                                   => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                             => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                               => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                 => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                   => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                     => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                       => ( ! [X1: $i,X2: $i] :
                                                              ( ( in @ X2 @ X1 )
                                                             => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                         => ( ! [X1: $i,X2: $i] :
                                                                ( ( in @ X2 @ X1 )
                                                               => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                  ( ( in @ X3 @ X1 )
                                                                 => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                    ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                   => ( ( X3 != X1 )
                                                                     => ( X3 = X2 ) ) )
                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                      ( ( in @ X3 @ X1 )
                                                                     => ! [X4: $i] :
                                                                          ( ( in @ X4 @ X2 )
                                                                         => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                        ( ( in @ X3 @ X1 )
                                                                       => ! [X4: $i] :
                                                                            ( ( in @ X4 @ X2 )
                                                                           => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                          ( ( in @ X3 @ X1 )
                                                                         => ! [X4: $i] :
                                                                              ( ( in @ X4 @ X2 )
                                                                             => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                            ( ( in @ X3 @ X1 )
                                                                           => ! [X4: $i] :
                                                                                ( ( in @ X4 @ X2 )
                                                                               => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                              ( ( in @ X3 @ X1 )
                                                                             => ! [X4: $i] :
                                                                                  ( ( in @ X4 @ X2 )
                                                                                 => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                ( ( in @ X3 @ X1 )
                                                                               => ! [X4: $i] :
                                                                                    ( ( in @ X4 @ X2 )
                                                                                   => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                  ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                 => ~ ! [X4: $i] :
                                                                                        ( ( in @ X4 @ X1 )
                                                                                       => ! [X5: $i] :
                                                                                            ( ( in @ X5 @ X2 )
                                                                                           => ( X3
                                                                                             != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                             => ( sP5
                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                      ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                     => ~ ! [X3: $i] :
                                                                                            ( ( in @ X3 @ X1 )
                                                                                           => ~ ( in @ X2 @ X3 ) ) )
                                                                                 => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                   => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                     => ( ! [X1: $i] :
                                                                                            ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                            = X1 )
                                                                                       => ( ! [X1: $i,X2: $i > $o] :
                                                                                              ( ! [X3: $i] :
                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                 => ! [X4: $i] :
                                                                                                      ( ( in @ X4 @ X1 )
                                                                                                     => ( ( X2 @ X3 )
                                                                                                       => ( ( X2 @ X4 )
                                                                                                         => ( X3 = X4 ) ) ) ) )
                                                                                             => ( ~ ! [X3: $i] :
                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                     => ~ ( X2 @ X3 ) )
                                                                                               => ~ ! [X3: $i] :
                                                                                                      ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                     => ( ( dsetconstr @ X1 @ X2 )
                                                                                                       != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                         => ( ! [X1: $i,X2: $i > $o] :
                                                                                                ( ~ ! [X3: $i] :
                                                                                                      ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                     => ( ( dsetconstr @ X1 @ X2 )
                                                                                                       != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                               => ~ ! [X3: $i] :
                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                     => ~ ( X2 @ X3 ) ) )
                                                                                           => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                 => ( ( X2 @ X3 )
                                                                                                   => ( ! [X4: $i] :
                                                                                                          ( ( in @ X4 @ X1 )
                                                                                                         => ( ( X2 @ X4 )
                                                                                                           => ( X4 = X3 ) ) )
                                                                                                     => ~ ! [X4: $i] :
                                                                                                            ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                           => ( ( dsetconstr @ X1 @ X2 )
                                                                                                             != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                             => ( ! [X1: $i,X2: $i > $o] :
                                                                                                    ( ! [X3: $i] :
                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                       => ! [X4: $i] :
                                                                                                            ( ( in @ X4 @ X1 )
                                                                                                           => ( ( X2 @ X3 )
                                                                                                             => ( ( X2 @ X4 )
                                                                                                               => ( X3 = X4 ) ) ) ) )
                                                                                                   => ( ~ ! [X3: $i] :
                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                           => ~ ( X2 @ X3 ) )
                                                                                                     => ~ ! [X3: $i] :
                                                                                                            ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                           => ( ( dsetconstr @ X1 @ X2 )
                                                                                                             != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                      ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                        = ( setadjoin @ X2 @ emptyset ) )
                                                                                                     => ( X1 = X2 ) )
                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                        ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                       => ( X1 = X3 ) )
                                                                                                   => ( ! [X1: $i] :
                                                                                                          ( ( iskpair @ X1 )
                                                                                                         => ~ ! [X2: $i] :
                                                                                                                ( ( in @ X2
                                                                                                                  @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                    @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                               => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                    @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                 != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                     => ( ! [X1: $i] :
                                                                                                            ( ~ ! [X2: $i] :
                                                                                                                  ( ( in @ X2 @ X1 )
                                                                                                                 => ( X1
                                                                                                                   != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                           => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                              ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                              = X1 )
                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                               => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                  ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                    = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                 => ( X1 = X3 ) )
                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                    ( ( ( kpair @ X1 @ X2 )
                                                                                                                      = ( kpair @ X3 @ X4 ) )
                                                                                                                   => ( X1 = X3 ) )
                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                      ( ( X1 = X2 )
                                                                                                                     => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                        = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                        ( ( X1 = X2 )
                                                                                                                       => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                          = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                          ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                            = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                         => ( ( X3 = X4 )
                                                                                                                           => ( X2 = X4 ) ) )
                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                            ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                              = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                           => ( X1 = X2 ) )
                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                              ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                             => ( X2 = X4 ) )
                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                ( ( ( kpair @ X1 @ X2 )
                                                                                                                                  = ( kpair @ X3 @ X4 ) )
                                                                                                                               => ( X2 = X4 ) )
                                                                                                                           => ( ! [X1: $i] :
                                                                                                                                  ( ( iskpair @ X1 )
                                                                                                                                 => ~ ! [X2: $i] :
                                                                                                                                        ( ( in @ X2
                                                                                                                                          @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                            @ ^ [X3: $i] :
                                                                                                                                                ( X1
                                                                                                                                                = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                       => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                            @ ^ [X3: $i] :
                                                                                                                                                ( X1
                                                                                                                                                = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                         != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                    ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                    = X2 )
                                                                                                                               => ( sP8
                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                       => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                          ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                         => ( in @ X3 @ X1 ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                            ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                           => ( in @ X4 @ X2 ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                                 => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                    = X3 ) ) )
                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                                   => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                      = X4 ) ) )
                                                                                                                                           => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                               => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                  = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h195,assumption,
    ! [X1: $i,X2: $i,X3: $i] :
      ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
     => ( in @ X3 @ X2 ) ),
    introduced(assumption,[]) ).

thf(h196,assumption,
    ~ ( ! [X1: $i,X2: $i] :
          ( ! [X3: $i] :
              ( ( in @ X3 @ X1 )
             => ~ ( in @ X3 @ X2 ) )
         => ( ( binintersect @ X1 @ X2 )
            = emptyset ) )
     => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
       => ( ! [X1: $i,X2: $i] :
              ( ( subset @ X2 @ X1 )
             => ( ( binintersect @ X1 @ X2 )
                = X2 ) )
         => ( ! [X1: $i,X2: $i] :
                ( ( ( binintersect @ X1 @ X2 )
                  = X1 )
               => ( subset @ X1 @ X2 ) )
           => ( ! [X1: $i,X2: $i,X3: $i] :
                  ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                  = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
             => ( ! [X1: $i,X2: $i,X3: $i] :
                    ( ( in @ X3 @ X1 )
                   => ( ~ ( in @ X3 @ X2 )
                     => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
               => ( ! [X1: $i,X2: $i,X3: $i] :
                      ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                     => ( in @ X3 @ X1 ) )
                 => ( ! [X1: $i,X2: $i,X3: $i] :
                        ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                       => ~ ( in @ X3 @ X2 ) )
                   => ( ! [X1: $i,X2: $i] :
                          ( ( subset @ X1 @ X2 )
                         => ( ( setminus @ X1 @ X2 )
                            = emptyset ) )
                     => ( ! [X1: $i,X2: $i,X3: $i] :
                            ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                           => ( ( in @ X3 @ X1 )
                             => ( in @ X3 @ X2 ) ) )
                       => ( ! [X1: $i,X2: $i,X3: $i] :
                              ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                             => ( ~ ( in @ X3 @ X2 )
                               => ~ ( in @ X3 @ X1 ) ) )
                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                ( ~ ( in @ X3 @ X1 )
                               => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                  ( ( in @ X3 @ X2 )
                                 => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                             => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                               => ( ! [X1: $i,X2: $i] :
                                      ( ( ( setminus @ X1 @ X2 )
                                        = emptyset )
                                     => ( subset @ X1 @ X2 ) )
                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                        ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                       => ! [X4: $o] :
                                            ( ( ( in @ X3 @ X1 )
                                             => ( ~ ( in @ X3 @ X2 )
                                               => X4 ) )
                                           => ( ( ~ ( in @ X3 @ X1 )
                                               => ( ( in @ X3 @ X2 )
                                                 => X4 ) )
                                             => X4 ) ) )
                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                          ( ( in @ X3 @ X1 )
                                         => ( ~ ( in @ X3 @ X2 )
                                           => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                            ( ~ ( in @ X3 @ X1 )
                                           => ( ( in @ X3 @ X2 )
                                             => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                              ( ( in @ X3 @ X1 )
                                             => ( ( in @ X3 @ X2 )
                                               => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                ( ~ ( in @ X3 @ X1 )
                                               => ( ~ ( in @ X3 @ X2 )
                                                 => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                           => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                             => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                               => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                 => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                   => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                     => ( ! [X1: $i,X2: $i] :
                                                            ( ( in @ X2 @ X1 )
                                                           => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                       => ( ! [X1: $i,X2: $i] :
                                                              ( ( in @ X2 @ X1 )
                                                             => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                ( ( in @ X3 @ X1 )
                                                               => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                  ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                 => ( ( X3 != X1 )
                                                                   => ( X3 = X2 ) ) )
                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                    ( ( in @ X3 @ X1 )
                                                                   => ! [X4: $i] :
                                                                        ( ( in @ X4 @ X2 )
                                                                       => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                      ( ( in @ X3 @ X1 )
                                                                     => ! [X4: $i] :
                                                                          ( ( in @ X4 @ X2 )
                                                                         => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                        ( ( in @ X3 @ X1 )
                                                                       => ! [X4: $i] :
                                                                            ( ( in @ X4 @ X2 )
                                                                           => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                          ( ( in @ X3 @ X1 )
                                                                         => ! [X4: $i] :
                                                                              ( ( in @ X4 @ X2 )
                                                                             => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                            ( ( in @ X3 @ X1 )
                                                                           => ! [X4: $i] :
                                                                                ( ( in @ X4 @ X2 )
                                                                               => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                              ( ( in @ X3 @ X1 )
                                                                             => ! [X4: $i] :
                                                                                  ( ( in @ X4 @ X2 )
                                                                                 => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                               => ~ ! [X4: $i] :
                                                                                      ( ( in @ X4 @ X1 )
                                                                                     => ! [X5: $i] :
                                                                                          ( ( in @ X5 @ X2 )
                                                                                         => ( X3
                                                                                           != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                           => ( sP5
                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                    ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                   => ~ ! [X3: $i] :
                                                                                          ( ( in @ X3 @ X1 )
                                                                                         => ~ ( in @ X2 @ X3 ) ) )
                                                                               => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                 => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                   => ( ! [X1: $i] :
                                                                                          ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                          = X1 )
                                                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                                                            ( ! [X3: $i] :
                                                                                                ( ( in @ X3 @ X1 )
                                                                                               => ! [X4: $i] :
                                                                                                    ( ( in @ X4 @ X1 )
                                                                                                   => ( ( X2 @ X3 )
                                                                                                     => ( ( X2 @ X4 )
                                                                                                       => ( X3 = X4 ) ) ) ) )
                                                                                           => ( ~ ! [X3: $i] :
                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                   => ~ ( X2 @ X3 ) )
                                                                                             => ~ ! [X3: $i] :
                                                                                                    ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                   => ( ( dsetconstr @ X1 @ X2 )
                                                                                                     != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                       => ( ! [X1: $i,X2: $i > $o] :
                                                                                              ( ~ ! [X3: $i] :
                                                                                                    ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                   => ( ( dsetconstr @ X1 @ X2 )
                                                                                                     != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                             => ~ ! [X3: $i] :
                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                   => ~ ( X2 @ X3 ) ) )
                                                                                         => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                ( ( in @ X3 @ X1 )
                                                                                               => ( ( X2 @ X3 )
                                                                                                 => ( ! [X4: $i] :
                                                                                                        ( ( in @ X4 @ X1 )
                                                                                                       => ( ( X2 @ X4 )
                                                                                                         => ( X4 = X3 ) ) )
                                                                                                   => ~ ! [X4: $i] :
                                                                                                          ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                         => ( ( dsetconstr @ X1 @ X2 )
                                                                                                           != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                           => ( ! [X1: $i,X2: $i > $o] :
                                                                                                  ( ! [X3: $i] :
                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                     => ! [X4: $i] :
                                                                                                          ( ( in @ X4 @ X1 )
                                                                                                         => ( ( X2 @ X3 )
                                                                                                           => ( ( X2 @ X4 )
                                                                                                             => ( X3 = X4 ) ) ) ) )
                                                                                                 => ( ~ ! [X3: $i] :
                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                         => ~ ( X2 @ X3 ) )
                                                                                                   => ~ ! [X3: $i] :
                                                                                                          ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                         => ( ( dsetconstr @ X1 @ X2 )
                                                                                                           != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                    ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                      = ( setadjoin @ X2 @ emptyset ) )
                                                                                                   => ( X1 = X2 ) )
                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                      ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                     => ( X1 = X3 ) )
                                                                                                 => ( ! [X1: $i] :
                                                                                                        ( ( iskpair @ X1 )
                                                                                                       => ~ ! [X2: $i] :
                                                                                                              ( ( in @ X2
                                                                                                                @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                  @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                             => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                  @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                               != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                   => ( ! [X1: $i] :
                                                                                                          ( ~ ! [X2: $i] :
                                                                                                                ( ( in @ X2 @ X1 )
                                                                                                               => ( X1
                                                                                                                 != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                         => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                            ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                            = X1 )
                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                              ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                             => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                  = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                               => ( X1 = X3 ) )
                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                  ( ( ( kpair @ X1 @ X2 )
                                                                                                                    = ( kpair @ X3 @ X4 ) )
                                                                                                                 => ( X1 = X3 ) )
                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                    ( ( X1 = X2 )
                                                                                                                   => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                      = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                      ( ( X1 = X2 )
                                                                                                                     => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                        = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                        ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                          = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                       => ( ( X3 = X4 )
                                                                                                                         => ( X2 = X4 ) ) )
                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                          ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                            = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                         => ( X1 = X2 ) )
                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                            ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                              = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                           => ( X2 = X4 ) )
                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                              ( ( ( kpair @ X1 @ X2 )
                                                                                                                                = ( kpair @ X3 @ X4 ) )
                                                                                                                             => ( X2 = X4 ) )
                                                                                                                         => ( ! [X1: $i] :
                                                                                                                                ( ( iskpair @ X1 )
                                                                                                                               => ~ ! [X2: $i] :
                                                                                                                                      ( ( in @ X2
                                                                                                                                        @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                          @ ^ [X3: $i] :
                                                                                                                                              ( X1
                                                                                                                                              = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                     => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                          @ ^ [X3: $i] :
                                                                                                                                              ( X1
                                                                                                                                              = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                       != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                  ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                  = X2 )
                                                                                                                             => ( sP8
                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                      ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                     => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                        ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                       => ( in @ X3 @ X1 ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                          ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                         => ( in @ X4 @ X2 ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                                               => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                  = X3 ) ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                                 => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                    = X4 ) ) )
                                                                                                                                         => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                              ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                             => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h197,assumption,
    ! [X1: $i,X2: $i] :
      ( ! [X3: $i] :
          ( ( in @ X3 @ X1 )
         => ~ ( in @ X3 @ X2 ) )
     => ( ( binintersect @ X1 @ X2 )
        = emptyset ) ),
    introduced(assumption,[]) ).

thf(h198,assumption,
    ~ ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
     => ( ! [X1: $i,X2: $i] :
            ( ( subset @ X2 @ X1 )
           => ( ( binintersect @ X1 @ X2 )
              = X2 ) )
       => ( ! [X1: $i,X2: $i] :
              ( ( ( binintersect @ X1 @ X2 )
                = X1 )
             => ( subset @ X1 @ X2 ) )
         => ( ! [X1: $i,X2: $i,X3: $i] :
                ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
           => ( ! [X1: $i,X2: $i,X3: $i] :
                  ( ( in @ X3 @ X1 )
                 => ( ~ ( in @ X3 @ X2 )
                   => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
             => ( ! [X1: $i,X2: $i,X3: $i] :
                    ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                   => ( in @ X3 @ X1 ) )
               => ( ! [X1: $i,X2: $i,X3: $i] :
                      ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                     => ~ ( in @ X3 @ X2 ) )
                 => ( ! [X1: $i,X2: $i] :
                        ( ( subset @ X1 @ X2 )
                       => ( ( setminus @ X1 @ X2 )
                          = emptyset ) )
                   => ( ! [X1: $i,X2: $i,X3: $i] :
                          ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                         => ( ( in @ X3 @ X1 )
                           => ( in @ X3 @ X2 ) ) )
                     => ( ! [X1: $i,X2: $i,X3: $i] :
                            ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                           => ( ~ ( in @ X3 @ X2 )
                             => ~ ( in @ X3 @ X1 ) ) )
                       => ( ! [X1: $i,X2: $i,X3: $i] :
                              ( ~ ( in @ X3 @ X1 )
                             => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                ( ( in @ X3 @ X2 )
                               => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                           => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                             => ( ! [X1: $i,X2: $i] :
                                    ( ( ( setminus @ X1 @ X2 )
                                      = emptyset )
                                   => ( subset @ X1 @ X2 ) )
                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                      ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                     => ! [X4: $o] :
                                          ( ( ( in @ X3 @ X1 )
                                           => ( ~ ( in @ X3 @ X2 )
                                             => X4 ) )
                                         => ( ( ~ ( in @ X3 @ X1 )
                                             => ( ( in @ X3 @ X2 )
                                               => X4 ) )
                                           => X4 ) ) )
                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                        ( ( in @ X3 @ X1 )
                                       => ( ~ ( in @ X3 @ X2 )
                                         => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                          ( ~ ( in @ X3 @ X1 )
                                         => ( ( in @ X3 @ X2 )
                                           => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                            ( ( in @ X3 @ X1 )
                                           => ( ( in @ X3 @ X2 )
                                             => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                              ( ~ ( in @ X3 @ X1 )
                                             => ( ~ ( in @ X3 @ X2 )
                                               => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                         => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                           => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                             => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                               => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                 => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                   => ( ! [X1: $i,X2: $i] :
                                                          ( ( in @ X2 @ X1 )
                                                         => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                     => ( ! [X1: $i,X2: $i] :
                                                            ( ( in @ X2 @ X1 )
                                                           => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                              ( ( in @ X3 @ X1 )
                                                             => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                               => ( ( X3 != X1 )
                                                                 => ( X3 = X2 ) ) )
                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                  ( ( in @ X3 @ X1 )
                                                                 => ! [X4: $i] :
                                                                      ( ( in @ X4 @ X2 )
                                                                     => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                    ( ( in @ X3 @ X1 )
                                                                   => ! [X4: $i] :
                                                                        ( ( in @ X4 @ X2 )
                                                                       => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                      ( ( in @ X3 @ X1 )
                                                                     => ! [X4: $i] :
                                                                          ( ( in @ X4 @ X2 )
                                                                         => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                        ( ( in @ X3 @ X1 )
                                                                       => ! [X4: $i] :
                                                                            ( ( in @ X4 @ X2 )
                                                                           => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                          ( ( in @ X3 @ X1 )
                                                                         => ! [X4: $i] :
                                                                              ( ( in @ X4 @ X2 )
                                                                             => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                            ( ( in @ X3 @ X1 )
                                                                           => ! [X4: $i] :
                                                                                ( ( in @ X4 @ X2 )
                                                                               => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                              ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                             => ~ ! [X4: $i] :
                                                                                    ( ( in @ X4 @ X1 )
                                                                                   => ! [X5: $i] :
                                                                                        ( ( in @ X5 @ X2 )
                                                                                       => ( X3
                                                                                         != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                         => ( sP5
                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                  ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                 => ~ ! [X3: $i] :
                                                                                        ( ( in @ X3 @ X1 )
                                                                                       => ~ ( in @ X2 @ X3 ) ) )
                                                                             => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                               => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                 => ( ! [X1: $i] :
                                                                                        ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                        = X1 )
                                                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                                                          ( ! [X3: $i] :
                                                                                              ( ( in @ X3 @ X1 )
                                                                                             => ! [X4: $i] :
                                                                                                  ( ( in @ X4 @ X1 )
                                                                                                 => ( ( X2 @ X3 )
                                                                                                   => ( ( X2 @ X4 )
                                                                                                     => ( X3 = X4 ) ) ) ) )
                                                                                         => ( ~ ! [X3: $i] :
                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                 => ~ ( X2 @ X3 ) )
                                                                                           => ~ ! [X3: $i] :
                                                                                                  ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                 => ( ( dsetconstr @ X1 @ X2 )
                                                                                                   != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                                                            ( ~ ! [X3: $i] :
                                                                                                  ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                 => ( ( dsetconstr @ X1 @ X2 )
                                                                                                   != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                           => ~ ! [X3: $i] :
                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                 => ~ ( X2 @ X3 ) ) )
                                                                                       => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                              ( ( in @ X3 @ X1 )
                                                                                             => ( ( X2 @ X3 )
                                                                                               => ( ! [X4: $i] :
                                                                                                      ( ( in @ X4 @ X1 )
                                                                                                     => ( ( X2 @ X4 )
                                                                                                       => ( X4 = X3 ) ) )
                                                                                                 => ~ ! [X4: $i] :
                                                                                                        ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                       => ( ( dsetconstr @ X1 @ X2 )
                                                                                                         != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                         => ( ! [X1: $i,X2: $i > $o] :
                                                                                                ( ! [X3: $i] :
                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                   => ! [X4: $i] :
                                                                                                        ( ( in @ X4 @ X1 )
                                                                                                       => ( ( X2 @ X3 )
                                                                                                         => ( ( X2 @ X4 )
                                                                                                           => ( X3 = X4 ) ) ) ) )
                                                                                               => ( ~ ! [X3: $i] :
                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                       => ~ ( X2 @ X3 ) )
                                                                                                 => ~ ! [X3: $i] :
                                                                                                        ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                       => ( ( dsetconstr @ X1 @ X2 )
                                                                                                         != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                  ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                    = ( setadjoin @ X2 @ emptyset ) )
                                                                                                 => ( X1 = X2 ) )
                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                    ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                   => ( X1 = X3 ) )
                                                                                               => ( ! [X1: $i] :
                                                                                                      ( ( iskpair @ X1 )
                                                                                                     => ~ ! [X2: $i] :
                                                                                                            ( ( in @ X2
                                                                                                              @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                           => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                             != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                 => ( ! [X1: $i] :
                                                                                                        ( ~ ! [X2: $i] :
                                                                                                              ( ( in @ X2 @ X1 )
                                                                                                             => ( X1
                                                                                                               != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                       => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                          ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                          = X1 )
                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                            ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                           => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                              ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                             => ( X1 = X3 ) )
                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                ( ( ( kpair @ X1 @ X2 )
                                                                                                                  = ( kpair @ X3 @ X4 ) )
                                                                                                               => ( X1 = X3 ) )
                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                  ( ( X1 = X2 )
                                                                                                                 => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                    = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                    ( ( X1 = X2 )
                                                                                                                   => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                      = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                      ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                        = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                     => ( ( X3 = X4 )
                                                                                                                       => ( X2 = X4 ) ) )
                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                        ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                          = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                       => ( X1 = X2 ) )
                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                          ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                            = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                         => ( X2 = X4 ) )
                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                            ( ( ( kpair @ X1 @ X2 )
                                                                                                                              = ( kpair @ X3 @ X4 ) )
                                                                                                                           => ( X2 = X4 ) )
                                                                                                                       => ( ! [X1: $i] :
                                                                                                                              ( ( iskpair @ X1 )
                                                                                                                             => ~ ! [X2: $i] :
                                                                                                                                    ( ( in @ X2
                                                                                                                                      @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                        @ ^ [X3: $i] :
                                                                                                                                            ( X1
                                                                                                                                            = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                   => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                        @ ^ [X3: $i] :
                                                                                                                                            ( X1
                                                                                                                                            = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                     != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                = X2 )
                                                                                                                           => ( sP8
                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                    ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                   => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                      ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                     => ( in @ X3 @ X1 ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                        ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                       => ( in @ X4 @ X2 ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                         => ! [X4: $i] :
                                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                                             => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                = X3 ) ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                           => ! [X4: $i] :
                                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                                               => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                  = X4 ) ) )
                                                                                                                                       => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                            ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                           => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                              = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h199,assumption,
    ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 ),
    introduced(assumption,[]) ).

thf(h200,assumption,
    ~ ( ! [X1: $i,X2: $i] :
          ( ( subset @ X2 @ X1 )
         => ( ( binintersect @ X1 @ X2 )
            = X2 ) )
     => ( ! [X1: $i,X2: $i] :
            ( ( ( binintersect @ X1 @ X2 )
              = X1 )
           => ( subset @ X1 @ X2 ) )
       => ( ! [X1: $i,X2: $i,X3: $i] :
              ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
              = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
         => ( ! [X1: $i,X2: $i,X3: $i] :
                ( ( in @ X3 @ X1 )
               => ( ~ ( in @ X3 @ X2 )
                 => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
           => ( ! [X1: $i,X2: $i,X3: $i] :
                  ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                 => ( in @ X3 @ X1 ) )
             => ( ! [X1: $i,X2: $i,X3: $i] :
                    ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                   => ~ ( in @ X3 @ X2 ) )
               => ( ! [X1: $i,X2: $i] :
                      ( ( subset @ X1 @ X2 )
                     => ( ( setminus @ X1 @ X2 )
                        = emptyset ) )
                 => ( ! [X1: $i,X2: $i,X3: $i] :
                        ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                       => ( ( in @ X3 @ X1 )
                         => ( in @ X3 @ X2 ) ) )
                   => ( ! [X1: $i,X2: $i,X3: $i] :
                          ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                         => ( ~ ( in @ X3 @ X2 )
                           => ~ ( in @ X3 @ X1 ) ) )
                     => ( ! [X1: $i,X2: $i,X3: $i] :
                            ( ~ ( in @ X3 @ X1 )
                           => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                       => ( ! [X1: $i,X2: $i,X3: $i] :
                              ( ( in @ X3 @ X2 )
                             => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                         => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                           => ( ! [X1: $i,X2: $i] :
                                  ( ( ( setminus @ X1 @ X2 )
                                    = emptyset )
                                 => ( subset @ X1 @ X2 ) )
                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                    ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                   => ! [X4: $o] :
                                        ( ( ( in @ X3 @ X1 )
                                         => ( ~ ( in @ X3 @ X2 )
                                           => X4 ) )
                                       => ( ( ~ ( in @ X3 @ X1 )
                                           => ( ( in @ X3 @ X2 )
                                             => X4 ) )
                                         => X4 ) ) )
                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                      ( ( in @ X3 @ X1 )
                                     => ( ~ ( in @ X3 @ X2 )
                                       => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                        ( ~ ( in @ X3 @ X1 )
                                       => ( ( in @ X3 @ X2 )
                                         => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                          ( ( in @ X3 @ X1 )
                                         => ( ( in @ X3 @ X2 )
                                           => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                            ( ~ ( in @ X3 @ X1 )
                                           => ( ~ ( in @ X3 @ X2 )
                                             => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                       => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                         => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                           => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                             => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                               => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                 => ( ! [X1: $i,X2: $i] :
                                                        ( ( in @ X2 @ X1 )
                                                       => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                   => ( ! [X1: $i,X2: $i] :
                                                          ( ( in @ X2 @ X1 )
                                                         => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                            ( ( in @ X3 @ X1 )
                                                           => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                              ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                             => ( ( X3 != X1 )
                                                               => ( X3 = X2 ) ) )
                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                ( ( in @ X3 @ X1 )
                                                               => ! [X4: $i] :
                                                                    ( ( in @ X4 @ X2 )
                                                                   => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                  ( ( in @ X3 @ X1 )
                                                                 => ! [X4: $i] :
                                                                      ( ( in @ X4 @ X2 )
                                                                     => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                    ( ( in @ X3 @ X1 )
                                                                   => ! [X4: $i] :
                                                                        ( ( in @ X4 @ X2 )
                                                                       => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                      ( ( in @ X3 @ X1 )
                                                                     => ! [X4: $i] :
                                                                          ( ( in @ X4 @ X2 )
                                                                         => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                        ( ( in @ X3 @ X1 )
                                                                       => ! [X4: $i] :
                                                                            ( ( in @ X4 @ X2 )
                                                                           => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                          ( ( in @ X3 @ X1 )
                                                                         => ! [X4: $i] :
                                                                              ( ( in @ X4 @ X2 )
                                                                             => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                            ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                           => ~ ! [X4: $i] :
                                                                                  ( ( in @ X4 @ X1 )
                                                                                 => ! [X5: $i] :
                                                                                      ( ( in @ X5 @ X2 )
                                                                                     => ( X3
                                                                                       != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                       => ( sP5
                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                               => ~ ! [X3: $i] :
                                                                                      ( ( in @ X3 @ X1 )
                                                                                     => ~ ( in @ X2 @ X3 ) ) )
                                                                           => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                             => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                               => ( ! [X1: $i] :
                                                                                      ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                      = X1 )
                                                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                                                        ( ! [X3: $i] :
                                                                                            ( ( in @ X3 @ X1 )
                                                                                           => ! [X4: $i] :
                                                                                                ( ( in @ X4 @ X1 )
                                                                                               => ( ( X2 @ X3 )
                                                                                                 => ( ( X2 @ X4 )
                                                                                                   => ( X3 = X4 ) ) ) ) )
                                                                                       => ( ~ ! [X3: $i] :
                                                                                                ( ( in @ X3 @ X1 )
                                                                                               => ~ ( X2 @ X3 ) )
                                                                                         => ~ ! [X3: $i] :
                                                                                                ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                               => ( ( dsetconstr @ X1 @ X2 )
                                                                                                 != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                                                          ( ~ ! [X3: $i] :
                                                                                                ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                               => ( ( dsetconstr @ X1 @ X2 )
                                                                                                 != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                         => ~ ! [X3: $i] :
                                                                                                ( ( in @ X3 @ X1 )
                                                                                               => ~ ( X2 @ X3 ) ) )
                                                                                     => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                            ( ( in @ X3 @ X1 )
                                                                                           => ( ( X2 @ X3 )
                                                                                             => ( ! [X4: $i] :
                                                                                                    ( ( in @ X4 @ X1 )
                                                                                                   => ( ( X2 @ X4 )
                                                                                                     => ( X4 = X3 ) ) )
                                                                                               => ~ ! [X4: $i] :
                                                                                                      ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                     => ( ( dsetconstr @ X1 @ X2 )
                                                                                                       != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                       => ( ! [X1: $i,X2: $i > $o] :
                                                                                              ( ! [X3: $i] :
                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                 => ! [X4: $i] :
                                                                                                      ( ( in @ X4 @ X1 )
                                                                                                     => ( ( X2 @ X3 )
                                                                                                       => ( ( X2 @ X4 )
                                                                                                         => ( X3 = X4 ) ) ) ) )
                                                                                             => ( ~ ! [X3: $i] :
                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                     => ~ ( X2 @ X3 ) )
                                                                                               => ~ ! [X3: $i] :
                                                                                                      ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                     => ( ( dsetconstr @ X1 @ X2 )
                                                                                                       != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                  = ( setadjoin @ X2 @ emptyset ) )
                                                                                               => ( X1 = X2 ) )
                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                  ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                 => ( X1 = X3 ) )
                                                                                             => ( ! [X1: $i] :
                                                                                                    ( ( iskpair @ X1 )
                                                                                                   => ~ ! [X2: $i] :
                                                                                                          ( ( in @ X2
                                                                                                            @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                              @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                         => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                              @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                           != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                               => ( ! [X1: $i] :
                                                                                                      ( ~ ! [X2: $i] :
                                                                                                            ( ( in @ X2 @ X1 )
                                                                                                           => ( X1
                                                                                                             != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                     => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                        ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                        = X1 )
                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                         => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                            ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                              = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                           => ( X1 = X3 ) )
                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                              ( ( ( kpair @ X1 @ X2 )
                                                                                                                = ( kpair @ X3 @ X4 ) )
                                                                                                             => ( X1 = X3 ) )
                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                ( ( X1 = X2 )
                                                                                                               => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                  = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                  ( ( X1 = X2 )
                                                                                                                 => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                    = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                    ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                      = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                   => ( ( X3 = X4 )
                                                                                                                     => ( X2 = X4 ) ) )
                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                      ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                        = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                     => ( X1 = X2 ) )
                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                        ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                          = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                       => ( X2 = X4 ) )
                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                          ( ( ( kpair @ X1 @ X2 )
                                                                                                                            = ( kpair @ X3 @ X4 ) )
                                                                                                                         => ( X2 = X4 ) )
                                                                                                                     => ( ! [X1: $i] :
                                                                                                                            ( ( iskpair @ X1 )
                                                                                                                           => ~ ! [X2: $i] :
                                                                                                                                  ( ( in @ X2
                                                                                                                                    @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                      @ ^ [X3: $i] :
                                                                                                                                          ( X1
                                                                                                                                          = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                 => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                      @ ^ [X3: $i] :
                                                                                                                                          ( X1
                                                                                                                                          = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                   != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                              ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                              = X2 )
                                                                                                                         => ( sP8
                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                  ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                 => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                    ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                   => ( in @ X3 @ X1 ) )
                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                      ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                     => ( in @ X4 @ X2 ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                       => ! [X4: $i] :
                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                           => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                              = X3 ) ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                         => ! [X4: $i] :
                                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                                             => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                = X4 ) ) )
                                                                                                                                     => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                         => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                            = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h201,assumption,
    ! [X1: $i,X2: $i] :
      ( ( subset @ X2 @ X1 )
     => ( ( binintersect @ X1 @ X2 )
        = X2 ) ),
    introduced(assumption,[]) ).

thf(h202,assumption,
    ~ ( ! [X1: $i,X2: $i] :
          ( ( ( binintersect @ X1 @ X2 )
            = X1 )
         => ( subset @ X1 @ X2 ) )
     => ( ! [X1: $i,X2: $i,X3: $i] :
            ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
            = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
       => ( ! [X1: $i,X2: $i,X3: $i] :
              ( ( in @ X3 @ X1 )
             => ( ~ ( in @ X3 @ X2 )
               => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
         => ( ! [X1: $i,X2: $i,X3: $i] :
                ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
               => ( in @ X3 @ X1 ) )
           => ( ! [X1: $i,X2: $i,X3: $i] :
                  ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                 => ~ ( in @ X3 @ X2 ) )
             => ( ! [X1: $i,X2: $i] :
                    ( ( subset @ X1 @ X2 )
                   => ( ( setminus @ X1 @ X2 )
                      = emptyset ) )
               => ( ! [X1: $i,X2: $i,X3: $i] :
                      ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                     => ( ( in @ X3 @ X1 )
                       => ( in @ X3 @ X2 ) ) )
                 => ( ! [X1: $i,X2: $i,X3: $i] :
                        ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                       => ( ~ ( in @ X3 @ X2 )
                         => ~ ( in @ X3 @ X1 ) ) )
                   => ( ! [X1: $i,X2: $i,X3: $i] :
                          ( ~ ( in @ X3 @ X1 )
                         => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                     => ( ! [X1: $i,X2: $i,X3: $i] :
                            ( ( in @ X3 @ X2 )
                           => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                       => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                         => ( ! [X1: $i,X2: $i] :
                                ( ( ( setminus @ X1 @ X2 )
                                  = emptyset )
                               => ( subset @ X1 @ X2 ) )
                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                  ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                 => ! [X4: $o] :
                                      ( ( ( in @ X3 @ X1 )
                                       => ( ~ ( in @ X3 @ X2 )
                                         => X4 ) )
                                     => ( ( ~ ( in @ X3 @ X1 )
                                         => ( ( in @ X3 @ X2 )
                                           => X4 ) )
                                       => X4 ) ) )
                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                    ( ( in @ X3 @ X1 )
                                   => ( ~ ( in @ X3 @ X2 )
                                     => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                      ( ~ ( in @ X3 @ X1 )
                                     => ( ( in @ X3 @ X2 )
                                       => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                        ( ( in @ X3 @ X1 )
                                       => ( ( in @ X3 @ X2 )
                                         => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                          ( ~ ( in @ X3 @ X1 )
                                         => ( ~ ( in @ X3 @ X2 )
                                           => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                     => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                       => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                         => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                           => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                             => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                               => ( ! [X1: $i,X2: $i] :
                                                      ( ( in @ X2 @ X1 )
                                                     => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                 => ( ! [X1: $i,X2: $i] :
                                                        ( ( in @ X2 @ X1 )
                                                       => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                          ( ( in @ X3 @ X1 )
                                                         => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                            ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                           => ( ( X3 != X1 )
                                                             => ( X3 = X2 ) ) )
                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                              ( ( in @ X3 @ X1 )
                                                             => ! [X4: $i] :
                                                                  ( ( in @ X4 @ X2 )
                                                                 => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                ( ( in @ X3 @ X1 )
                                                               => ! [X4: $i] :
                                                                    ( ( in @ X4 @ X2 )
                                                                   => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                  ( ( in @ X3 @ X1 )
                                                                 => ! [X4: $i] :
                                                                      ( ( in @ X4 @ X2 )
                                                                     => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                    ( ( in @ X3 @ X1 )
                                                                   => ! [X4: $i] :
                                                                        ( ( in @ X4 @ X2 )
                                                                       => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                      ( ( in @ X3 @ X1 )
                                                                     => ! [X4: $i] :
                                                                          ( ( in @ X4 @ X2 )
                                                                         => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                        ( ( in @ X3 @ X1 )
                                                                       => ! [X4: $i] :
                                                                            ( ( in @ X4 @ X2 )
                                                                           => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                         => ~ ! [X4: $i] :
                                                                                ( ( in @ X4 @ X1 )
                                                                               => ! [X5: $i] :
                                                                                    ( ( in @ X5 @ X2 )
                                                                                   => ( X3
                                                                                     != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                     => ( sP5
                                                                       => ( ! [X1: $i,X2: $i] :
                                                                              ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                             => ~ ! [X3: $i] :
                                                                                    ( ( in @ X3 @ X1 )
                                                                                   => ~ ( in @ X2 @ X3 ) ) )
                                                                         => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                           => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                             => ( ! [X1: $i] :
                                                                                    ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                    = X1 )
                                                                               => ( ! [X1: $i,X2: $i > $o] :
                                                                                      ( ! [X3: $i] :
                                                                                          ( ( in @ X3 @ X1 )
                                                                                         => ! [X4: $i] :
                                                                                              ( ( in @ X4 @ X1 )
                                                                                             => ( ( X2 @ X3 )
                                                                                               => ( ( X2 @ X4 )
                                                                                                 => ( X3 = X4 ) ) ) ) )
                                                                                     => ( ~ ! [X3: $i] :
                                                                                              ( ( in @ X3 @ X1 )
                                                                                             => ~ ( X2 @ X3 ) )
                                                                                       => ~ ! [X3: $i] :
                                                                                              ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                             => ( ( dsetconstr @ X1 @ X2 )
                                                                                               != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                                                        ( ~ ! [X3: $i] :
                                                                                              ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                             => ( ( dsetconstr @ X1 @ X2 )
                                                                                               != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                       => ~ ! [X3: $i] :
                                                                                              ( ( in @ X3 @ X1 )
                                                                                             => ~ ( X2 @ X3 ) ) )
                                                                                   => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                          ( ( in @ X3 @ X1 )
                                                                                         => ( ( X2 @ X3 )
                                                                                           => ( ! [X4: $i] :
                                                                                                  ( ( in @ X4 @ X1 )
                                                                                                 => ( ( X2 @ X4 )
                                                                                                   => ( X4 = X3 ) ) )
                                                                                             => ~ ! [X4: $i] :
                                                                                                    ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                   => ( ( dsetconstr @ X1 @ X2 )
                                                                                                     != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                                                            ( ! [X3: $i] :
                                                                                                ( ( in @ X3 @ X1 )
                                                                                               => ! [X4: $i] :
                                                                                                    ( ( in @ X4 @ X1 )
                                                                                                   => ( ( X2 @ X3 )
                                                                                                     => ( ( X2 @ X4 )
                                                                                                       => ( X3 = X4 ) ) ) ) )
                                                                                           => ( ~ ! [X3: $i] :
                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                   => ~ ( X2 @ X3 ) )
                                                                                             => ~ ! [X3: $i] :
                                                                                                    ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                   => ( ( dsetconstr @ X1 @ X2 )
                                                                                                     != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                              ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                = ( setadjoin @ X2 @ emptyset ) )
                                                                                             => ( X1 = X2 ) )
                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                               => ( X1 = X3 ) )
                                                                                           => ( ! [X1: $i] :
                                                                                                  ( ( iskpair @ X1 )
                                                                                                 => ~ ! [X2: $i] :
                                                                                                        ( ( in @ X2
                                                                                                          @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                            @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                       => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                            @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                         != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                             => ( ! [X1: $i] :
                                                                                                    ( ~ ! [X2: $i] :
                                                                                                          ( ( in @ X2 @ X1 )
                                                                                                         => ( X1
                                                                                                           != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                   => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                      ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                      = X1 )
                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                       => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                          ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                            = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                         => ( X1 = X3 ) )
                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                            ( ( ( kpair @ X1 @ X2 )
                                                                                                              = ( kpair @ X3 @ X4 ) )
                                                                                                           => ( X1 = X3 ) )
                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                              ( ( X1 = X2 )
                                                                                                             => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                ( ( X1 = X2 )
                                                                                                               => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                  = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                  ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                    = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                 => ( ( X3 = X4 )
                                                                                                                   => ( X2 = X4 ) ) )
                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                    ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                      = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                   => ( X1 = X2 ) )
                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                      ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                        = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                     => ( X2 = X4 ) )
                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                        ( ( ( kpair @ X1 @ X2 )
                                                                                                                          = ( kpair @ X3 @ X4 ) )
                                                                                                                       => ( X2 = X4 ) )
                                                                                                                   => ( ! [X1: $i] :
                                                                                                                          ( ( iskpair @ X1 )
                                                                                                                         => ~ ! [X2: $i] :
                                                                                                                                ( ( in @ X2
                                                                                                                                  @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                    @ ^ [X3: $i] :
                                                                                                                                        ( X1
                                                                                                                                        = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                               => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                    @ ^ [X3: $i] :
                                                                                                                                        ( X1
                                                                                                                                        = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                 != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                            ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                            = X2 )
                                                                                                                       => ( sP8
                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                               => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                  ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                 => ( in @ X3 @ X1 ) )
                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                    ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                   => ( in @ X4 @ X2 ) )
                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                     => ! [X4: $i] :
                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                         => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                            = X3 ) ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                       => ! [X4: $i] :
                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                           => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                              = X4 ) ) )
                                                                                                                                   => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                       => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                          = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h203,assumption,
    ! [X1: $i,X2: $i] :
      ( ( ( binintersect @ X1 @ X2 )
        = X1 )
     => ( subset @ X1 @ X2 ) ),
    introduced(assumption,[]) ).

thf(h204,assumption,
    ~ ( ! [X1: $i,X2: $i,X3: $i] :
          ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
          = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
     => ( ! [X1: $i,X2: $i,X3: $i] :
            ( ( in @ X3 @ X1 )
           => ( ~ ( in @ X3 @ X2 )
             => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
       => ( ! [X1: $i,X2: $i,X3: $i] :
              ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
             => ( in @ X3 @ X1 ) )
         => ( ! [X1: $i,X2: $i,X3: $i] :
                ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
               => ~ ( in @ X3 @ X2 ) )
           => ( ! [X1: $i,X2: $i] :
                  ( ( subset @ X1 @ X2 )
                 => ( ( setminus @ X1 @ X2 )
                    = emptyset ) )
             => ( ! [X1: $i,X2: $i,X3: $i] :
                    ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                   => ( ( in @ X3 @ X1 )
                     => ( in @ X3 @ X2 ) ) )
               => ( ! [X1: $i,X2: $i,X3: $i] :
                      ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                     => ( ~ ( in @ X3 @ X2 )
                       => ~ ( in @ X3 @ X1 ) ) )
                 => ( ! [X1: $i,X2: $i,X3: $i] :
                        ( ~ ( in @ X3 @ X1 )
                       => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                   => ( ! [X1: $i,X2: $i,X3: $i] :
                          ( ( in @ X3 @ X2 )
                         => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                     => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                       => ( ! [X1: $i,X2: $i] :
                              ( ( ( setminus @ X1 @ X2 )
                                = emptyset )
                             => ( subset @ X1 @ X2 ) )
                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                               => ! [X4: $o] :
                                    ( ( ( in @ X3 @ X1 )
                                     => ( ~ ( in @ X3 @ X2 )
                                       => X4 ) )
                                   => ( ( ~ ( in @ X3 @ X1 )
                                       => ( ( in @ X3 @ X2 )
                                         => X4 ) )
                                     => X4 ) ) )
                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                  ( ( in @ X3 @ X1 )
                                 => ( ~ ( in @ X3 @ X2 )
                                   => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                    ( ~ ( in @ X3 @ X1 )
                                   => ( ( in @ X3 @ X2 )
                                     => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                      ( ( in @ X3 @ X1 )
                                     => ( ( in @ X3 @ X2 )
                                       => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                        ( ~ ( in @ X3 @ X1 )
                                       => ( ~ ( in @ X3 @ X2 )
                                         => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                   => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                     => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                       => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                         => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                           => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                             => ( ! [X1: $i,X2: $i] :
                                                    ( ( in @ X2 @ X1 )
                                                   => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                               => ( ! [X1: $i,X2: $i] :
                                                      ( ( in @ X2 @ X1 )
                                                     => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                        ( ( in @ X3 @ X1 )
                                                       => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                          ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                         => ( ( X3 != X1 )
                                                           => ( X3 = X2 ) ) )
                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                            ( ( in @ X3 @ X1 )
                                                           => ! [X4: $i] :
                                                                ( ( in @ X4 @ X2 )
                                                               => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                              ( ( in @ X3 @ X1 )
                                                             => ! [X4: $i] :
                                                                  ( ( in @ X4 @ X2 )
                                                                 => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                ( ( in @ X3 @ X1 )
                                                               => ! [X4: $i] :
                                                                    ( ( in @ X4 @ X2 )
                                                                   => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                  ( ( in @ X3 @ X1 )
                                                                 => ! [X4: $i] :
                                                                      ( ( in @ X4 @ X2 )
                                                                     => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                    ( ( in @ X3 @ X1 )
                                                                   => ! [X4: $i] :
                                                                        ( ( in @ X4 @ X2 )
                                                                       => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                      ( ( in @ X3 @ X1 )
                                                                     => ! [X4: $i] :
                                                                          ( ( in @ X4 @ X2 )
                                                                         => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                       => ~ ! [X4: $i] :
                                                                              ( ( in @ X4 @ X1 )
                                                                             => ! [X5: $i] :
                                                                                  ( ( in @ X5 @ X2 )
                                                                                 => ( X3
                                                                                   != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                   => ( sP5
                                                                     => ( ! [X1: $i,X2: $i] :
                                                                            ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                           => ~ ! [X3: $i] :
                                                                                  ( ( in @ X3 @ X1 )
                                                                                 => ~ ( in @ X2 @ X3 ) ) )
                                                                       => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                         => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                           => ( ! [X1: $i] :
                                                                                  ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                  = X1 )
                                                                             => ( ! [X1: $i,X2: $i > $o] :
                                                                                    ( ! [X3: $i] :
                                                                                        ( ( in @ X3 @ X1 )
                                                                                       => ! [X4: $i] :
                                                                                            ( ( in @ X4 @ X1 )
                                                                                           => ( ( X2 @ X3 )
                                                                                             => ( ( X2 @ X4 )
                                                                                               => ( X3 = X4 ) ) ) ) )
                                                                                   => ( ~ ! [X3: $i] :
                                                                                            ( ( in @ X3 @ X1 )
                                                                                           => ~ ( X2 @ X3 ) )
                                                                                     => ~ ! [X3: $i] :
                                                                                            ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                           => ( ( dsetconstr @ X1 @ X2 )
                                                                                             != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                               => ( ! [X1: $i,X2: $i > $o] :
                                                                                      ( ~ ! [X3: $i] :
                                                                                            ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                           => ( ( dsetconstr @ X1 @ X2 )
                                                                                             != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                     => ~ ! [X3: $i] :
                                                                                            ( ( in @ X3 @ X1 )
                                                                                           => ~ ( X2 @ X3 ) ) )
                                                                                 => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                        ( ( in @ X3 @ X1 )
                                                                                       => ( ( X2 @ X3 )
                                                                                         => ( ! [X4: $i] :
                                                                                                ( ( in @ X4 @ X1 )
                                                                                               => ( ( X2 @ X4 )
                                                                                                 => ( X4 = X3 ) ) )
                                                                                           => ~ ! [X4: $i] :
                                                                                                  ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                 => ( ( dsetconstr @ X1 @ X2 )
                                                                                                   != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                                                          ( ! [X3: $i] :
                                                                                              ( ( in @ X3 @ X1 )
                                                                                             => ! [X4: $i] :
                                                                                                  ( ( in @ X4 @ X1 )
                                                                                                 => ( ( X2 @ X3 )
                                                                                                   => ( ( X2 @ X4 )
                                                                                                     => ( X3 = X4 ) ) ) ) )
                                                                                         => ( ~ ! [X3: $i] :
                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                 => ~ ( X2 @ X3 ) )
                                                                                           => ~ ! [X3: $i] :
                                                                                                  ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                 => ( ( dsetconstr @ X1 @ X2 )
                                                                                                   != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                            ( ( ( setadjoin @ X1 @ emptyset )
                                                                                              = ( setadjoin @ X2 @ emptyset ) )
                                                                                           => ( X1 = X2 ) )
                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                              ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                             => ( X1 = X3 ) )
                                                                                         => ( ! [X1: $i] :
                                                                                                ( ( iskpair @ X1 )
                                                                                               => ~ ! [X2: $i] :
                                                                                                      ( ( in @ X2
                                                                                                        @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                          @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                     => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                          @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                       != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                           => ( ! [X1: $i] :
                                                                                                  ( ~ ! [X2: $i] :
                                                                                                        ( ( in @ X2 @ X1 )
                                                                                                       => ( X1
                                                                                                         != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                 => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                    ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                    = X1 )
                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                      ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                     => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                        ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                          = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                       => ( X1 = X3 ) )
                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                          ( ( ( kpair @ X1 @ X2 )
                                                                                                            = ( kpair @ X3 @ X4 ) )
                                                                                                         => ( X1 = X3 ) )
                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                            ( ( X1 = X2 )
                                                                                                           => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                              = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                              ( ( X1 = X2 )
                                                                                                             => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                  = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                               => ( ( X3 = X4 )
                                                                                                                 => ( X2 = X4 ) ) )
                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                  ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                    = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                 => ( X1 = X2 ) )
                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                    ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                      = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                   => ( X2 = X4 ) )
                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                      ( ( ( kpair @ X1 @ X2 )
                                                                                                                        = ( kpair @ X3 @ X4 ) )
                                                                                                                     => ( X2 = X4 ) )
                                                                                                                 => ( ! [X1: $i] :
                                                                                                                        ( ( iskpair @ X1 )
                                                                                                                       => ~ ! [X2: $i] :
                                                                                                                              ( ( in @ X2
                                                                                                                                @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                  @ ^ [X3: $i] :
                                                                                                                                      ( X1
                                                                                                                                      = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                             => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                  @ ^ [X3: $i] :
                                                                                                                                      ( X1
                                                                                                                                      = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                               != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                          ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                          = X2 )
                                                                                                                     => ( sP8
                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                              ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                             => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                               => ( in @ X3 @ X1 ) )
                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                  ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                 => ( in @ X4 @ X2 ) )
                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                   => ! [X4: $i] :
                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                       => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                          = X3 ) ) )
                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                     => ! [X4: $i] :
                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                         => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                            = X4 ) ) )
                                                                                                                                 => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                      ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                     => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                        = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h205,assumption,
    ! [X1: $i,X2: $i,X3: $i] :
      ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
      = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) ),
    introduced(assumption,[]) ).

thf(h206,assumption,
    ~ ( ! [X1: $i,X2: $i,X3: $i] :
          ( ( in @ X3 @ X1 )
         => ( ~ ( in @ X3 @ X2 )
           => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
     => ( ! [X1: $i,X2: $i,X3: $i] :
            ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
           => ( in @ X3 @ X1 ) )
       => ( ! [X1: $i,X2: $i,X3: $i] :
              ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
             => ~ ( in @ X3 @ X2 ) )
         => ( ! [X1: $i,X2: $i] :
                ( ( subset @ X1 @ X2 )
               => ( ( setminus @ X1 @ X2 )
                  = emptyset ) )
           => ( ! [X1: $i,X2: $i,X3: $i] :
                  ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                 => ( ( in @ X3 @ X1 )
                   => ( in @ X3 @ X2 ) ) )
             => ( ! [X1: $i,X2: $i,X3: $i] :
                    ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                   => ( ~ ( in @ X3 @ X2 )
                     => ~ ( in @ X3 @ X1 ) ) )
               => ( ! [X1: $i,X2: $i,X3: $i] :
                      ( ~ ( in @ X3 @ X1 )
                     => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                 => ( ! [X1: $i,X2: $i,X3: $i] :
                        ( ( in @ X3 @ X2 )
                       => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                   => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                     => ( ! [X1: $i,X2: $i] :
                            ( ( ( setminus @ X1 @ X2 )
                              = emptyset )
                           => ( subset @ X1 @ X2 ) )
                       => ( ! [X1: $i,X2: $i,X3: $i] :
                              ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                             => ! [X4: $o] :
                                  ( ( ( in @ X3 @ X1 )
                                   => ( ~ ( in @ X3 @ X2 )
                                     => X4 ) )
                                 => ( ( ~ ( in @ X3 @ X1 )
                                     => ( ( in @ X3 @ X2 )
                                       => X4 ) )
                                   => X4 ) ) )
                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                ( ( in @ X3 @ X1 )
                               => ( ~ ( in @ X3 @ X2 )
                                 => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                  ( ~ ( in @ X3 @ X1 )
                                 => ( ( in @ X3 @ X2 )
                                   => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                    ( ( in @ X3 @ X1 )
                                   => ( ( in @ X3 @ X2 )
                                     => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                      ( ~ ( in @ X3 @ X1 )
                                     => ( ~ ( in @ X3 @ X2 )
                                       => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                 => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                   => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                     => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                       => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                         => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                           => ( ! [X1: $i,X2: $i] :
                                                  ( ( in @ X2 @ X1 )
                                                 => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                             => ( ! [X1: $i,X2: $i] :
                                                    ( ( in @ X2 @ X1 )
                                                   => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                      ( ( in @ X3 @ X1 )
                                                     => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                        ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                       => ( ( X3 != X1 )
                                                         => ( X3 = X2 ) ) )
                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                          ( ( in @ X3 @ X1 )
                                                         => ! [X4: $i] :
                                                              ( ( in @ X4 @ X2 )
                                                             => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                            ( ( in @ X3 @ X1 )
                                                           => ! [X4: $i] :
                                                                ( ( in @ X4 @ X2 )
                                                               => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                              ( ( in @ X3 @ X1 )
                                                             => ! [X4: $i] :
                                                                  ( ( in @ X4 @ X2 )
                                                                 => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                ( ( in @ X3 @ X1 )
                                                               => ! [X4: $i] :
                                                                    ( ( in @ X4 @ X2 )
                                                                   => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                  ( ( in @ X3 @ X1 )
                                                                 => ! [X4: $i] :
                                                                      ( ( in @ X4 @ X2 )
                                                                     => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                    ( ( in @ X3 @ X1 )
                                                                   => ! [X4: $i] :
                                                                        ( ( in @ X4 @ X2 )
                                                                       => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                      ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                     => ~ ! [X4: $i] :
                                                                            ( ( in @ X4 @ X1 )
                                                                           => ! [X5: $i] :
                                                                                ( ( in @ X5 @ X2 )
                                                                               => ( X3
                                                                                 != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                 => ( sP5
                                                                   => ( ! [X1: $i,X2: $i] :
                                                                          ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                         => ~ ! [X3: $i] :
                                                                                ( ( in @ X3 @ X1 )
                                                                               => ~ ( in @ X2 @ X3 ) ) )
                                                                     => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                       => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                         => ( ! [X1: $i] :
                                                                                ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                = X1 )
                                                                           => ( ! [X1: $i,X2: $i > $o] :
                                                                                  ( ! [X3: $i] :
                                                                                      ( ( in @ X3 @ X1 )
                                                                                     => ! [X4: $i] :
                                                                                          ( ( in @ X4 @ X1 )
                                                                                         => ( ( X2 @ X3 )
                                                                                           => ( ( X2 @ X4 )
                                                                                             => ( X3 = X4 ) ) ) ) )
                                                                                 => ( ~ ! [X3: $i] :
                                                                                          ( ( in @ X3 @ X1 )
                                                                                         => ~ ( X2 @ X3 ) )
                                                                                   => ~ ! [X3: $i] :
                                                                                          ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                         => ( ( dsetconstr @ X1 @ X2 )
                                                                                           != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                             => ( ! [X1: $i,X2: $i > $o] :
                                                                                    ( ~ ! [X3: $i] :
                                                                                          ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                         => ( ( dsetconstr @ X1 @ X2 )
                                                                                           != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                   => ~ ! [X3: $i] :
                                                                                          ( ( in @ X3 @ X1 )
                                                                                         => ~ ( X2 @ X3 ) ) )
                                                                               => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                      ( ( in @ X3 @ X1 )
                                                                                     => ( ( X2 @ X3 )
                                                                                       => ( ! [X4: $i] :
                                                                                              ( ( in @ X4 @ X1 )
                                                                                             => ( ( X2 @ X4 )
                                                                                               => ( X4 = X3 ) ) )
                                                                                         => ~ ! [X4: $i] :
                                                                                                ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                               => ( ( dsetconstr @ X1 @ X2 )
                                                                                                 != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                                                        ( ! [X3: $i] :
                                                                                            ( ( in @ X3 @ X1 )
                                                                                           => ! [X4: $i] :
                                                                                                ( ( in @ X4 @ X1 )
                                                                                               => ( ( X2 @ X3 )
                                                                                                 => ( ( X2 @ X4 )
                                                                                                   => ( X3 = X4 ) ) ) ) )
                                                                                       => ( ~ ! [X3: $i] :
                                                                                                ( ( in @ X3 @ X1 )
                                                                                               => ~ ( X2 @ X3 ) )
                                                                                         => ~ ! [X3: $i] :
                                                                                                ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                               => ( ( dsetconstr @ X1 @ X2 )
                                                                                                 != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                          ( ( ( setadjoin @ X1 @ emptyset )
                                                                                            = ( setadjoin @ X2 @ emptyset ) )
                                                                                         => ( X1 = X2 ) )
                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                            ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                           => ( X1 = X3 ) )
                                                                                       => ( ! [X1: $i] :
                                                                                              ( ( iskpair @ X1 )
                                                                                             => ~ ! [X2: $i] :
                                                                                                    ( ( in @ X2
                                                                                                      @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                        @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                   => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                        @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                     != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                         => ( ! [X1: $i] :
                                                                                                ( ~ ! [X2: $i] :
                                                                                                      ( ( in @ X2 @ X1 )
                                                                                                     => ( X1
                                                                                                       != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                               => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                  ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                  = X1 )
                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                    ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                   => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                      ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                        = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                     => ( X1 = X3 ) )
                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                        ( ( ( kpair @ X1 @ X2 )
                                                                                                          = ( kpair @ X3 @ X4 ) )
                                                                                                       => ( X1 = X3 ) )
                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                          ( ( X1 = X2 )
                                                                                                         => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                            = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                            ( ( X1 = X2 )
                                                                                                           => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                              = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                              ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                             => ( ( X3 = X4 )
                                                                                                               => ( X2 = X4 ) ) )
                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                  = ( setadjoin @ X3 @ emptyset ) )
                                                                                                               => ( X1 = X2 ) )
                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                  ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                    = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                 => ( X2 = X4 ) )
                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                    ( ( ( kpair @ X1 @ X2 )
                                                                                                                      = ( kpair @ X3 @ X4 ) )
                                                                                                                   => ( X2 = X4 ) )
                                                                                                               => ( ! [X1: $i] :
                                                                                                                      ( ( iskpair @ X1 )
                                                                                                                     => ~ ! [X2: $i] :
                                                                                                                            ( ( in @ X2
                                                                                                                              @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                @ ^ [X3: $i] :
                                                                                                                                    ( X1
                                                                                                                                    = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                           => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                @ ^ [X3: $i] :
                                                                                                                                    ( X1
                                                                                                                                    = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                             != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                        ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                        = X2 )
                                                                                                                   => ( sP8
                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                            ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                           => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                              ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                             => ( in @ X3 @ X1 ) )
                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                               => ( in @ X4 @ X2 ) )
                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                 => ! [X4: $i] :
                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                     => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                        = X3 ) ) )
                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                   => ! [X4: $i] :
                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                       => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                          = X4 ) ) )
                                                                                                                               => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                    ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                   => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                      = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h207,assumption,
    ! [X1: $i,X2: $i,X3: $i] :
      ( ( in @ X3 @ X1 )
     => ( ~ ( in @ X3 @ X2 )
       => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) ),
    introduced(assumption,[]) ).

thf(h208,assumption,
    ~ ( ! [X1: $i,X2: $i,X3: $i] :
          ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
         => ( in @ X3 @ X1 ) )
     => ( ! [X1: $i,X2: $i,X3: $i] :
            ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
           => ~ ( in @ X3 @ X2 ) )
       => ( ! [X1: $i,X2: $i] :
              ( ( subset @ X1 @ X2 )
             => ( ( setminus @ X1 @ X2 )
                = emptyset ) )
         => ( ! [X1: $i,X2: $i,X3: $i] :
                ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
               => ( ( in @ X3 @ X1 )
                 => ( in @ X3 @ X2 ) ) )
           => ( ! [X1: $i,X2: $i,X3: $i] :
                  ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                 => ( ~ ( in @ X3 @ X2 )
                   => ~ ( in @ X3 @ X1 ) ) )
             => ( ! [X1: $i,X2: $i,X3: $i] :
                    ( ~ ( in @ X3 @ X1 )
                   => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
               => ( ! [X1: $i,X2: $i,X3: $i] :
                      ( ( in @ X3 @ X2 )
                     => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                 => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                   => ( ! [X1: $i,X2: $i] :
                          ( ( ( setminus @ X1 @ X2 )
                            = emptyset )
                         => ( subset @ X1 @ X2 ) )
                     => ( ! [X1: $i,X2: $i,X3: $i] :
                            ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                           => ! [X4: $o] :
                                ( ( ( in @ X3 @ X1 )
                                 => ( ~ ( in @ X3 @ X2 )
                                   => X4 ) )
                               => ( ( ~ ( in @ X3 @ X1 )
                                   => ( ( in @ X3 @ X2 )
                                     => X4 ) )
                                 => X4 ) ) )
                       => ( ! [X1: $i,X2: $i,X3: $i] :
                              ( ( in @ X3 @ X1 )
                             => ( ~ ( in @ X3 @ X2 )
                               => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                ( ~ ( in @ X3 @ X1 )
                               => ( ( in @ X3 @ X2 )
                                 => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                  ( ( in @ X3 @ X1 )
                                 => ( ( in @ X3 @ X2 )
                                   => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                    ( ~ ( in @ X3 @ X1 )
                                   => ( ~ ( in @ X3 @ X2 )
                                     => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                               => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                 => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                   => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                     => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                       => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                         => ( ! [X1: $i,X2: $i] :
                                                ( ( in @ X2 @ X1 )
                                               => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                           => ( ! [X1: $i,X2: $i] :
                                                  ( ( in @ X2 @ X1 )
                                                 => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                    ( ( in @ X3 @ X1 )
                                                   => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                      ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                     => ( ( X3 != X1 )
                                                       => ( X3 = X2 ) ) )
                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                        ( ( in @ X3 @ X1 )
                                                       => ! [X4: $i] :
                                                            ( ( in @ X4 @ X2 )
                                                           => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                          ( ( in @ X3 @ X1 )
                                                         => ! [X4: $i] :
                                                              ( ( in @ X4 @ X2 )
                                                             => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                            ( ( in @ X3 @ X1 )
                                                           => ! [X4: $i] :
                                                                ( ( in @ X4 @ X2 )
                                                               => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                              ( ( in @ X3 @ X1 )
                                                             => ! [X4: $i] :
                                                                  ( ( in @ X4 @ X2 )
                                                                 => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                ( ( in @ X3 @ X1 )
                                                               => ! [X4: $i] :
                                                                    ( ( in @ X4 @ X2 )
                                                                   => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                  ( ( in @ X3 @ X1 )
                                                                 => ! [X4: $i] :
                                                                      ( ( in @ X4 @ X2 )
                                                                     => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                    ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                   => ~ ! [X4: $i] :
                                                                          ( ( in @ X4 @ X1 )
                                                                         => ! [X5: $i] :
                                                                              ( ( in @ X5 @ X2 )
                                                                             => ( X3
                                                                               != ( kpair @ X4 @ X5 ) ) ) ) )
                                                               => ( sP5
                                                                 => ( ! [X1: $i,X2: $i] :
                                                                        ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                       => ~ ! [X3: $i] :
                                                                              ( ( in @ X3 @ X1 )
                                                                             => ~ ( in @ X2 @ X3 ) ) )
                                                                   => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                     => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                       => ( ! [X1: $i] :
                                                                              ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                              = X1 )
                                                                         => ( ! [X1: $i,X2: $i > $o] :
                                                                                ( ! [X3: $i] :
                                                                                    ( ( in @ X3 @ X1 )
                                                                                   => ! [X4: $i] :
                                                                                        ( ( in @ X4 @ X1 )
                                                                                       => ( ( X2 @ X3 )
                                                                                         => ( ( X2 @ X4 )
                                                                                           => ( X3 = X4 ) ) ) ) )
                                                                               => ( ~ ! [X3: $i] :
                                                                                        ( ( in @ X3 @ X1 )
                                                                                       => ~ ( X2 @ X3 ) )
                                                                                 => ~ ! [X3: $i] :
                                                                                        ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                       => ( ( dsetconstr @ X1 @ X2 )
                                                                                         != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                           => ( ! [X1: $i,X2: $i > $o] :
                                                                                  ( ~ ! [X3: $i] :
                                                                                        ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                       => ( ( dsetconstr @ X1 @ X2 )
                                                                                         != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                 => ~ ! [X3: $i] :
                                                                                        ( ( in @ X3 @ X1 )
                                                                                       => ~ ( X2 @ X3 ) ) )
                                                                             => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                    ( ( in @ X3 @ X1 )
                                                                                   => ( ( X2 @ X3 )
                                                                                     => ( ! [X4: $i] :
                                                                                            ( ( in @ X4 @ X1 )
                                                                                           => ( ( X2 @ X4 )
                                                                                             => ( X4 = X3 ) ) )
                                                                                       => ~ ! [X4: $i] :
                                                                                              ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                             => ( ( dsetconstr @ X1 @ X2 )
                                                                                               != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                               => ( ! [X1: $i,X2: $i > $o] :
                                                                                      ( ! [X3: $i] :
                                                                                          ( ( in @ X3 @ X1 )
                                                                                         => ! [X4: $i] :
                                                                                              ( ( in @ X4 @ X1 )
                                                                                             => ( ( X2 @ X3 )
                                                                                               => ( ( X2 @ X4 )
                                                                                                 => ( X3 = X4 ) ) ) ) )
                                                                                     => ( ~ ! [X3: $i] :
                                                                                              ( ( in @ X3 @ X1 )
                                                                                             => ~ ( X2 @ X3 ) )
                                                                                       => ~ ! [X3: $i] :
                                                                                              ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                             => ( ( dsetconstr @ X1 @ X2 )
                                                                                               != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                        ( ( ( setadjoin @ X1 @ emptyset )
                                                                                          = ( setadjoin @ X2 @ emptyset ) )
                                                                                       => ( X1 = X2 ) )
                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                          ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                         => ( X1 = X3 ) )
                                                                                     => ( ! [X1: $i] :
                                                                                            ( ( iskpair @ X1 )
                                                                                           => ~ ! [X2: $i] :
                                                                                                  ( ( in @ X2
                                                                                                    @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                      @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                 => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                      @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                   != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                       => ( ! [X1: $i] :
                                                                                              ( ~ ! [X2: $i] :
                                                                                                    ( ( in @ X2 @ X1 )
                                                                                                   => ( X1
                                                                                                     != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                             => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                = X1 )
                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                  ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                 => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                    ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                      = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                   => ( X1 = X3 ) )
                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                      ( ( ( kpair @ X1 @ X2 )
                                                                                                        = ( kpair @ X3 @ X4 ) )
                                                                                                     => ( X1 = X3 ) )
                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                        ( ( X1 = X2 )
                                                                                                       => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                          = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                          ( ( X1 = X2 )
                                                                                                         => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                            = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                            ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                              = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                           => ( ( X3 = X4 )
                                                                                                             => ( X2 = X4 ) ) )
                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                              ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                = ( setadjoin @ X3 @ emptyset ) )
                                                                                                             => ( X1 = X2 ) )
                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                  = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                               => ( X2 = X4 ) )
                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                  ( ( ( kpair @ X1 @ X2 )
                                                                                                                    = ( kpair @ X3 @ X4 ) )
                                                                                                                 => ( X2 = X4 ) )
                                                                                                             => ( ! [X1: $i] :
                                                                                                                    ( ( iskpair @ X1 )
                                                                                                                   => ~ ! [X2: $i] :
                                                                                                                          ( ( in @ X2
                                                                                                                            @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                              @ ^ [X3: $i] :
                                                                                                                                  ( X1
                                                                                                                                  = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                         => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                              @ ^ [X3: $i] :
                                                                                                                                  ( X1
                                                                                                                                  = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                           != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                      ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                      = X2 )
                                                                                                                 => ( sP8
                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                         => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                            ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                           => ( in @ X3 @ X1 ) )
                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                              ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                             => ( in @ X4 @ X2 ) )
                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                               => ! [X4: $i] :
                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                   => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                      = X3 ) ) )
                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                 => ! [X4: $i] :
                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                     => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                        = X4 ) ) )
                                                                                                                             => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                  ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                 => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                    = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h209,assumption,
    ! [X1: $i,X2: $i,X3: $i] :
      ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
     => ( in @ X3 @ X1 ) ),
    introduced(assumption,[]) ).

thf(h210,assumption,
    ~ ( ! [X1: $i,X2: $i,X3: $i] :
          ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
         => ~ ( in @ X3 @ X2 ) )
     => ( ! [X1: $i,X2: $i] :
            ( ( subset @ X1 @ X2 )
           => ( ( setminus @ X1 @ X2 )
              = emptyset ) )
       => ( ! [X1: $i,X2: $i,X3: $i] :
              ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
             => ( ( in @ X3 @ X1 )
               => ( in @ X3 @ X2 ) ) )
         => ( ! [X1: $i,X2: $i,X3: $i] :
                ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
               => ( ~ ( in @ X3 @ X2 )
                 => ~ ( in @ X3 @ X1 ) ) )
           => ( ! [X1: $i,X2: $i,X3: $i] :
                  ( ~ ( in @ X3 @ X1 )
                 => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
             => ( ! [X1: $i,X2: $i,X3: $i] :
                    ( ( in @ X3 @ X2 )
                   => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
               => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                 => ( ! [X1: $i,X2: $i] :
                        ( ( ( setminus @ X1 @ X2 )
                          = emptyset )
                       => ( subset @ X1 @ X2 ) )
                   => ( ! [X1: $i,X2: $i,X3: $i] :
                          ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                         => ! [X4: $o] :
                              ( ( ( in @ X3 @ X1 )
                               => ( ~ ( in @ X3 @ X2 )
                                 => X4 ) )
                             => ( ( ~ ( in @ X3 @ X1 )
                                 => ( ( in @ X3 @ X2 )
                                   => X4 ) )
                               => X4 ) ) )
                     => ( ! [X1: $i,X2: $i,X3: $i] :
                            ( ( in @ X3 @ X1 )
                           => ( ~ ( in @ X3 @ X2 )
                             => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                       => ( ! [X1: $i,X2: $i,X3: $i] :
                              ( ~ ( in @ X3 @ X1 )
                             => ( ( in @ X3 @ X2 )
                               => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                ( ( in @ X3 @ X1 )
                               => ( ( in @ X3 @ X2 )
                                 => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                  ( ~ ( in @ X3 @ X1 )
                                 => ( ~ ( in @ X3 @ X2 )
                                   => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                             => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                               => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                 => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                   => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                     => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                       => ( ! [X1: $i,X2: $i] :
                                              ( ( in @ X2 @ X1 )
                                             => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                         => ( ! [X1: $i,X2: $i] :
                                                ( ( in @ X2 @ X1 )
                                               => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                  ( ( in @ X3 @ X1 )
                                                 => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                    ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                   => ( ( X3 != X1 )
                                                     => ( X3 = X2 ) ) )
                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                      ( ( in @ X3 @ X1 )
                                                     => ! [X4: $i] :
                                                          ( ( in @ X4 @ X2 )
                                                         => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                        ( ( in @ X3 @ X1 )
                                                       => ! [X4: $i] :
                                                            ( ( in @ X4 @ X2 )
                                                           => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                          ( ( in @ X3 @ X1 )
                                                         => ! [X4: $i] :
                                                              ( ( in @ X4 @ X2 )
                                                             => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                            ( ( in @ X3 @ X1 )
                                                           => ! [X4: $i] :
                                                                ( ( in @ X4 @ X2 )
                                                               => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                              ( ( in @ X3 @ X1 )
                                                             => ! [X4: $i] :
                                                                  ( ( in @ X4 @ X2 )
                                                                 => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                ( ( in @ X3 @ X1 )
                                                               => ! [X4: $i] :
                                                                    ( ( in @ X4 @ X2 )
                                                                   => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                  ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                 => ~ ! [X4: $i] :
                                                                        ( ( in @ X4 @ X1 )
                                                                       => ! [X5: $i] :
                                                                            ( ( in @ X5 @ X2 )
                                                                           => ( X3
                                                                             != ( kpair @ X4 @ X5 ) ) ) ) )
                                                             => ( sP5
                                                               => ( ! [X1: $i,X2: $i] :
                                                                      ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                     => ~ ! [X3: $i] :
                                                                            ( ( in @ X3 @ X1 )
                                                                           => ~ ( in @ X2 @ X3 ) ) )
                                                                 => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                   => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                     => ( ! [X1: $i] :
                                                                            ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                            = X1 )
                                                                       => ( ! [X1: $i,X2: $i > $o] :
                                                                              ( ! [X3: $i] :
                                                                                  ( ( in @ X3 @ X1 )
                                                                                 => ! [X4: $i] :
                                                                                      ( ( in @ X4 @ X1 )
                                                                                     => ( ( X2 @ X3 )
                                                                                       => ( ( X2 @ X4 )
                                                                                         => ( X3 = X4 ) ) ) ) )
                                                                             => ( ~ ! [X3: $i] :
                                                                                      ( ( in @ X3 @ X1 )
                                                                                     => ~ ( X2 @ X3 ) )
                                                                               => ~ ! [X3: $i] :
                                                                                      ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                     => ( ( dsetconstr @ X1 @ X2 )
                                                                                       != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                         => ( ! [X1: $i,X2: $i > $o] :
                                                                                ( ~ ! [X3: $i] :
                                                                                      ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                     => ( ( dsetconstr @ X1 @ X2 )
                                                                                       != ( setadjoin @ X3 @ emptyset ) ) )
                                                                               => ~ ! [X3: $i] :
                                                                                      ( ( in @ X3 @ X1 )
                                                                                     => ~ ( X2 @ X3 ) ) )
                                                                           => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                  ( ( in @ X3 @ X1 )
                                                                                 => ( ( X2 @ X3 )
                                                                                   => ( ! [X4: $i] :
                                                                                          ( ( in @ X4 @ X1 )
                                                                                         => ( ( X2 @ X4 )
                                                                                           => ( X4 = X3 ) ) )
                                                                                     => ~ ! [X4: $i] :
                                                                                            ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                           => ( ( dsetconstr @ X1 @ X2 )
                                                                                             != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                             => ( ! [X1: $i,X2: $i > $o] :
                                                                                    ( ! [X3: $i] :
                                                                                        ( ( in @ X3 @ X1 )
                                                                                       => ! [X4: $i] :
                                                                                            ( ( in @ X4 @ X1 )
                                                                                           => ( ( X2 @ X3 )
                                                                                             => ( ( X2 @ X4 )
                                                                                               => ( X3 = X4 ) ) ) ) )
                                                                                   => ( ~ ! [X3: $i] :
                                                                                            ( ( in @ X3 @ X1 )
                                                                                           => ~ ( X2 @ X3 ) )
                                                                                     => ~ ! [X3: $i] :
                                                                                            ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                           => ( ( dsetconstr @ X1 @ X2 )
                                                                                             != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                      ( ( ( setadjoin @ X1 @ emptyset )
                                                                                        = ( setadjoin @ X2 @ emptyset ) )
                                                                                     => ( X1 = X2 ) )
                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                        ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                       => ( X1 = X3 ) )
                                                                                   => ( ! [X1: $i] :
                                                                                          ( ( iskpair @ X1 )
                                                                                         => ~ ! [X2: $i] :
                                                                                                ( ( in @ X2
                                                                                                  @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                    @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                               => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                    @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                 != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                     => ( ! [X1: $i] :
                                                                                            ( ~ ! [X2: $i] :
                                                                                                  ( ( in @ X2 @ X1 )
                                                                                                 => ( X1
                                                                                                   != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                           => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                              ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                              = X1 )
                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                               => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                  ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                    = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                 => ( X1 = X3 ) )
                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                    ( ( ( kpair @ X1 @ X2 )
                                                                                                      = ( kpair @ X3 @ X4 ) )
                                                                                                   => ( X1 = X3 ) )
                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                      ( ( X1 = X2 )
                                                                                                     => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                        = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                        ( ( X1 = X2 )
                                                                                                       => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                          = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                          ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                            = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                         => ( ( X3 = X4 )
                                                                                                           => ( X2 = X4 ) ) )
                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                            ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                              = ( setadjoin @ X3 @ emptyset ) )
                                                                                                           => ( X1 = X2 ) )
                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                              ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                             => ( X2 = X4 ) )
                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                ( ( ( kpair @ X1 @ X2 )
                                                                                                                  = ( kpair @ X3 @ X4 ) )
                                                                                                               => ( X2 = X4 ) )
                                                                                                           => ( ! [X1: $i] :
                                                                                                                  ( ( iskpair @ X1 )
                                                                                                                 => ~ ! [X2: $i] :
                                                                                                                        ( ( in @ X2
                                                                                                                          @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                            @ ^ [X3: $i] :
                                                                                                                                ( X1
                                                                                                                                = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                       => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                            @ ^ [X3: $i] :
                                                                                                                                ( X1
                                                                                                                                = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                         != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                    ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                    = X2 )
                                                                                                               => ( sP8
                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                       => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                          ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                         => ( in @ X3 @ X1 ) )
                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                            ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                           => ( in @ X4 @ X2 ) )
                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                             => ! [X4: $i] :
                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                 => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                    = X3 ) ) )
                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                               => ! [X4: $i] :
                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                   => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                      = X4 ) ) )
                                                                                                                           => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                               => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                  = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h211,assumption,
    ! [X1: $i,X2: $i,X3: $i] :
      ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
     => ~ ( in @ X3 @ X2 ) ),
    introduced(assumption,[]) ).

thf(h212,assumption,
    ~ ( ! [X1: $i,X2: $i] :
          ( ( subset @ X1 @ X2 )
         => ( ( setminus @ X1 @ X2 )
            = emptyset ) )
     => ( ! [X1: $i,X2: $i,X3: $i] :
            ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
           => ( ( in @ X3 @ X1 )
             => ( in @ X3 @ X2 ) ) )
       => ( ! [X1: $i,X2: $i,X3: $i] :
              ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
             => ( ~ ( in @ X3 @ X2 )
               => ~ ( in @ X3 @ X1 ) ) )
         => ( ! [X1: $i,X2: $i,X3: $i] :
                ( ~ ( in @ X3 @ X1 )
               => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
           => ( ! [X1: $i,X2: $i,X3: $i] :
                  ( ( in @ X3 @ X2 )
                 => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
             => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
               => ( ! [X1: $i,X2: $i] :
                      ( ( ( setminus @ X1 @ X2 )
                        = emptyset )
                     => ( subset @ X1 @ X2 ) )
                 => ( ! [X1: $i,X2: $i,X3: $i] :
                        ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                       => ! [X4: $o] :
                            ( ( ( in @ X3 @ X1 )
                             => ( ~ ( in @ X3 @ X2 )
                               => X4 ) )
                           => ( ( ~ ( in @ X3 @ X1 )
                               => ( ( in @ X3 @ X2 )
                                 => X4 ) )
                             => X4 ) ) )
                   => ( ! [X1: $i,X2: $i,X3: $i] :
                          ( ( in @ X3 @ X1 )
                         => ( ~ ( in @ X3 @ X2 )
                           => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                     => ( ! [X1: $i,X2: $i,X3: $i] :
                            ( ~ ( in @ X3 @ X1 )
                           => ( ( in @ X3 @ X2 )
                             => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                       => ( ! [X1: $i,X2: $i,X3: $i] :
                              ( ( in @ X3 @ X1 )
                             => ( ( in @ X3 @ X2 )
                               => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                ( ~ ( in @ X3 @ X1 )
                               => ( ~ ( in @ X3 @ X2 )
                                 => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                           => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                             => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                               => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                 => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                   => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                     => ( ! [X1: $i,X2: $i] :
                                            ( ( in @ X2 @ X1 )
                                           => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                       => ( ! [X1: $i,X2: $i] :
                                              ( ( in @ X2 @ X1 )
                                             => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                ( ( in @ X3 @ X1 )
                                               => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                  ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                 => ( ( X3 != X1 )
                                                   => ( X3 = X2 ) ) )
                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                    ( ( in @ X3 @ X1 )
                                                   => ! [X4: $i] :
                                                        ( ( in @ X4 @ X2 )
                                                       => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                      ( ( in @ X3 @ X1 )
                                                     => ! [X4: $i] :
                                                          ( ( in @ X4 @ X2 )
                                                         => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                        ( ( in @ X3 @ X1 )
                                                       => ! [X4: $i] :
                                                            ( ( in @ X4 @ X2 )
                                                           => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                          ( ( in @ X3 @ X1 )
                                                         => ! [X4: $i] :
                                                              ( ( in @ X4 @ X2 )
                                                             => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                            ( ( in @ X3 @ X1 )
                                                           => ! [X4: $i] :
                                                                ( ( in @ X4 @ X2 )
                                                               => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                              ( ( in @ X3 @ X1 )
                                                             => ! [X4: $i] :
                                                                  ( ( in @ X4 @ X2 )
                                                                 => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                               => ~ ! [X4: $i] :
                                                                      ( ( in @ X4 @ X1 )
                                                                     => ! [X5: $i] :
                                                                          ( ( in @ X5 @ X2 )
                                                                         => ( X3
                                                                           != ( kpair @ X4 @ X5 ) ) ) ) )
                                                           => ( sP5
                                                             => ( ! [X1: $i,X2: $i] :
                                                                    ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                   => ~ ! [X3: $i] :
                                                                          ( ( in @ X3 @ X1 )
                                                                         => ~ ( in @ X2 @ X3 ) ) )
                                                               => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                 => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                   => ( ! [X1: $i] :
                                                                          ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                          = X1 )
                                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                                            ( ! [X3: $i] :
                                                                                ( ( in @ X3 @ X1 )
                                                                               => ! [X4: $i] :
                                                                                    ( ( in @ X4 @ X1 )
                                                                                   => ( ( X2 @ X3 )
                                                                                     => ( ( X2 @ X4 )
                                                                                       => ( X3 = X4 ) ) ) ) )
                                                                           => ( ~ ! [X3: $i] :
                                                                                    ( ( in @ X3 @ X1 )
                                                                                   => ~ ( X2 @ X3 ) )
                                                                             => ~ ! [X3: $i] :
                                                                                    ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                   => ( ( dsetconstr @ X1 @ X2 )
                                                                                     != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                       => ( ! [X1: $i,X2: $i > $o] :
                                                                              ( ~ ! [X3: $i] :
                                                                                    ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                   => ( ( dsetconstr @ X1 @ X2 )
                                                                                     != ( setadjoin @ X3 @ emptyset ) ) )
                                                                             => ~ ! [X3: $i] :
                                                                                    ( ( in @ X3 @ X1 )
                                                                                   => ~ ( X2 @ X3 ) ) )
                                                                         => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                ( ( in @ X3 @ X1 )
                                                                               => ( ( X2 @ X3 )
                                                                                 => ( ! [X4: $i] :
                                                                                        ( ( in @ X4 @ X1 )
                                                                                       => ( ( X2 @ X4 )
                                                                                         => ( X4 = X3 ) ) )
                                                                                   => ~ ! [X4: $i] :
                                                                                          ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                         => ( ( dsetconstr @ X1 @ X2 )
                                                                                           != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                           => ( ! [X1: $i,X2: $i > $o] :
                                                                                  ( ! [X3: $i] :
                                                                                      ( ( in @ X3 @ X1 )
                                                                                     => ! [X4: $i] :
                                                                                          ( ( in @ X4 @ X1 )
                                                                                         => ( ( X2 @ X3 )
                                                                                           => ( ( X2 @ X4 )
                                                                                             => ( X3 = X4 ) ) ) ) )
                                                                                 => ( ~ ! [X3: $i] :
                                                                                          ( ( in @ X3 @ X1 )
                                                                                         => ~ ( X2 @ X3 ) )
                                                                                   => ~ ! [X3: $i] :
                                                                                          ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                         => ( ( dsetconstr @ X1 @ X2 )
                                                                                           != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                    ( ( ( setadjoin @ X1 @ emptyset )
                                                                                      = ( setadjoin @ X2 @ emptyset ) )
                                                                                   => ( X1 = X2 ) )
                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                      ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                     => ( X1 = X3 ) )
                                                                                 => ( ! [X1: $i] :
                                                                                        ( ( iskpair @ X1 )
                                                                                       => ~ ! [X2: $i] :
                                                                                              ( ( in @ X2
                                                                                                @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                  @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                             => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                  @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                               != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                   => ( ! [X1: $i] :
                                                                                          ( ~ ! [X2: $i] :
                                                                                                ( ( in @ X2 @ X1 )
                                                                                               => ( X1
                                                                                                 != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                         => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                            ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                            = X1 )
                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                              ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                             => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                  = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                               => ( X1 = X3 ) )
                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                  ( ( ( kpair @ X1 @ X2 )
                                                                                                    = ( kpair @ X3 @ X4 ) )
                                                                                                 => ( X1 = X3 ) )
                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                    ( ( X1 = X2 )
                                                                                                   => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                      = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                      ( ( X1 = X2 )
                                                                                                     => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                        = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                        ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                          = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                       => ( ( X3 = X4 )
                                                                                                         => ( X2 = X4 ) ) )
                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                          ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                            = ( setadjoin @ X3 @ emptyset ) )
                                                                                                         => ( X1 = X2 ) )
                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                            ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                              = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                           => ( X2 = X4 ) )
                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                              ( ( ( kpair @ X1 @ X2 )
                                                                                                                = ( kpair @ X3 @ X4 ) )
                                                                                                             => ( X2 = X4 ) )
                                                                                                         => ( ! [X1: $i] :
                                                                                                                ( ( iskpair @ X1 )
                                                                                                               => ~ ! [X2: $i] :
                                                                                                                      ( ( in @ X2
                                                                                                                        @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                          @ ^ [X3: $i] :
                                                                                                                              ( X1
                                                                                                                              = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                     => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                          @ ^ [X3: $i] :
                                                                                                                              ( X1
                                                                                                                              = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                       != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                  ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                  = X2 )
                                                                                                             => ( sP8
                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                      ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                     => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                        ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                       => ( in @ X3 @ X1 ) )
                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                          ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                         => ( in @ X4 @ X2 ) )
                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                           => ! [X4: $i] :
                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                               => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                  = X3 ) ) )
                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                             => ! [X4: $i] :
                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                 => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                    = X4 ) ) )
                                                                                                                         => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                              ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                             => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h213,assumption,
    ! [X1: $i,X2: $i] :
      ( ( subset @ X1 @ X2 )
     => ( ( setminus @ X1 @ X2 )
        = emptyset ) ),
    introduced(assumption,[]) ).

thf(h214,assumption,
    ~ ( ! [X1: $i,X2: $i,X3: $i] :
          ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
         => ( ( in @ X3 @ X1 )
           => ( in @ X3 @ X2 ) ) )
     => ( ! [X1: $i,X2: $i,X3: $i] :
            ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
           => ( ~ ( in @ X3 @ X2 )
             => ~ ( in @ X3 @ X1 ) ) )
       => ( ! [X1: $i,X2: $i,X3: $i] :
              ( ~ ( in @ X3 @ X1 )
             => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
         => ( ! [X1: $i,X2: $i,X3: $i] :
                ( ( in @ X3 @ X2 )
               => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
           => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
             => ( ! [X1: $i,X2: $i] :
                    ( ( ( setminus @ X1 @ X2 )
                      = emptyset )
                   => ( subset @ X1 @ X2 ) )
               => ( ! [X1: $i,X2: $i,X3: $i] :
                      ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                     => ! [X4: $o] :
                          ( ( ( in @ X3 @ X1 )
                           => ( ~ ( in @ X3 @ X2 )
                             => X4 ) )
                         => ( ( ~ ( in @ X3 @ X1 )
                             => ( ( in @ X3 @ X2 )
                               => X4 ) )
                           => X4 ) ) )
                 => ( ! [X1: $i,X2: $i,X3: $i] :
                        ( ( in @ X3 @ X1 )
                       => ( ~ ( in @ X3 @ X2 )
                         => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                   => ( ! [X1: $i,X2: $i,X3: $i] :
                          ( ~ ( in @ X3 @ X1 )
                         => ( ( in @ X3 @ X2 )
                           => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                     => ( ! [X1: $i,X2: $i,X3: $i] :
                            ( ( in @ X3 @ X1 )
                           => ( ( in @ X3 @ X2 )
                             => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                       => ( ! [X1: $i,X2: $i,X3: $i] :
                              ( ~ ( in @ X3 @ X1 )
                             => ( ~ ( in @ X3 @ X2 )
                               => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                         => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                           => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                             => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                               => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                 => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                   => ( ! [X1: $i,X2: $i] :
                                          ( ( in @ X2 @ X1 )
                                         => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                     => ( ! [X1: $i,X2: $i] :
                                            ( ( in @ X2 @ X1 )
                                           => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                              ( ( in @ X3 @ X1 )
                                             => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                               => ( ( X3 != X1 )
                                                 => ( X3 = X2 ) ) )
                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                  ( ( in @ X3 @ X1 )
                                                 => ! [X4: $i] :
                                                      ( ( in @ X4 @ X2 )
                                                     => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                    ( ( in @ X3 @ X1 )
                                                   => ! [X4: $i] :
                                                        ( ( in @ X4 @ X2 )
                                                       => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                      ( ( in @ X3 @ X1 )
                                                     => ! [X4: $i] :
                                                          ( ( in @ X4 @ X2 )
                                                         => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                        ( ( in @ X3 @ X1 )
                                                       => ! [X4: $i] :
                                                            ( ( in @ X4 @ X2 )
                                                           => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                          ( ( in @ X3 @ X1 )
                                                         => ! [X4: $i] :
                                                              ( ( in @ X4 @ X2 )
                                                             => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                            ( ( in @ X3 @ X1 )
                                                           => ! [X4: $i] :
                                                                ( ( in @ X4 @ X2 )
                                                               => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                              ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                             => ~ ! [X4: $i] :
                                                                    ( ( in @ X4 @ X1 )
                                                                   => ! [X5: $i] :
                                                                        ( ( in @ X5 @ X2 )
                                                                       => ( X3
                                                                         != ( kpair @ X4 @ X5 ) ) ) ) )
                                                         => ( sP5
                                                           => ( ! [X1: $i,X2: $i] :
                                                                  ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                 => ~ ! [X3: $i] :
                                                                        ( ( in @ X3 @ X1 )
                                                                       => ~ ( in @ X2 @ X3 ) ) )
                                                             => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                               => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                 => ( ! [X1: $i] :
                                                                        ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                        = X1 )
                                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                                          ( ! [X3: $i] :
                                                                              ( ( in @ X3 @ X1 )
                                                                             => ! [X4: $i] :
                                                                                  ( ( in @ X4 @ X1 )
                                                                                 => ( ( X2 @ X3 )
                                                                                   => ( ( X2 @ X4 )
                                                                                     => ( X3 = X4 ) ) ) ) )
                                                                         => ( ~ ! [X3: $i] :
                                                                                  ( ( in @ X3 @ X1 )
                                                                                 => ~ ( X2 @ X3 ) )
                                                                           => ~ ! [X3: $i] :
                                                                                  ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                 => ( ( dsetconstr @ X1 @ X2 )
                                                                                   != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                                            ( ~ ! [X3: $i] :
                                                                                  ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                 => ( ( dsetconstr @ X1 @ X2 )
                                                                                   != ( setadjoin @ X3 @ emptyset ) ) )
                                                                           => ~ ! [X3: $i] :
                                                                                  ( ( in @ X3 @ X1 )
                                                                                 => ~ ( X2 @ X3 ) ) )
                                                                       => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                              ( ( in @ X3 @ X1 )
                                                                             => ( ( X2 @ X3 )
                                                                               => ( ! [X4: $i] :
                                                                                      ( ( in @ X4 @ X1 )
                                                                                     => ( ( X2 @ X4 )
                                                                                       => ( X4 = X3 ) ) )
                                                                                 => ~ ! [X4: $i] :
                                                                                        ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                       => ( ( dsetconstr @ X1 @ X2 )
                                                                                         != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                         => ( ! [X1: $i,X2: $i > $o] :
                                                                                ( ! [X3: $i] :
                                                                                    ( ( in @ X3 @ X1 )
                                                                                   => ! [X4: $i] :
                                                                                        ( ( in @ X4 @ X1 )
                                                                                       => ( ( X2 @ X3 )
                                                                                         => ( ( X2 @ X4 )
                                                                                           => ( X3 = X4 ) ) ) ) )
                                                                               => ( ~ ! [X3: $i] :
                                                                                        ( ( in @ X3 @ X1 )
                                                                                       => ~ ( X2 @ X3 ) )
                                                                                 => ~ ! [X3: $i] :
                                                                                        ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                       => ( ( dsetconstr @ X1 @ X2 )
                                                                                         != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                  ( ( ( setadjoin @ X1 @ emptyset )
                                                                                    = ( setadjoin @ X2 @ emptyset ) )
                                                                                 => ( X1 = X2 ) )
                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                    ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                   => ( X1 = X3 ) )
                                                                               => ( ! [X1: $i] :
                                                                                      ( ( iskpair @ X1 )
                                                                                     => ~ ! [X2: $i] :
                                                                                            ( ( in @ X2
                                                                                              @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                           => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                             != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                 => ( ! [X1: $i] :
                                                                                        ( ~ ! [X2: $i] :
                                                                                              ( ( in @ X2 @ X1 )
                                                                                             => ( X1
                                                                                               != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                       => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                          ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                          = X1 )
                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                            ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                           => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                              ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                             => ( X1 = X3 ) )
                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                ( ( ( kpair @ X1 @ X2 )
                                                                                                  = ( kpair @ X3 @ X4 ) )
                                                                                               => ( X1 = X3 ) )
                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                  ( ( X1 = X2 )
                                                                                                 => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                    = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                    ( ( X1 = X2 )
                                                                                                   => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                      = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                      ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                        = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                     => ( ( X3 = X4 )
                                                                                                       => ( X2 = X4 ) ) )
                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                        ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                          = ( setadjoin @ X3 @ emptyset ) )
                                                                                                       => ( X1 = X2 ) )
                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                          ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                            = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                         => ( X2 = X4 ) )
                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                            ( ( ( kpair @ X1 @ X2 )
                                                                                                              = ( kpair @ X3 @ X4 ) )
                                                                                                           => ( X2 = X4 ) )
                                                                                                       => ( ! [X1: $i] :
                                                                                                              ( ( iskpair @ X1 )
                                                                                                             => ~ ! [X2: $i] :
                                                                                                                    ( ( in @ X2
                                                                                                                      @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                        @ ^ [X3: $i] :
                                                                                                                            ( X1
                                                                                                                            = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                   => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                        @ ^ [X3: $i] :
                                                                                                                            ( X1
                                                                                                                            = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                     != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                = X2 )
                                                                                                           => ( sP8
                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                    ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                   => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                      ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                     => ( in @ X3 @ X1 ) )
                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                        ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                       => ( in @ X4 @ X2 ) )
                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                         => ! [X4: $i] :
                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                             => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                = X3 ) ) )
                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                           => ! [X4: $i] :
                                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                                               => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                  = X4 ) ) )
                                                                                                                       => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                            ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                           => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                              = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h215,assumption,
    ! [X1: $i,X2: $i,X3: $i] :
      ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
     => ( ( in @ X3 @ X1 )
       => ( in @ X3 @ X2 ) ) ),
    introduced(assumption,[]) ).

thf(h216,assumption,
    ~ ( ! [X1: $i,X2: $i,X3: $i] :
          ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
         => ( ~ ( in @ X3 @ X2 )
           => ~ ( in @ X3 @ X1 ) ) )
     => ( ! [X1: $i,X2: $i,X3: $i] :
            ( ~ ( in @ X3 @ X1 )
           => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
       => ( ! [X1: $i,X2: $i,X3: $i] :
              ( ( in @ X3 @ X2 )
             => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
         => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
           => ( ! [X1: $i,X2: $i] :
                  ( ( ( setminus @ X1 @ X2 )
                    = emptyset )
                 => ( subset @ X1 @ X2 ) )
             => ( ! [X1: $i,X2: $i,X3: $i] :
                    ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                   => ! [X4: $o] :
                        ( ( ( in @ X3 @ X1 )
                         => ( ~ ( in @ X3 @ X2 )
                           => X4 ) )
                       => ( ( ~ ( in @ X3 @ X1 )
                           => ( ( in @ X3 @ X2 )
                             => X4 ) )
                         => X4 ) ) )
               => ( ! [X1: $i,X2: $i,X3: $i] :
                      ( ( in @ X3 @ X1 )
                     => ( ~ ( in @ X3 @ X2 )
                       => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                 => ( ! [X1: $i,X2: $i,X3: $i] :
                        ( ~ ( in @ X3 @ X1 )
                       => ( ( in @ X3 @ X2 )
                         => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                   => ( ! [X1: $i,X2: $i,X3: $i] :
                          ( ( in @ X3 @ X1 )
                         => ( ( in @ X3 @ X2 )
                           => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                     => ( ! [X1: $i,X2: $i,X3: $i] :
                            ( ~ ( in @ X3 @ X1 )
                           => ( ~ ( in @ X3 @ X2 )
                             => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                       => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                         => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                           => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                             => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                               => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                 => ( ! [X1: $i,X2: $i] :
                                        ( ( in @ X2 @ X1 )
                                       => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                   => ( ! [X1: $i,X2: $i] :
                                          ( ( in @ X2 @ X1 )
                                         => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                            ( ( in @ X3 @ X1 )
                                           => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                              ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                             => ( ( X3 != X1 )
                                               => ( X3 = X2 ) ) )
                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                ( ( in @ X3 @ X1 )
                                               => ! [X4: $i] :
                                                    ( ( in @ X4 @ X2 )
                                                   => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                  ( ( in @ X3 @ X1 )
                                                 => ! [X4: $i] :
                                                      ( ( in @ X4 @ X2 )
                                                     => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                    ( ( in @ X3 @ X1 )
                                                   => ! [X4: $i] :
                                                        ( ( in @ X4 @ X2 )
                                                       => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                      ( ( in @ X3 @ X1 )
                                                     => ! [X4: $i] :
                                                          ( ( in @ X4 @ X2 )
                                                         => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                        ( ( in @ X3 @ X1 )
                                                       => ! [X4: $i] :
                                                            ( ( in @ X4 @ X2 )
                                                           => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                          ( ( in @ X3 @ X1 )
                                                         => ! [X4: $i] :
                                                              ( ( in @ X4 @ X2 )
                                                             => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                            ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                           => ~ ! [X4: $i] :
                                                                  ( ( in @ X4 @ X1 )
                                                                 => ! [X5: $i] :
                                                                      ( ( in @ X5 @ X2 )
                                                                     => ( X3
                                                                       != ( kpair @ X4 @ X5 ) ) ) ) )
                                                       => ( sP5
                                                         => ( ! [X1: $i,X2: $i] :
                                                                ( ( in @ X2 @ ( setunion @ X1 ) )
                                                               => ~ ! [X3: $i] :
                                                                      ( ( in @ X3 @ X1 )
                                                                     => ~ ( in @ X2 @ X3 ) ) )
                                                           => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                             => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                               => ( ! [X1: $i] :
                                                                      ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                      = X1 )
                                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                                        ( ! [X3: $i] :
                                                                            ( ( in @ X3 @ X1 )
                                                                           => ! [X4: $i] :
                                                                                ( ( in @ X4 @ X1 )
                                                                               => ( ( X2 @ X3 )
                                                                                 => ( ( X2 @ X4 )
                                                                                   => ( X3 = X4 ) ) ) ) )
                                                                       => ( ~ ! [X3: $i] :
                                                                                ( ( in @ X3 @ X1 )
                                                                               => ~ ( X2 @ X3 ) )
                                                                         => ~ ! [X3: $i] :
                                                                                ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                               => ( ( dsetconstr @ X1 @ X2 )
                                                                                 != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                                          ( ~ ! [X3: $i] :
                                                                                ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                               => ( ( dsetconstr @ X1 @ X2 )
                                                                                 != ( setadjoin @ X3 @ emptyset ) ) )
                                                                         => ~ ! [X3: $i] :
                                                                                ( ( in @ X3 @ X1 )
                                                                               => ~ ( X2 @ X3 ) ) )
                                                                     => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                            ( ( in @ X3 @ X1 )
                                                                           => ( ( X2 @ X3 )
                                                                             => ( ! [X4: $i] :
                                                                                    ( ( in @ X4 @ X1 )
                                                                                   => ( ( X2 @ X4 )
                                                                                     => ( X4 = X3 ) ) )
                                                                               => ~ ! [X4: $i] :
                                                                                      ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                     => ( ( dsetconstr @ X1 @ X2 )
                                                                                       != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                       => ( ! [X1: $i,X2: $i > $o] :
                                                                              ( ! [X3: $i] :
                                                                                  ( ( in @ X3 @ X1 )
                                                                                 => ! [X4: $i] :
                                                                                      ( ( in @ X4 @ X1 )
                                                                                     => ( ( X2 @ X3 )
                                                                                       => ( ( X2 @ X4 )
                                                                                         => ( X3 = X4 ) ) ) ) )
                                                                             => ( ~ ! [X3: $i] :
                                                                                      ( ( in @ X3 @ X1 )
                                                                                     => ~ ( X2 @ X3 ) )
                                                                               => ~ ! [X3: $i] :
                                                                                      ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                     => ( ( dsetconstr @ X1 @ X2 )
                                                                                       != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                ( ( ( setadjoin @ X1 @ emptyset )
                                                                                  = ( setadjoin @ X2 @ emptyset ) )
                                                                               => ( X1 = X2 ) )
                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                  ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                 => ( X1 = X3 ) )
                                                                             => ( ! [X1: $i] :
                                                                                    ( ( iskpair @ X1 )
                                                                                   => ~ ! [X2: $i] :
                                                                                          ( ( in @ X2
                                                                                            @ ( dsetconstr @ ( setunion @ X1 )
                                                                                              @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                         => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                              @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                           != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                               => ( ! [X1: $i] :
                                                                                      ( ~ ! [X2: $i] :
                                                                                            ( ( in @ X2 @ X1 )
                                                                                           => ( X1
                                                                                             != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                     => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                        ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                        = X1 )
                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                         => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                            ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                              = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                           => ( X1 = X3 ) )
                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                              ( ( ( kpair @ X1 @ X2 )
                                                                                                = ( kpair @ X3 @ X4 ) )
                                                                                             => ( X1 = X3 ) )
                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                ( ( X1 = X2 )
                                                                                               => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                  = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                  ( ( X1 = X2 )
                                                                                                 => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                    = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                    ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                      = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                   => ( ( X3 = X4 )
                                                                                                     => ( X2 = X4 ) ) )
                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                      ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                        = ( setadjoin @ X3 @ emptyset ) )
                                                                                                     => ( X1 = X2 ) )
                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                        ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                          = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                       => ( X2 = X4 ) )
                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                          ( ( ( kpair @ X1 @ X2 )
                                                                                                            = ( kpair @ X3 @ X4 ) )
                                                                                                         => ( X2 = X4 ) )
                                                                                                     => ( ! [X1: $i] :
                                                                                                            ( ( iskpair @ X1 )
                                                                                                           => ~ ! [X2: $i] :
                                                                                                                  ( ( in @ X2
                                                                                                                    @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                      @ ^ [X3: $i] :
                                                                                                                          ( X1
                                                                                                                          = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                 => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                      @ ^ [X3: $i] :
                                                                                                                          ( X1
                                                                                                                          = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                   != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                              ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                              = X2 )
                                                                                                         => ( sP8
                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                  ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                 => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                    ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                   => ( in @ X3 @ X1 ) )
                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                      ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                     => ( in @ X4 @ X2 ) )
                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                       => ! [X4: $i] :
                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                           => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                              = X3 ) ) )
                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                         => ! [X4: $i] :
                                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                                             => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                = X4 ) ) )
                                                                                                                     => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                         => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                            = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h217,assumption,
    ! [X1: $i,X2: $i,X3: $i] :
      ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
     => ( ~ ( in @ X3 @ X2 )
       => ~ ( in @ X3 @ X1 ) ) ),
    introduced(assumption,[]) ).

thf(h218,assumption,
    ~ ( ! [X1: $i,X2: $i,X3: $i] :
          ( ~ ( in @ X3 @ X1 )
         => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
     => ( ! [X1: $i,X2: $i,X3: $i] :
            ( ( in @ X3 @ X2 )
           => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
       => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
         => ( ! [X1: $i,X2: $i] :
                ( ( ( setminus @ X1 @ X2 )
                  = emptyset )
               => ( subset @ X1 @ X2 ) )
           => ( ! [X1: $i,X2: $i,X3: $i] :
                  ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                 => ! [X4: $o] :
                      ( ( ( in @ X3 @ X1 )
                       => ( ~ ( in @ X3 @ X2 )
                         => X4 ) )
                     => ( ( ~ ( in @ X3 @ X1 )
                         => ( ( in @ X3 @ X2 )
                           => X4 ) )
                       => X4 ) ) )
             => ( ! [X1: $i,X2: $i,X3: $i] :
                    ( ( in @ X3 @ X1 )
                   => ( ~ ( in @ X3 @ X2 )
                     => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
               => ( ! [X1: $i,X2: $i,X3: $i] :
                      ( ~ ( in @ X3 @ X1 )
                     => ( ( in @ X3 @ X2 )
                       => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                 => ( ! [X1: $i,X2: $i,X3: $i] :
                        ( ( in @ X3 @ X1 )
                       => ( ( in @ X3 @ X2 )
                         => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                   => ( ! [X1: $i,X2: $i,X3: $i] :
                          ( ~ ( in @ X3 @ X1 )
                         => ( ~ ( in @ X3 @ X2 )
                           => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                     => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                       => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                         => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                           => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                             => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                               => ( ! [X1: $i,X2: $i] :
                                      ( ( in @ X2 @ X1 )
                                     => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                 => ( ! [X1: $i,X2: $i] :
                                        ( ( in @ X2 @ X1 )
                                       => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                          ( ( in @ X3 @ X1 )
                                         => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                            ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                           => ( ( X3 != X1 )
                                             => ( X3 = X2 ) ) )
                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                              ( ( in @ X3 @ X1 )
                                             => ! [X4: $i] :
                                                  ( ( in @ X4 @ X2 )
                                                 => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                ( ( in @ X3 @ X1 )
                                               => ! [X4: $i] :
                                                    ( ( in @ X4 @ X2 )
                                                   => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                  ( ( in @ X3 @ X1 )
                                                 => ! [X4: $i] :
                                                      ( ( in @ X4 @ X2 )
                                                     => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                    ( ( in @ X3 @ X1 )
                                                   => ! [X4: $i] :
                                                        ( ( in @ X4 @ X2 )
                                                       => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                      ( ( in @ X3 @ X1 )
                                                     => ! [X4: $i] :
                                                          ( ( in @ X4 @ X2 )
                                                         => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                        ( ( in @ X3 @ X1 )
                                                       => ! [X4: $i] :
                                                            ( ( in @ X4 @ X2 )
                                                           => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                         => ~ ! [X4: $i] :
                                                                ( ( in @ X4 @ X1 )
                                                               => ! [X5: $i] :
                                                                    ( ( in @ X5 @ X2 )
                                                                   => ( X3
                                                                     != ( kpair @ X4 @ X5 ) ) ) ) )
                                                     => ( sP5
                                                       => ( ! [X1: $i,X2: $i] :
                                                              ( ( in @ X2 @ ( setunion @ X1 ) )
                                                             => ~ ! [X3: $i] :
                                                                    ( ( in @ X3 @ X1 )
                                                                   => ~ ( in @ X2 @ X3 ) ) )
                                                         => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                           => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                             => ( ! [X1: $i] :
                                                                    ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                    = X1 )
                                                               => ( ! [X1: $i,X2: $i > $o] :
                                                                      ( ! [X3: $i] :
                                                                          ( ( in @ X3 @ X1 )
                                                                         => ! [X4: $i] :
                                                                              ( ( in @ X4 @ X1 )
                                                                             => ( ( X2 @ X3 )
                                                                               => ( ( X2 @ X4 )
                                                                                 => ( X3 = X4 ) ) ) ) )
                                                                     => ( ~ ! [X3: $i] :
                                                                              ( ( in @ X3 @ X1 )
                                                                             => ~ ( X2 @ X3 ) )
                                                                       => ~ ! [X3: $i] :
                                                                              ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                             => ( ( dsetconstr @ X1 @ X2 )
                                                                               != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                                        ( ~ ! [X3: $i] :
                                                                              ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                             => ( ( dsetconstr @ X1 @ X2 )
                                                                               != ( setadjoin @ X3 @ emptyset ) ) )
                                                                       => ~ ! [X3: $i] :
                                                                              ( ( in @ X3 @ X1 )
                                                                             => ~ ( X2 @ X3 ) ) )
                                                                   => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                          ( ( in @ X3 @ X1 )
                                                                         => ( ( X2 @ X3 )
                                                                           => ( ! [X4: $i] :
                                                                                  ( ( in @ X4 @ X1 )
                                                                                 => ( ( X2 @ X4 )
                                                                                   => ( X4 = X3 ) ) )
                                                                             => ~ ! [X4: $i] :
                                                                                    ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                   => ( ( dsetconstr @ X1 @ X2 )
                                                                                     != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                                            ( ! [X3: $i] :
                                                                                ( ( in @ X3 @ X1 )
                                                                               => ! [X4: $i] :
                                                                                    ( ( in @ X4 @ X1 )
                                                                                   => ( ( X2 @ X3 )
                                                                                     => ( ( X2 @ X4 )
                                                                                       => ( X3 = X4 ) ) ) ) )
                                                                           => ( ~ ! [X3: $i] :
                                                                                    ( ( in @ X3 @ X1 )
                                                                                   => ~ ( X2 @ X3 ) )
                                                                             => ~ ! [X3: $i] :
                                                                                    ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                   => ( ( dsetconstr @ X1 @ X2 )
                                                                                     != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                       => ( ! [X1: $i,X2: $i] :
                                                                              ( ( ( setadjoin @ X1 @ emptyset )
                                                                                = ( setadjoin @ X2 @ emptyset ) )
                                                                             => ( X1 = X2 ) )
                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                               => ( X1 = X3 ) )
                                                                           => ( ! [X1: $i] :
                                                                                  ( ( iskpair @ X1 )
                                                                                 => ~ ! [X2: $i] :
                                                                                        ( ( in @ X2
                                                                                          @ ( dsetconstr @ ( setunion @ X1 )
                                                                                            @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                       => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                            @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                         != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                             => ( ! [X1: $i] :
                                                                                    ( ~ ! [X2: $i] :
                                                                                          ( ( in @ X2 @ X1 )
                                                                                         => ( X1
                                                                                           != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                   => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                      ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                      = X1 )
                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                       => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                          ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                            = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                         => ( X1 = X3 ) )
                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                            ( ( ( kpair @ X1 @ X2 )
                                                                                              = ( kpair @ X3 @ X4 ) )
                                                                                           => ( X1 = X3 ) )
                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                              ( ( X1 = X2 )
                                                                                             => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                ( ( X1 = X2 )
                                                                                               => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                  = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                  ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                    = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                 => ( ( X3 = X4 )
                                                                                                   => ( X2 = X4 ) ) )
                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                    ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                      = ( setadjoin @ X3 @ emptyset ) )
                                                                                                   => ( X1 = X2 ) )
                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                      ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                        = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                     => ( X2 = X4 ) )
                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                        ( ( ( kpair @ X1 @ X2 )
                                                                                                          = ( kpair @ X3 @ X4 ) )
                                                                                                       => ( X2 = X4 ) )
                                                                                                   => ( ! [X1: $i] :
                                                                                                          ( ( iskpair @ X1 )
                                                                                                         => ~ ! [X2: $i] :
                                                                                                                ( ( in @ X2
                                                                                                                  @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                    @ ^ [X3: $i] :
                                                                                                                        ( X1
                                                                                                                        = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                               => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                    @ ^ [X3: $i] :
                                                                                                                        ( X1
                                                                                                                        = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                 != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                            ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                            = X2 )
                                                                                                       => ( sP8
                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                               => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                  ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                 => ( in @ X3 @ X1 ) )
                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                    ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                   => ( in @ X4 @ X2 ) )
                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                     => ! [X4: $i] :
                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                         => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                            = X3 ) ) )
                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                       => ! [X4: $i] :
                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                           => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                              = X4 ) ) )
                                                                                                                   => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                       => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                          = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h219,assumption,
    ! [X1: $i,X2: $i,X3: $i] :
      ( ~ ( in @ X3 @ X1 )
     => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ),
    introduced(assumption,[]) ).

thf(h220,assumption,
    ~ ( ! [X1: $i,X2: $i,X3: $i] :
          ( ( in @ X3 @ X2 )
         => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
     => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
       => ( ! [X1: $i,X2: $i] :
              ( ( ( setminus @ X1 @ X2 )
                = emptyset )
             => ( subset @ X1 @ X2 ) )
         => ( ! [X1: $i,X2: $i,X3: $i] :
                ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
               => ! [X4: $o] :
                    ( ( ( in @ X3 @ X1 )
                     => ( ~ ( in @ X3 @ X2 )
                       => X4 ) )
                   => ( ( ~ ( in @ X3 @ X1 )
                       => ( ( in @ X3 @ X2 )
                         => X4 ) )
                     => X4 ) ) )
           => ( ! [X1: $i,X2: $i,X3: $i] :
                  ( ( in @ X3 @ X1 )
                 => ( ~ ( in @ X3 @ X2 )
                   => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
             => ( ! [X1: $i,X2: $i,X3: $i] :
                    ( ~ ( in @ X3 @ X1 )
                   => ( ( in @ X3 @ X2 )
                     => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
               => ( ! [X1: $i,X2: $i,X3: $i] :
                      ( ( in @ X3 @ X1 )
                     => ( ( in @ X3 @ X2 )
                       => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                 => ( ! [X1: $i,X2: $i,X3: $i] :
                        ( ~ ( in @ X3 @ X1 )
                       => ( ~ ( in @ X3 @ X2 )
                         => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                   => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                     => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                       => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                         => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                           => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                             => ( ! [X1: $i,X2: $i] :
                                    ( ( in @ X2 @ X1 )
                                   => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                               => ( ! [X1: $i,X2: $i] :
                                      ( ( in @ X2 @ X1 )
                                     => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                        ( ( in @ X3 @ X1 )
                                       => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                          ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                         => ( ( X3 != X1 )
                                           => ( X3 = X2 ) ) )
                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                            ( ( in @ X3 @ X1 )
                                           => ! [X4: $i] :
                                                ( ( in @ X4 @ X2 )
                                               => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                              ( ( in @ X3 @ X1 )
                                             => ! [X4: $i] :
                                                  ( ( in @ X4 @ X2 )
                                                 => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                ( ( in @ X3 @ X1 )
                                               => ! [X4: $i] :
                                                    ( ( in @ X4 @ X2 )
                                                   => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                  ( ( in @ X3 @ X1 )
                                                 => ! [X4: $i] :
                                                      ( ( in @ X4 @ X2 )
                                                     => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                    ( ( in @ X3 @ X1 )
                                                   => ! [X4: $i] :
                                                        ( ( in @ X4 @ X2 )
                                                       => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                      ( ( in @ X3 @ X1 )
                                                     => ! [X4: $i] :
                                                          ( ( in @ X4 @ X2 )
                                                         => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                       => ~ ! [X4: $i] :
                                                              ( ( in @ X4 @ X1 )
                                                             => ! [X5: $i] :
                                                                  ( ( in @ X5 @ X2 )
                                                                 => ( X3
                                                                   != ( kpair @ X4 @ X5 ) ) ) ) )
                                                   => ( sP5
                                                     => ( ! [X1: $i,X2: $i] :
                                                            ( ( in @ X2 @ ( setunion @ X1 ) )
                                                           => ~ ! [X3: $i] :
                                                                  ( ( in @ X3 @ X1 )
                                                                 => ~ ( in @ X2 @ X3 ) ) )
                                                       => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                         => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                           => ( ! [X1: $i] :
                                                                  ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                  = X1 )
                                                             => ( ! [X1: $i,X2: $i > $o] :
                                                                    ( ! [X3: $i] :
                                                                        ( ( in @ X3 @ X1 )
                                                                       => ! [X4: $i] :
                                                                            ( ( in @ X4 @ X1 )
                                                                           => ( ( X2 @ X3 )
                                                                             => ( ( X2 @ X4 )
                                                                               => ( X3 = X4 ) ) ) ) )
                                                                   => ( ~ ! [X3: $i] :
                                                                            ( ( in @ X3 @ X1 )
                                                                           => ~ ( X2 @ X3 ) )
                                                                     => ~ ! [X3: $i] :
                                                                            ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                           => ( ( dsetconstr @ X1 @ X2 )
                                                                             != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                               => ( ! [X1: $i,X2: $i > $o] :
                                                                      ( ~ ! [X3: $i] :
                                                                            ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                           => ( ( dsetconstr @ X1 @ X2 )
                                                                             != ( setadjoin @ X3 @ emptyset ) ) )
                                                                     => ~ ! [X3: $i] :
                                                                            ( ( in @ X3 @ X1 )
                                                                           => ~ ( X2 @ X3 ) ) )
                                                                 => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                        ( ( in @ X3 @ X1 )
                                                                       => ( ( X2 @ X3 )
                                                                         => ( ! [X4: $i] :
                                                                                ( ( in @ X4 @ X1 )
                                                                               => ( ( X2 @ X4 )
                                                                                 => ( X4 = X3 ) ) )
                                                                           => ~ ! [X4: $i] :
                                                                                  ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                 => ( ( dsetconstr @ X1 @ X2 )
                                                                                   != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                                          ( ! [X3: $i] :
                                                                              ( ( in @ X3 @ X1 )
                                                                             => ! [X4: $i] :
                                                                                  ( ( in @ X4 @ X1 )
                                                                                 => ( ( X2 @ X3 )
                                                                                   => ( ( X2 @ X4 )
                                                                                     => ( X3 = X4 ) ) ) ) )
                                                                         => ( ~ ! [X3: $i] :
                                                                                  ( ( in @ X3 @ X1 )
                                                                                 => ~ ( X2 @ X3 ) )
                                                                           => ~ ! [X3: $i] :
                                                                                  ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                 => ( ( dsetconstr @ X1 @ X2 )
                                                                                   != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                     => ( ! [X1: $i,X2: $i] :
                                                                            ( ( ( setadjoin @ X1 @ emptyset )
                                                                              = ( setadjoin @ X2 @ emptyset ) )
                                                                           => ( X1 = X2 ) )
                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                              ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                             => ( X1 = X3 ) )
                                                                         => ( ! [X1: $i] :
                                                                                ( ( iskpair @ X1 )
                                                                               => ~ ! [X2: $i] :
                                                                                      ( ( in @ X2
                                                                                        @ ( dsetconstr @ ( setunion @ X1 )
                                                                                          @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                     => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                          @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                       != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                           => ( ! [X1: $i] :
                                                                                  ( ~ ! [X2: $i] :
                                                                                        ( ( in @ X2 @ X1 )
                                                                                       => ( X1
                                                                                         != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                 => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                    ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                    = X1 )
                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                      ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                     => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                        ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                          = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                       => ( X1 = X3 ) )
                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                          ( ( ( kpair @ X1 @ X2 )
                                                                                            = ( kpair @ X3 @ X4 ) )
                                                                                         => ( X1 = X3 ) )
                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                            ( ( X1 = X2 )
                                                                                           => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                              = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                              ( ( X1 = X2 )
                                                                                             => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                  = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                               => ( ( X3 = X4 )
                                                                                                 => ( X2 = X4 ) ) )
                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                  ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                    = ( setadjoin @ X3 @ emptyset ) )
                                                                                                 => ( X1 = X2 ) )
                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                    ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                      = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                   => ( X2 = X4 ) )
                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                      ( ( ( kpair @ X1 @ X2 )
                                                                                                        = ( kpair @ X3 @ X4 ) )
                                                                                                     => ( X2 = X4 ) )
                                                                                                 => ( ! [X1: $i] :
                                                                                                        ( ( iskpair @ X1 )
                                                                                                       => ~ ! [X2: $i] :
                                                                                                              ( ( in @ X2
                                                                                                                @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                  @ ^ [X3: $i] :
                                                                                                                      ( X1
                                                                                                                      = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                             => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                  @ ^ [X3: $i] :
                                                                                                                      ( X1
                                                                                                                      = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                               != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                          ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                          = X2 )
                                                                                                     => ( sP8
                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                              ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                             => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                               => ( in @ X3 @ X1 ) )
                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                  ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                 => ( in @ X4 @ X2 ) )
                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                   => ! [X4: $i] :
                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                       => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                          = X3 ) ) )
                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                     => ! [X4: $i] :
                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                         => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                            = X4 ) ) )
                                                                                                                 => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                      ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                     => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                        = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h221,assumption,
    ! [X1: $i,X2: $i,X3: $i] :
      ( ( in @ X3 @ X2 )
     => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ),
    introduced(assumption,[]) ).

thf(h222,assumption,
    ~ ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
     => ( ! [X1: $i,X2: $i] :
            ( ( ( setminus @ X1 @ X2 )
              = emptyset )
           => ( subset @ X1 @ X2 ) )
       => ( ! [X1: $i,X2: $i,X3: $i] :
              ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
             => ! [X4: $o] :
                  ( ( ( in @ X3 @ X1 )
                   => ( ~ ( in @ X3 @ X2 )
                     => X4 ) )
                 => ( ( ~ ( in @ X3 @ X1 )
                     => ( ( in @ X3 @ X2 )
                       => X4 ) )
                   => X4 ) ) )
         => ( ! [X1: $i,X2: $i,X3: $i] :
                ( ( in @ X3 @ X1 )
               => ( ~ ( in @ X3 @ X2 )
                 => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
           => ( ! [X1: $i,X2: $i,X3: $i] :
                  ( ~ ( in @ X3 @ X1 )
                 => ( ( in @ X3 @ X2 )
                   => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
             => ( ! [X1: $i,X2: $i,X3: $i] :
                    ( ( in @ X3 @ X1 )
                   => ( ( in @ X3 @ X2 )
                     => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
               => ( ! [X1: $i,X2: $i,X3: $i] :
                      ( ~ ( in @ X3 @ X1 )
                     => ( ~ ( in @ X3 @ X2 )
                       => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                 => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                   => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                     => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                       => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                         => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                           => ( ! [X1: $i,X2: $i] :
                                  ( ( in @ X2 @ X1 )
                                 => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                             => ( ! [X1: $i,X2: $i] :
                                    ( ( in @ X2 @ X1 )
                                   => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                      ( ( in @ X3 @ X1 )
                                     => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                        ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                       => ( ( X3 != X1 )
                                         => ( X3 = X2 ) ) )
                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                          ( ( in @ X3 @ X1 )
                                         => ! [X4: $i] :
                                              ( ( in @ X4 @ X2 )
                                             => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                            ( ( in @ X3 @ X1 )
                                           => ! [X4: $i] :
                                                ( ( in @ X4 @ X2 )
                                               => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                              ( ( in @ X3 @ X1 )
                                             => ! [X4: $i] :
                                                  ( ( in @ X4 @ X2 )
                                                 => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                ( ( in @ X3 @ X1 )
                                               => ! [X4: $i] :
                                                    ( ( in @ X4 @ X2 )
                                                   => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                  ( ( in @ X3 @ X1 )
                                                 => ! [X4: $i] :
                                                      ( ( in @ X4 @ X2 )
                                                     => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                    ( ( in @ X3 @ X1 )
                                                   => ! [X4: $i] :
                                                        ( ( in @ X4 @ X2 )
                                                       => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                      ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                     => ~ ! [X4: $i] :
                                                            ( ( in @ X4 @ X1 )
                                                           => ! [X5: $i] :
                                                                ( ( in @ X5 @ X2 )
                                                               => ( X3
                                                                 != ( kpair @ X4 @ X5 ) ) ) ) )
                                                 => ( sP5
                                                   => ( ! [X1: $i,X2: $i] :
                                                          ( ( in @ X2 @ ( setunion @ X1 ) )
                                                         => ~ ! [X3: $i] :
                                                                ( ( in @ X3 @ X1 )
                                                               => ~ ( in @ X2 @ X3 ) ) )
                                                     => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                       => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                         => ( ! [X1: $i] :
                                                                ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                = X1 )
                                                           => ( ! [X1: $i,X2: $i > $o] :
                                                                  ( ! [X3: $i] :
                                                                      ( ( in @ X3 @ X1 )
                                                                     => ! [X4: $i] :
                                                                          ( ( in @ X4 @ X1 )
                                                                         => ( ( X2 @ X3 )
                                                                           => ( ( X2 @ X4 )
                                                                             => ( X3 = X4 ) ) ) ) )
                                                                 => ( ~ ! [X3: $i] :
                                                                          ( ( in @ X3 @ X1 )
                                                                         => ~ ( X2 @ X3 ) )
                                                                   => ~ ! [X3: $i] :
                                                                          ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                         => ( ( dsetconstr @ X1 @ X2 )
                                                                           != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                             => ( ! [X1: $i,X2: $i > $o] :
                                                                    ( ~ ! [X3: $i] :
                                                                          ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                         => ( ( dsetconstr @ X1 @ X2 )
                                                                           != ( setadjoin @ X3 @ emptyset ) ) )
                                                                   => ~ ! [X3: $i] :
                                                                          ( ( in @ X3 @ X1 )
                                                                         => ~ ( X2 @ X3 ) ) )
                                                               => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                      ( ( in @ X3 @ X1 )
                                                                     => ( ( X2 @ X3 )
                                                                       => ( ! [X4: $i] :
                                                                              ( ( in @ X4 @ X1 )
                                                                             => ( ( X2 @ X4 )
                                                                               => ( X4 = X3 ) ) )
                                                                         => ~ ! [X4: $i] :
                                                                                ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                               => ( ( dsetconstr @ X1 @ X2 )
                                                                                 != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                                        ( ! [X3: $i] :
                                                                            ( ( in @ X3 @ X1 )
                                                                           => ! [X4: $i] :
                                                                                ( ( in @ X4 @ X1 )
                                                                               => ( ( X2 @ X3 )
                                                                                 => ( ( X2 @ X4 )
                                                                                   => ( X3 = X4 ) ) ) ) )
                                                                       => ( ~ ! [X3: $i] :
                                                                                ( ( in @ X3 @ X1 )
                                                                               => ~ ( X2 @ X3 ) )
                                                                         => ~ ! [X3: $i] :
                                                                                ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                               => ( ( dsetconstr @ X1 @ X2 )
                                                                                 != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                   => ( ! [X1: $i,X2: $i] :
                                                                          ( ( ( setadjoin @ X1 @ emptyset )
                                                                            = ( setadjoin @ X2 @ emptyset ) )
                                                                         => ( X1 = X2 ) )
                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                            ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                           => ( X1 = X3 ) )
                                                                       => ( ! [X1: $i] :
                                                                              ( ( iskpair @ X1 )
                                                                             => ~ ! [X2: $i] :
                                                                                    ( ( in @ X2
                                                                                      @ ( dsetconstr @ ( setunion @ X1 )
                                                                                        @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                   => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                        @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                     != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                         => ( ! [X1: $i] :
                                                                                ( ~ ! [X2: $i] :
                                                                                      ( ( in @ X2 @ X1 )
                                                                                     => ( X1
                                                                                       != ( setadjoin @ X2 @ emptyset ) ) )
                                                                               => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                  ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                  = X1 )
                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                    ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                   => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                      ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                        = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                     => ( X1 = X3 ) )
                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                        ( ( ( kpair @ X1 @ X2 )
                                                                                          = ( kpair @ X3 @ X4 ) )
                                                                                       => ( X1 = X3 ) )
                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                          ( ( X1 = X2 )
                                                                                         => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                            = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                            ( ( X1 = X2 )
                                                                                           => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                              = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                              ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                             => ( ( X3 = X4 )
                                                                                               => ( X2 = X4 ) ) )
                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                  = ( setadjoin @ X3 @ emptyset ) )
                                                                                               => ( X1 = X2 ) )
                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                  ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                    = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                 => ( X2 = X4 ) )
                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                    ( ( ( kpair @ X1 @ X2 )
                                                                                                      = ( kpair @ X3 @ X4 ) )
                                                                                                   => ( X2 = X4 ) )
                                                                                               => ( ! [X1: $i] :
                                                                                                      ( ( iskpair @ X1 )
                                                                                                     => ~ ! [X2: $i] :
                                                                                                            ( ( in @ X2
                                                                                                              @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                @ ^ [X3: $i] :
                                                                                                                    ( X1
                                                                                                                    = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                           => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                @ ^ [X3: $i] :
                                                                                                                    ( X1
                                                                                                                    = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                             != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                        ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                        = X2 )
                                                                                                   => ( sP8
                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                            ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                           => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                              ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                             => ( in @ X3 @ X1 ) )
                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                               => ( in @ X4 @ X2 ) )
                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                 => ! [X4: $i] :
                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                     => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                        = X3 ) ) )
                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                   => ! [X4: $i] :
                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                       => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                          = X4 ) ) )
                                                                                                               => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                    ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                   => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                      = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h223,assumption,
    ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 ),
    introduced(assumption,[]) ).

thf(h224,assumption,
    ~ ( ! [X1: $i,X2: $i] :
          ( ( ( setminus @ X1 @ X2 )
            = emptyset )
         => ( subset @ X1 @ X2 ) )
     => ( ! [X1: $i,X2: $i,X3: $i] :
            ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
           => ! [X4: $o] :
                ( ( ( in @ X3 @ X1 )
                 => ( ~ ( in @ X3 @ X2 )
                   => X4 ) )
               => ( ( ~ ( in @ X3 @ X1 )
                   => ( ( in @ X3 @ X2 )
                     => X4 ) )
                 => X4 ) ) )
       => ( ! [X1: $i,X2: $i,X3: $i] :
              ( ( in @ X3 @ X1 )
             => ( ~ ( in @ X3 @ X2 )
               => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
         => ( ! [X1: $i,X2: $i,X3: $i] :
                ( ~ ( in @ X3 @ X1 )
               => ( ( in @ X3 @ X2 )
                 => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
           => ( ! [X1: $i,X2: $i,X3: $i] :
                  ( ( in @ X3 @ X1 )
                 => ( ( in @ X3 @ X2 )
                   => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
             => ( ! [X1: $i,X2: $i,X3: $i] :
                    ( ~ ( in @ X3 @ X1 )
                   => ( ~ ( in @ X3 @ X2 )
                     => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
               => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                 => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                   => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                     => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                       => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                         => ( ! [X1: $i,X2: $i] :
                                ( ( in @ X2 @ X1 )
                               => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                           => ( ! [X1: $i,X2: $i] :
                                  ( ( in @ X2 @ X1 )
                                 => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                    ( ( in @ X3 @ X1 )
                                   => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                      ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                     => ( ( X3 != X1 )
                                       => ( X3 = X2 ) ) )
                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                        ( ( in @ X3 @ X1 )
                                       => ! [X4: $i] :
                                            ( ( in @ X4 @ X2 )
                                           => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                          ( ( in @ X3 @ X1 )
                                         => ! [X4: $i] :
                                              ( ( in @ X4 @ X2 )
                                             => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                            ( ( in @ X3 @ X1 )
                                           => ! [X4: $i] :
                                                ( ( in @ X4 @ X2 )
                                               => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                              ( ( in @ X3 @ X1 )
                                             => ! [X4: $i] :
                                                  ( ( in @ X4 @ X2 )
                                                 => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                ( ( in @ X3 @ X1 )
                                               => ! [X4: $i] :
                                                    ( ( in @ X4 @ X2 )
                                                   => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                  ( ( in @ X3 @ X1 )
                                                 => ! [X4: $i] :
                                                      ( ( in @ X4 @ X2 )
                                                     => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                    ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                   => ~ ! [X4: $i] :
                                                          ( ( in @ X4 @ X1 )
                                                         => ! [X5: $i] :
                                                              ( ( in @ X5 @ X2 )
                                                             => ( X3
                                                               != ( kpair @ X4 @ X5 ) ) ) ) )
                                               => ( sP5
                                                 => ( ! [X1: $i,X2: $i] :
                                                        ( ( in @ X2 @ ( setunion @ X1 ) )
                                                       => ~ ! [X3: $i] :
                                                              ( ( in @ X3 @ X1 )
                                                             => ~ ( in @ X2 @ X3 ) ) )
                                                   => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                     => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                       => ( ! [X1: $i] :
                                                              ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                              = X1 )
                                                         => ( ! [X1: $i,X2: $i > $o] :
                                                                ( ! [X3: $i] :
                                                                    ( ( in @ X3 @ X1 )
                                                                   => ! [X4: $i] :
                                                                        ( ( in @ X4 @ X1 )
                                                                       => ( ( X2 @ X3 )
                                                                         => ( ( X2 @ X4 )
                                                                           => ( X3 = X4 ) ) ) ) )
                                                               => ( ~ ! [X3: $i] :
                                                                        ( ( in @ X3 @ X1 )
                                                                       => ~ ( X2 @ X3 ) )
                                                                 => ~ ! [X3: $i] :
                                                                        ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                       => ( ( dsetconstr @ X1 @ X2 )
                                                                         != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                           => ( ! [X1: $i,X2: $i > $o] :
                                                                  ( ~ ! [X3: $i] :
                                                                        ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                       => ( ( dsetconstr @ X1 @ X2 )
                                                                         != ( setadjoin @ X3 @ emptyset ) ) )
                                                                 => ~ ! [X3: $i] :
                                                                        ( ( in @ X3 @ X1 )
                                                                       => ~ ( X2 @ X3 ) ) )
                                                             => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                    ( ( in @ X3 @ X1 )
                                                                   => ( ( X2 @ X3 )
                                                                     => ( ! [X4: $i] :
                                                                            ( ( in @ X4 @ X1 )
                                                                           => ( ( X2 @ X4 )
                                                                             => ( X4 = X3 ) ) )
                                                                       => ~ ! [X4: $i] :
                                                                              ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                             => ( ( dsetconstr @ X1 @ X2 )
                                                                               != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                               => ( ! [X1: $i,X2: $i > $o] :
                                                                      ( ! [X3: $i] :
                                                                          ( ( in @ X3 @ X1 )
                                                                         => ! [X4: $i] :
                                                                              ( ( in @ X4 @ X1 )
                                                                             => ( ( X2 @ X3 )
                                                                               => ( ( X2 @ X4 )
                                                                                 => ( X3 = X4 ) ) ) ) )
                                                                     => ( ~ ! [X3: $i] :
                                                                              ( ( in @ X3 @ X1 )
                                                                             => ~ ( X2 @ X3 ) )
                                                                       => ~ ! [X3: $i] :
                                                                              ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                             => ( ( dsetconstr @ X1 @ X2 )
                                                                               != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                 => ( ! [X1: $i,X2: $i] :
                                                                        ( ( ( setadjoin @ X1 @ emptyset )
                                                                          = ( setadjoin @ X2 @ emptyset ) )
                                                                       => ( X1 = X2 ) )
                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                          ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                         => ( X1 = X3 ) )
                                                                     => ( ! [X1: $i] :
                                                                            ( ( iskpair @ X1 )
                                                                           => ~ ! [X2: $i] :
                                                                                  ( ( in @ X2
                                                                                    @ ( dsetconstr @ ( setunion @ X1 )
                                                                                      @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                 => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                      @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                   != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                       => ( ! [X1: $i] :
                                                                              ( ~ ! [X2: $i] :
                                                                                    ( ( in @ X2 @ X1 )
                                                                                   => ( X1
                                                                                     != ( setadjoin @ X2 @ emptyset ) ) )
                                                                             => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                = X1 )
                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                  ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                 => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                    ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                      = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                   => ( X1 = X3 ) )
                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                      ( ( ( kpair @ X1 @ X2 )
                                                                                        = ( kpair @ X3 @ X4 ) )
                                                                                     => ( X1 = X3 ) )
                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                        ( ( X1 = X2 )
                                                                                       => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                          = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                          ( ( X1 = X2 )
                                                                                         => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                            = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                            ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                              = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                           => ( ( X3 = X4 )
                                                                                             => ( X2 = X4 ) ) )
                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                              ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                = ( setadjoin @ X3 @ emptyset ) )
                                                                                             => ( X1 = X2 ) )
                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                  = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                               => ( X2 = X4 ) )
                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                  ( ( ( kpair @ X1 @ X2 )
                                                                                                    = ( kpair @ X3 @ X4 ) )
                                                                                                 => ( X2 = X4 ) )
                                                                                             => ( ! [X1: $i] :
                                                                                                    ( ( iskpair @ X1 )
                                                                                                   => ~ ! [X2: $i] :
                                                                                                          ( ( in @ X2
                                                                                                            @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                              @ ^ [X3: $i] :
                                                                                                                  ( X1
                                                                                                                  = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                         => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                              @ ^ [X3: $i] :
                                                                                                                  ( X1
                                                                                                                  = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                           != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                      ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                      = X2 )
                                                                                                 => ( sP8
                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                         => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                            ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                           => ( in @ X3 @ X1 ) )
                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                              ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                             => ( in @ X4 @ X2 ) )
                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                               => ! [X4: $i] :
                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                   => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                      = X3 ) ) )
                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                 => ! [X4: $i] :
                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                     => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                        = X4 ) ) )
                                                                                                             => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                  ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                 => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                    = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h225,assumption,
    ! [X1: $i,X2: $i] :
      ( ( ( setminus @ X1 @ X2 )
        = emptyset )
     => ( subset @ X1 @ X2 ) ),
    introduced(assumption,[]) ).

thf(h226,assumption,
    ~ ( ! [X1: $i,X2: $i,X3: $i] :
          ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
         => ! [X4: $o] :
              ( ( ( in @ X3 @ X1 )
               => ( ~ ( in @ X3 @ X2 )
                 => X4 ) )
             => ( ( ~ ( in @ X3 @ X1 )
                 => ( ( in @ X3 @ X2 )
                   => X4 ) )
               => X4 ) ) )
     => ( ! [X1: $i,X2: $i,X3: $i] :
            ( ( in @ X3 @ X1 )
           => ( ~ ( in @ X3 @ X2 )
             => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
       => ( ! [X1: $i,X2: $i,X3: $i] :
              ( ~ ( in @ X3 @ X1 )
             => ( ( in @ X3 @ X2 )
               => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
         => ( ! [X1: $i,X2: $i,X3: $i] :
                ( ( in @ X3 @ X1 )
               => ( ( in @ X3 @ X2 )
                 => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
           => ( ! [X1: $i,X2: $i,X3: $i] :
                  ( ~ ( in @ X3 @ X1 )
                 => ( ~ ( in @ X3 @ X2 )
                   => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
             => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
               => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                 => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                   => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                     => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                       => ( ! [X1: $i,X2: $i] :
                              ( ( in @ X2 @ X1 )
                             => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                         => ( ! [X1: $i,X2: $i] :
                                ( ( in @ X2 @ X1 )
                               => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                  ( ( in @ X3 @ X1 )
                                 => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                    ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                   => ( ( X3 != X1 )
                                     => ( X3 = X2 ) ) )
                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                      ( ( in @ X3 @ X1 )
                                     => ! [X4: $i] :
                                          ( ( in @ X4 @ X2 )
                                         => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                        ( ( in @ X3 @ X1 )
                                       => ! [X4: $i] :
                                            ( ( in @ X4 @ X2 )
                                           => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                          ( ( in @ X3 @ X1 )
                                         => ! [X4: $i] :
                                              ( ( in @ X4 @ X2 )
                                             => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                            ( ( in @ X3 @ X1 )
                                           => ! [X4: $i] :
                                                ( ( in @ X4 @ X2 )
                                               => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                              ( ( in @ X3 @ X1 )
                                             => ! [X4: $i] :
                                                  ( ( in @ X4 @ X2 )
                                                 => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                ( ( in @ X3 @ X1 )
                                               => ! [X4: $i] :
                                                    ( ( in @ X4 @ X2 )
                                                   => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                  ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                 => ~ ! [X4: $i] :
                                                        ( ( in @ X4 @ X1 )
                                                       => ! [X5: $i] :
                                                            ( ( in @ X5 @ X2 )
                                                           => ( X3
                                                             != ( kpair @ X4 @ X5 ) ) ) ) )
                                             => ( sP5
                                               => ( ! [X1: $i,X2: $i] :
                                                      ( ( in @ X2 @ ( setunion @ X1 ) )
                                                     => ~ ! [X3: $i] :
                                                            ( ( in @ X3 @ X1 )
                                                           => ~ ( in @ X2 @ X3 ) ) )
                                                 => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                   => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                     => ( ! [X1: $i] :
                                                            ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                            = X1 )
                                                       => ( ! [X1: $i,X2: $i > $o] :
                                                              ( ! [X3: $i] :
                                                                  ( ( in @ X3 @ X1 )
                                                                 => ! [X4: $i] :
                                                                      ( ( in @ X4 @ X1 )
                                                                     => ( ( X2 @ X3 )
                                                                       => ( ( X2 @ X4 )
                                                                         => ( X3 = X4 ) ) ) ) )
                                                             => ( ~ ! [X3: $i] :
                                                                      ( ( in @ X3 @ X1 )
                                                                     => ~ ( X2 @ X3 ) )
                                                               => ~ ! [X3: $i] :
                                                                      ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                     => ( ( dsetconstr @ X1 @ X2 )
                                                                       != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                         => ( ! [X1: $i,X2: $i > $o] :
                                                                ( ~ ! [X3: $i] :
                                                                      ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                     => ( ( dsetconstr @ X1 @ X2 )
                                                                       != ( setadjoin @ X3 @ emptyset ) ) )
                                                               => ~ ! [X3: $i] :
                                                                      ( ( in @ X3 @ X1 )
                                                                     => ~ ( X2 @ X3 ) ) )
                                                           => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                  ( ( in @ X3 @ X1 )
                                                                 => ( ( X2 @ X3 )
                                                                   => ( ! [X4: $i] :
                                                                          ( ( in @ X4 @ X1 )
                                                                         => ( ( X2 @ X4 )
                                                                           => ( X4 = X3 ) ) )
                                                                     => ~ ! [X4: $i] :
                                                                            ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                           => ( ( dsetconstr @ X1 @ X2 )
                                                                             != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                             => ( ! [X1: $i,X2: $i > $o] :
                                                                    ( ! [X3: $i] :
                                                                        ( ( in @ X3 @ X1 )
                                                                       => ! [X4: $i] :
                                                                            ( ( in @ X4 @ X1 )
                                                                           => ( ( X2 @ X3 )
                                                                             => ( ( X2 @ X4 )
                                                                               => ( X3 = X4 ) ) ) ) )
                                                                   => ( ~ ! [X3: $i] :
                                                                            ( ( in @ X3 @ X1 )
                                                                           => ~ ( X2 @ X3 ) )
                                                                     => ~ ! [X3: $i] :
                                                                            ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                           => ( ( dsetconstr @ X1 @ X2 )
                                                                             != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                               => ( ! [X1: $i,X2: $i] :
                                                                      ( ( ( setadjoin @ X1 @ emptyset )
                                                                        = ( setadjoin @ X2 @ emptyset ) )
                                                                     => ( X1 = X2 ) )
                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                        ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                       => ( X1 = X3 ) )
                                                                   => ( ! [X1: $i] :
                                                                          ( ( iskpair @ X1 )
                                                                         => ~ ! [X2: $i] :
                                                                                ( ( in @ X2
                                                                                  @ ( dsetconstr @ ( setunion @ X1 )
                                                                                    @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                               => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                    @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                 != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                     => ( ! [X1: $i] :
                                                                            ( ~ ! [X2: $i] :
                                                                                  ( ( in @ X2 @ X1 )
                                                                                 => ( X1
                                                                                   != ( setadjoin @ X2 @ emptyset ) ) )
                                                                           => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                       => ( ! [X1: $i,X2: $i] :
                                                                              ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                              = X1 )
                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                               => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                  ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                    = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                 => ( X1 = X3 ) )
                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                    ( ( ( kpair @ X1 @ X2 )
                                                                                      = ( kpair @ X3 @ X4 ) )
                                                                                   => ( X1 = X3 ) )
                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                      ( ( X1 = X2 )
                                                                                     => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                        = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                        ( ( X1 = X2 )
                                                                                       => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                          = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                          ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                            = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                         => ( ( X3 = X4 )
                                                                                           => ( X2 = X4 ) ) )
                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                            ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                              = ( setadjoin @ X3 @ emptyset ) )
                                                                                           => ( X1 = X2 ) )
                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                              ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                             => ( X2 = X4 ) )
                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                ( ( ( kpair @ X1 @ X2 )
                                                                                                  = ( kpair @ X3 @ X4 ) )
                                                                                               => ( X2 = X4 ) )
                                                                                           => ( ! [X1: $i] :
                                                                                                  ( ( iskpair @ X1 )
                                                                                                 => ~ ! [X2: $i] :
                                                                                                        ( ( in @ X2
                                                                                                          @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                            @ ^ [X3: $i] :
                                                                                                                ( X1
                                                                                                                = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                       => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                            @ ^ [X3: $i] :
                                                                                                                ( X1
                                                                                                                = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                         != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                    ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                    = X2 )
                                                                                               => ( sP8
                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                       => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                          ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                         => ( in @ X3 @ X1 ) )
                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                            ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                           => ( in @ X4 @ X2 ) )
                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                             => ! [X4: $i] :
                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                 => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                    = X3 ) ) )
                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                               => ! [X4: $i] :
                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                   => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                      = X4 ) ) )
                                                                                                           => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                               => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                  = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h227,assumption,
    ! [X1: $i,X2: $i,X3: $i] :
      ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
     => ! [X4: $o] :
          ( ( ( in @ X3 @ X1 )
           => ( ~ ( in @ X3 @ X2 )
             => X4 ) )
         => ( ( ~ ( in @ X3 @ X1 )
             => ( ( in @ X3 @ X2 )
               => X4 ) )
           => X4 ) ) ),
    introduced(assumption,[]) ).

thf(h228,assumption,
    ~ ( ! [X1: $i,X2: $i,X3: $i] :
          ( ( in @ X3 @ X1 )
         => ( ~ ( in @ X3 @ X2 )
           => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
     => ( ! [X1: $i,X2: $i,X3: $i] :
            ( ~ ( in @ X3 @ X1 )
           => ( ( in @ X3 @ X2 )
             => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
       => ( ! [X1: $i,X2: $i,X3: $i] :
              ( ( in @ X3 @ X1 )
             => ( ( in @ X3 @ X2 )
               => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
         => ( ! [X1: $i,X2: $i,X3: $i] :
                ( ~ ( in @ X3 @ X1 )
               => ( ~ ( in @ X3 @ X2 )
                 => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
           => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
             => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
               => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                 => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                   => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                     => ( ! [X1: $i,X2: $i] :
                            ( ( in @ X2 @ X1 )
                           => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                       => ( ! [X1: $i,X2: $i] :
                              ( ( in @ X2 @ X1 )
                             => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                ( ( in @ X3 @ X1 )
                               => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                  ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                 => ( ( X3 != X1 )
                                   => ( X3 = X2 ) ) )
                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                    ( ( in @ X3 @ X1 )
                                   => ! [X4: $i] :
                                        ( ( in @ X4 @ X2 )
                                       => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                      ( ( in @ X3 @ X1 )
                                     => ! [X4: $i] :
                                          ( ( in @ X4 @ X2 )
                                         => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                        ( ( in @ X3 @ X1 )
                                       => ! [X4: $i] :
                                            ( ( in @ X4 @ X2 )
                                           => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                          ( ( in @ X3 @ X1 )
                                         => ! [X4: $i] :
                                              ( ( in @ X4 @ X2 )
                                             => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                            ( ( in @ X3 @ X1 )
                                           => ! [X4: $i] :
                                                ( ( in @ X4 @ X2 )
                                               => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                              ( ( in @ X3 @ X1 )
                                             => ! [X4: $i] :
                                                  ( ( in @ X4 @ X2 )
                                                 => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                               => ~ ! [X4: $i] :
                                                      ( ( in @ X4 @ X1 )
                                                     => ! [X5: $i] :
                                                          ( ( in @ X5 @ X2 )
                                                         => ( X3
                                                           != ( kpair @ X4 @ X5 ) ) ) ) )
                                           => ( sP5
                                             => ( ! [X1: $i,X2: $i] :
                                                    ( ( in @ X2 @ ( setunion @ X1 ) )
                                                   => ~ ! [X3: $i] :
                                                          ( ( in @ X3 @ X1 )
                                                         => ~ ( in @ X2 @ X3 ) ) )
                                               => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                 => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                   => ( ! [X1: $i] :
                                                          ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                          = X1 )
                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                            ( ! [X3: $i] :
                                                                ( ( in @ X3 @ X1 )
                                                               => ! [X4: $i] :
                                                                    ( ( in @ X4 @ X1 )
                                                                   => ( ( X2 @ X3 )
                                                                     => ( ( X2 @ X4 )
                                                                       => ( X3 = X4 ) ) ) ) )
                                                           => ( ~ ! [X3: $i] :
                                                                    ( ( in @ X3 @ X1 )
                                                                   => ~ ( X2 @ X3 ) )
                                                             => ~ ! [X3: $i] :
                                                                    ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                   => ( ( dsetconstr @ X1 @ X2 )
                                                                     != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                       => ( ! [X1: $i,X2: $i > $o] :
                                                              ( ~ ! [X3: $i] :
                                                                    ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                   => ( ( dsetconstr @ X1 @ X2 )
                                                                     != ( setadjoin @ X3 @ emptyset ) ) )
                                                             => ~ ! [X3: $i] :
                                                                    ( ( in @ X3 @ X1 )
                                                                   => ~ ( X2 @ X3 ) ) )
                                                         => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                ( ( in @ X3 @ X1 )
                                                               => ( ( X2 @ X3 )
                                                                 => ( ! [X4: $i] :
                                                                        ( ( in @ X4 @ X1 )
                                                                       => ( ( X2 @ X4 )
                                                                         => ( X4 = X3 ) ) )
                                                                   => ~ ! [X4: $i] :
                                                                          ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                         => ( ( dsetconstr @ X1 @ X2 )
                                                                           != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                           => ( ! [X1: $i,X2: $i > $o] :
                                                                  ( ! [X3: $i] :
                                                                      ( ( in @ X3 @ X1 )
                                                                     => ! [X4: $i] :
                                                                          ( ( in @ X4 @ X1 )
                                                                         => ( ( X2 @ X3 )
                                                                           => ( ( X2 @ X4 )
                                                                             => ( X3 = X4 ) ) ) ) )
                                                                 => ( ~ ! [X3: $i] :
                                                                          ( ( in @ X3 @ X1 )
                                                                         => ~ ( X2 @ X3 ) )
                                                                   => ~ ! [X3: $i] :
                                                                          ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                         => ( ( dsetconstr @ X1 @ X2 )
                                                                           != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                             => ( ! [X1: $i,X2: $i] :
                                                                    ( ( ( setadjoin @ X1 @ emptyset )
                                                                      = ( setadjoin @ X2 @ emptyset ) )
                                                                   => ( X1 = X2 ) )
                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                      ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                     => ( X1 = X3 ) )
                                                                 => ( ! [X1: $i] :
                                                                        ( ( iskpair @ X1 )
                                                                       => ~ ! [X2: $i] :
                                                                              ( ( in @ X2
                                                                                @ ( dsetconstr @ ( setunion @ X1 )
                                                                                  @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                             => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                  @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                               != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                   => ( ! [X1: $i] :
                                                                          ( ~ ! [X2: $i] :
                                                                                ( ( in @ X2 @ X1 )
                                                                               => ( X1
                                                                                 != ( setadjoin @ X2 @ emptyset ) ) )
                                                                         => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                     => ( ! [X1: $i,X2: $i] :
                                                                            ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                            = X1 )
                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                              ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                             => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                  = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                               => ( X1 = X3 ) )
                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                  ( ( ( kpair @ X1 @ X2 )
                                                                                    = ( kpair @ X3 @ X4 ) )
                                                                                 => ( X1 = X3 ) )
                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                    ( ( X1 = X2 )
                                                                                   => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                      = ( setadjoin @ X1 @ emptyset ) ) )
                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                      ( ( X1 = X2 )
                                                                                     => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                        = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                        ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                          = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                       => ( ( X3 = X4 )
                                                                                         => ( X2 = X4 ) ) )
                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                          ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                            = ( setadjoin @ X3 @ emptyset ) )
                                                                                         => ( X1 = X2 ) )
                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                            ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                              = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                           => ( X2 = X4 ) )
                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                              ( ( ( kpair @ X1 @ X2 )
                                                                                                = ( kpair @ X3 @ X4 ) )
                                                                                             => ( X2 = X4 ) )
                                                                                         => ( ! [X1: $i] :
                                                                                                ( ( iskpair @ X1 )
                                                                                               => ~ ! [X2: $i] :
                                                                                                      ( ( in @ X2
                                                                                                        @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                          @ ^ [X3: $i] :
                                                                                                              ( X1
                                                                                                              = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                     => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                          @ ^ [X3: $i] :
                                                                                                              ( X1
                                                                                                              = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                       != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                  ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                  = X2 )
                                                                                             => ( sP8
                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                      ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                     => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                        ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                       => ( in @ X3 @ X1 ) )
                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                          ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                         => ( in @ X4 @ X2 ) )
                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                           => ! [X4: $i] :
                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                               => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                  = X3 ) ) )
                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                             => ! [X4: $i] :
                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                 => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                    = X4 ) ) )
                                                                                                         => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                              ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                             => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h229,assumption,
    ! [X1: $i,X2: $i,X3: $i] :
      ( ( in @ X3 @ X1 )
     => ( ~ ( in @ X3 @ X2 )
       => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) ),
    introduced(assumption,[]) ).

thf(h230,assumption,
    ~ ( ! [X1: $i,X2: $i,X3: $i] :
          ( ~ ( in @ X3 @ X1 )
         => ( ( in @ X3 @ X2 )
           => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
     => ( ! [X1: $i,X2: $i,X3: $i] :
            ( ( in @ X3 @ X1 )
           => ( ( in @ X3 @ X2 )
             => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
       => ( ! [X1: $i,X2: $i,X3: $i] :
              ( ~ ( in @ X3 @ X1 )
             => ( ~ ( in @ X3 @ X2 )
               => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
         => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
           => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
             => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
               => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                 => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                   => ( ! [X1: $i,X2: $i] :
                          ( ( in @ X2 @ X1 )
                         => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                     => ( ! [X1: $i,X2: $i] :
                            ( ( in @ X2 @ X1 )
                           => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                       => ( ! [X1: $i,X2: $i,X3: $i] :
                              ( ( in @ X3 @ X1 )
                             => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                               => ( ( X3 != X1 )
                                 => ( X3 = X2 ) ) )
                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                  ( ( in @ X3 @ X1 )
                                 => ! [X4: $i] :
                                      ( ( in @ X4 @ X2 )
                                     => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                    ( ( in @ X3 @ X1 )
                                   => ! [X4: $i] :
                                        ( ( in @ X4 @ X2 )
                                       => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                      ( ( in @ X3 @ X1 )
                                     => ! [X4: $i] :
                                          ( ( in @ X4 @ X2 )
                                         => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                        ( ( in @ X3 @ X1 )
                                       => ! [X4: $i] :
                                            ( ( in @ X4 @ X2 )
                                           => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                          ( ( in @ X3 @ X1 )
                                         => ! [X4: $i] :
                                              ( ( in @ X4 @ X2 )
                                             => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                            ( ( in @ X3 @ X1 )
                                           => ! [X4: $i] :
                                                ( ( in @ X4 @ X2 )
                                               => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                              ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                             => ~ ! [X4: $i] :
                                                    ( ( in @ X4 @ X1 )
                                                   => ! [X5: $i] :
                                                        ( ( in @ X5 @ X2 )
                                                       => ( X3
                                                         != ( kpair @ X4 @ X5 ) ) ) ) )
                                         => ( sP5
                                           => ( ! [X1: $i,X2: $i] :
                                                  ( ( in @ X2 @ ( setunion @ X1 ) )
                                                 => ~ ! [X3: $i] :
                                                        ( ( in @ X3 @ X1 )
                                                       => ~ ( in @ X2 @ X3 ) ) )
                                             => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                               => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                 => ( ! [X1: $i] :
                                                        ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                        = X1 )
                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                          ( ! [X3: $i] :
                                                              ( ( in @ X3 @ X1 )
                                                             => ! [X4: $i] :
                                                                  ( ( in @ X4 @ X1 )
                                                                 => ( ( X2 @ X3 )
                                                                   => ( ( X2 @ X4 )
                                                                     => ( X3 = X4 ) ) ) ) )
                                                         => ( ~ ! [X3: $i] :
                                                                  ( ( in @ X3 @ X1 )
                                                                 => ~ ( X2 @ X3 ) )
                                                           => ~ ! [X3: $i] :
                                                                  ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                 => ( ( dsetconstr @ X1 @ X2 )
                                                                   != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                            ( ~ ! [X3: $i] :
                                                                  ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                 => ( ( dsetconstr @ X1 @ X2 )
                                                                   != ( setadjoin @ X3 @ emptyset ) ) )
                                                           => ~ ! [X3: $i] :
                                                                  ( ( in @ X3 @ X1 )
                                                                 => ~ ( X2 @ X3 ) ) )
                                                       => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                              ( ( in @ X3 @ X1 )
                                                             => ( ( X2 @ X3 )
                                                               => ( ! [X4: $i] :
                                                                      ( ( in @ X4 @ X1 )
                                                                     => ( ( X2 @ X4 )
                                                                       => ( X4 = X3 ) ) )
                                                                 => ~ ! [X4: $i] :
                                                                        ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                       => ( ( dsetconstr @ X1 @ X2 )
                                                                         != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                         => ( ! [X1: $i,X2: $i > $o] :
                                                                ( ! [X3: $i] :
                                                                    ( ( in @ X3 @ X1 )
                                                                   => ! [X4: $i] :
                                                                        ( ( in @ X4 @ X1 )
                                                                       => ( ( X2 @ X3 )
                                                                         => ( ( X2 @ X4 )
                                                                           => ( X3 = X4 ) ) ) ) )
                                                               => ( ~ ! [X3: $i] :
                                                                        ( ( in @ X3 @ X1 )
                                                                       => ~ ( X2 @ X3 ) )
                                                                 => ~ ! [X3: $i] :
                                                                        ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                       => ( ( dsetconstr @ X1 @ X2 )
                                                                         != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                           => ( ! [X1: $i,X2: $i] :
                                                                  ( ( ( setadjoin @ X1 @ emptyset )
                                                                    = ( setadjoin @ X2 @ emptyset ) )
                                                                 => ( X1 = X2 ) )
                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                    ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                   => ( X1 = X3 ) )
                                                               => ( ! [X1: $i] :
                                                                      ( ( iskpair @ X1 )
                                                                     => ~ ! [X2: $i] :
                                                                            ( ( in @ X2
                                                                              @ ( dsetconstr @ ( setunion @ X1 )
                                                                                @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                           => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                             != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                 => ( ! [X1: $i] :
                                                                        ( ~ ! [X2: $i] :
                                                                              ( ( in @ X2 @ X1 )
                                                                             => ( X1
                                                                               != ( setadjoin @ X2 @ emptyset ) ) )
                                                                       => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                   => ( ! [X1: $i,X2: $i] :
                                                                          ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                          = X1 )
                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                            ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                           => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                              ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                             => ( X1 = X3 ) )
                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                ( ( ( kpair @ X1 @ X2 )
                                                                                  = ( kpair @ X3 @ X4 ) )
                                                                               => ( X1 = X3 ) )
                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                  ( ( X1 = X2 )
                                                                                 => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                    = ( setadjoin @ X1 @ emptyset ) ) )
                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                    ( ( X1 = X2 )
                                                                                   => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                      = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                      ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                        = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                     => ( ( X3 = X4 )
                                                                                       => ( X2 = X4 ) ) )
                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                        ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                          = ( setadjoin @ X3 @ emptyset ) )
                                                                                       => ( X1 = X2 ) )
                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                          ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                            = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                         => ( X2 = X4 ) )
                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                            ( ( ( kpair @ X1 @ X2 )
                                                                                              = ( kpair @ X3 @ X4 ) )
                                                                                           => ( X2 = X4 ) )
                                                                                       => ( ! [X1: $i] :
                                                                                              ( ( iskpair @ X1 )
                                                                                             => ~ ! [X2: $i] :
                                                                                                    ( ( in @ X2
                                                                                                      @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                        @ ^ [X3: $i] :
                                                                                                            ( X1
                                                                                                            = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                   => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                        @ ^ [X3: $i] :
                                                                                                            ( X1
                                                                                                            = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                     != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                = X2 )
                                                                                           => ( sP8
                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                    ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                   => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                      ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                     => ( in @ X3 @ X1 ) )
                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                        ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                       => ( in @ X4 @ X2 ) )
                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                         => ! [X4: $i] :
                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                             => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                = X3 ) ) )
                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                           => ! [X4: $i] :
                                                                                                                ( ( in @ X4 @ X2 )
                                                                                                               => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                  = X4 ) ) )
                                                                                                       => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                            ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                           => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                              = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h231,assumption,
    ! [X1: $i,X2: $i,X3: $i] :
      ( ~ ( in @ X3 @ X1 )
     => ( ( in @ X3 @ X2 )
       => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) ),
    introduced(assumption,[]) ).

thf(h232,assumption,
    ~ ( ! [X1: $i,X2: $i,X3: $i] :
          ( ( in @ X3 @ X1 )
         => ( ( in @ X3 @ X2 )
           => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
     => ( ! [X1: $i,X2: $i,X3: $i] :
            ( ~ ( in @ X3 @ X1 )
           => ( ~ ( in @ X3 @ X2 )
             => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
       => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
         => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
           => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
             => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
               => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                 => ( ! [X1: $i,X2: $i] :
                        ( ( in @ X2 @ X1 )
                       => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                   => ( ! [X1: $i,X2: $i] :
                          ( ( in @ X2 @ X1 )
                         => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                     => ( ! [X1: $i,X2: $i,X3: $i] :
                            ( ( in @ X3 @ X1 )
                           => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                       => ( ! [X1: $i,X2: $i,X3: $i] :
                              ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                             => ( ( X3 != X1 )
                               => ( X3 = X2 ) ) )
                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                ( ( in @ X3 @ X1 )
                               => ! [X4: $i] :
                                    ( ( in @ X4 @ X2 )
                                   => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                  ( ( in @ X3 @ X1 )
                                 => ! [X4: $i] :
                                      ( ( in @ X4 @ X2 )
                                     => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                    ( ( in @ X3 @ X1 )
                                   => ! [X4: $i] :
                                        ( ( in @ X4 @ X2 )
                                       => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                      ( ( in @ X3 @ X1 )
                                     => ! [X4: $i] :
                                          ( ( in @ X4 @ X2 )
                                         => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                        ( ( in @ X3 @ X1 )
                                       => ! [X4: $i] :
                                            ( ( in @ X4 @ X2 )
                                           => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                          ( ( in @ X3 @ X1 )
                                         => ! [X4: $i] :
                                              ( ( in @ X4 @ X2 )
                                             => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                            ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                           => ~ ! [X4: $i] :
                                                  ( ( in @ X4 @ X1 )
                                                 => ! [X5: $i] :
                                                      ( ( in @ X5 @ X2 )
                                                     => ( X3
                                                       != ( kpair @ X4 @ X5 ) ) ) ) )
                                       => ( sP5
                                         => ( ! [X1: $i,X2: $i] :
                                                ( ( in @ X2 @ ( setunion @ X1 ) )
                                               => ~ ! [X3: $i] :
                                                      ( ( in @ X3 @ X1 )
                                                     => ~ ( in @ X2 @ X3 ) ) )
                                           => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                             => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                               => ( ! [X1: $i] :
                                                      ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                      = X1 )
                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                        ( ! [X3: $i] :
                                                            ( ( in @ X3 @ X1 )
                                                           => ! [X4: $i] :
                                                                ( ( in @ X4 @ X1 )
                                                               => ( ( X2 @ X3 )
                                                                 => ( ( X2 @ X4 )
                                                                   => ( X3 = X4 ) ) ) ) )
                                                       => ( ~ ! [X3: $i] :
                                                                ( ( in @ X3 @ X1 )
                                                               => ~ ( X2 @ X3 ) )
                                                         => ~ ! [X3: $i] :
                                                                ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                               => ( ( dsetconstr @ X1 @ X2 )
                                                                 != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                          ( ~ ! [X3: $i] :
                                                                ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                               => ( ( dsetconstr @ X1 @ X2 )
                                                                 != ( setadjoin @ X3 @ emptyset ) ) )
                                                         => ~ ! [X3: $i] :
                                                                ( ( in @ X3 @ X1 )
                                                               => ~ ( X2 @ X3 ) ) )
                                                     => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                            ( ( in @ X3 @ X1 )
                                                           => ( ( X2 @ X3 )
                                                             => ( ! [X4: $i] :
                                                                    ( ( in @ X4 @ X1 )
                                                                   => ( ( X2 @ X4 )
                                                                     => ( X4 = X3 ) ) )
                                                               => ~ ! [X4: $i] :
                                                                      ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                     => ( ( dsetconstr @ X1 @ X2 )
                                                                       != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                       => ( ! [X1: $i,X2: $i > $o] :
                                                              ( ! [X3: $i] :
                                                                  ( ( in @ X3 @ X1 )
                                                                 => ! [X4: $i] :
                                                                      ( ( in @ X4 @ X1 )
                                                                     => ( ( X2 @ X3 )
                                                                       => ( ( X2 @ X4 )
                                                                         => ( X3 = X4 ) ) ) ) )
                                                             => ( ~ ! [X3: $i] :
                                                                      ( ( in @ X3 @ X1 )
                                                                     => ~ ( X2 @ X3 ) )
                                                               => ~ ! [X3: $i] :
                                                                      ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                     => ( ( dsetconstr @ X1 @ X2 )
                                                                       != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                         => ( ! [X1: $i,X2: $i] :
                                                                ( ( ( setadjoin @ X1 @ emptyset )
                                                                  = ( setadjoin @ X2 @ emptyset ) )
                                                               => ( X1 = X2 ) )
                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                  ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                 => ( X1 = X3 ) )
                                                             => ( ! [X1: $i] :
                                                                    ( ( iskpair @ X1 )
                                                                   => ~ ! [X2: $i] :
                                                                          ( ( in @ X2
                                                                            @ ( dsetconstr @ ( setunion @ X1 )
                                                                              @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                         => ( ( dsetconstr @ ( setunion @ X1 )
                                                                              @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                           != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                               => ( ! [X1: $i] :
                                                                      ( ~ ! [X2: $i] :
                                                                            ( ( in @ X2 @ X1 )
                                                                           => ( X1
                                                                             != ( setadjoin @ X2 @ emptyset ) ) )
                                                                     => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                 => ( ! [X1: $i,X2: $i] :
                                                                        ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                        = X1 )
                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                         => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                            ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                              = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                           => ( X1 = X3 ) )
                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                              ( ( ( kpair @ X1 @ X2 )
                                                                                = ( kpair @ X3 @ X4 ) )
                                                                             => ( X1 = X3 ) )
                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                ( ( X1 = X2 )
                                                                               => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                  = ( setadjoin @ X1 @ emptyset ) ) )
                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                  ( ( X1 = X2 )
                                                                                 => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                    = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                    ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                      = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                   => ( ( X3 = X4 )
                                                                                     => ( X2 = X4 ) ) )
                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                      ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                        = ( setadjoin @ X3 @ emptyset ) )
                                                                                     => ( X1 = X2 ) )
                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                        ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                          = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                       => ( X2 = X4 ) )
                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                          ( ( ( kpair @ X1 @ X2 )
                                                                                            = ( kpair @ X3 @ X4 ) )
                                                                                         => ( X2 = X4 ) )
                                                                                     => ( ! [X1: $i] :
                                                                                            ( ( iskpair @ X1 )
                                                                                           => ~ ! [X2: $i] :
                                                                                                  ( ( in @ X2
                                                                                                    @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                      @ ^ [X3: $i] :
                                                                                                          ( X1
                                                                                                          = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                 => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                      @ ^ [X3: $i] :
                                                                                                          ( X1
                                                                                                          = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                   != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                              ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                              = X2 )
                                                                                         => ( sP8
                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                  ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                 => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                    ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                   => ( in @ X3 @ X1 ) )
                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                      ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                     => ( in @ X4 @ X2 ) )
                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                       => ! [X4: $i] :
                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                           => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                              = X3 ) ) )
                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                         => ! [X4: $i] :
                                                                                                              ( ( in @ X4 @ X2 )
                                                                                                             => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                = X4 ) ) )
                                                                                                     => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                         => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                            = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h233,assumption,
    ! [X1: $i,X2: $i,X3: $i] :
      ( ( in @ X3 @ X1 )
     => ( ( in @ X3 @ X2 )
       => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) ),
    introduced(assumption,[]) ).

thf(h234,assumption,
    ~ ( ! [X1: $i,X2: $i,X3: $i] :
          ( ~ ( in @ X3 @ X1 )
         => ( ~ ( in @ X3 @ X2 )
           => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
     => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
       => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
         => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
           => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
             => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
               => ( ! [X1: $i,X2: $i] :
                      ( ( in @ X2 @ X1 )
                     => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                 => ( ! [X1: $i,X2: $i] :
                        ( ( in @ X2 @ X1 )
                       => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                   => ( ! [X1: $i,X2: $i,X3: $i] :
                          ( ( in @ X3 @ X1 )
                         => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                     => ( ! [X1: $i,X2: $i,X3: $i] :
                            ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                           => ( ( X3 != X1 )
                             => ( X3 = X2 ) ) )
                       => ( ! [X1: $i,X2: $i,X3: $i] :
                              ( ( in @ X3 @ X1 )
                             => ! [X4: $i] :
                                  ( ( in @ X4 @ X2 )
                                 => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                ( ( in @ X3 @ X1 )
                               => ! [X4: $i] :
                                    ( ( in @ X4 @ X2 )
                                   => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                  ( ( in @ X3 @ X1 )
                                 => ! [X4: $i] :
                                      ( ( in @ X4 @ X2 )
                                     => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                    ( ( in @ X3 @ X1 )
                                   => ! [X4: $i] :
                                        ( ( in @ X4 @ X2 )
                                       => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                      ( ( in @ X3 @ X1 )
                                     => ! [X4: $i] :
                                          ( ( in @ X4 @ X2 )
                                         => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                        ( ( in @ X3 @ X1 )
                                       => ! [X4: $i] :
                                            ( ( in @ X4 @ X2 )
                                           => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                         => ~ ! [X4: $i] :
                                                ( ( in @ X4 @ X1 )
                                               => ! [X5: $i] :
                                                    ( ( in @ X5 @ X2 )
                                                   => ( X3
                                                     != ( kpair @ X4 @ X5 ) ) ) ) )
                                     => ( sP5
                                       => ( ! [X1: $i,X2: $i] :
                                              ( ( in @ X2 @ ( setunion @ X1 ) )
                                             => ~ ! [X3: $i] :
                                                    ( ( in @ X3 @ X1 )
                                                   => ~ ( in @ X2 @ X3 ) ) )
                                         => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                           => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                             => ( ! [X1: $i] :
                                                    ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                    = X1 )
                                               => ( ! [X1: $i,X2: $i > $o] :
                                                      ( ! [X3: $i] :
                                                          ( ( in @ X3 @ X1 )
                                                         => ! [X4: $i] :
                                                              ( ( in @ X4 @ X1 )
                                                             => ( ( X2 @ X3 )
                                                               => ( ( X2 @ X4 )
                                                                 => ( X3 = X4 ) ) ) ) )
                                                     => ( ~ ! [X3: $i] :
                                                              ( ( in @ X3 @ X1 )
                                                             => ~ ( X2 @ X3 ) )
                                                       => ~ ! [X3: $i] :
                                                              ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                             => ( ( dsetconstr @ X1 @ X2 )
                                                               != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                        ( ~ ! [X3: $i] :
                                                              ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                             => ( ( dsetconstr @ X1 @ X2 )
                                                               != ( setadjoin @ X3 @ emptyset ) ) )
                                                       => ~ ! [X3: $i] :
                                                              ( ( in @ X3 @ X1 )
                                                             => ~ ( X2 @ X3 ) ) )
                                                   => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                          ( ( in @ X3 @ X1 )
                                                         => ( ( X2 @ X3 )
                                                           => ( ! [X4: $i] :
                                                                  ( ( in @ X4 @ X1 )
                                                                 => ( ( X2 @ X4 )
                                                                   => ( X4 = X3 ) ) )
                                                             => ~ ! [X4: $i] :
                                                                    ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                   => ( ( dsetconstr @ X1 @ X2 )
                                                                     != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                            ( ! [X3: $i] :
                                                                ( ( in @ X3 @ X1 )
                                                               => ! [X4: $i] :
                                                                    ( ( in @ X4 @ X1 )
                                                                   => ( ( X2 @ X3 )
                                                                     => ( ( X2 @ X4 )
                                                                       => ( X3 = X4 ) ) ) ) )
                                                           => ( ~ ! [X3: $i] :
                                                                    ( ( in @ X3 @ X1 )
                                                                   => ~ ( X2 @ X3 ) )
                                                             => ~ ! [X3: $i] :
                                                                    ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                   => ( ( dsetconstr @ X1 @ X2 )
                                                                     != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                       => ( ! [X1: $i,X2: $i] :
                                                              ( ( ( setadjoin @ X1 @ emptyset )
                                                                = ( setadjoin @ X2 @ emptyset ) )
                                                             => ( X1 = X2 ) )
                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                               => ( X1 = X3 ) )
                                                           => ( ! [X1: $i] :
                                                                  ( ( iskpair @ X1 )
                                                                 => ~ ! [X2: $i] :
                                                                        ( ( in @ X2
                                                                          @ ( dsetconstr @ ( setunion @ X1 )
                                                                            @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                       => ( ( dsetconstr @ ( setunion @ X1 )
                                                                            @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                         != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                             => ( ! [X1: $i] :
                                                                    ( ~ ! [X2: $i] :
                                                                          ( ( in @ X2 @ X1 )
                                                                         => ( X1
                                                                           != ( setadjoin @ X2 @ emptyset ) ) )
                                                                   => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                               => ( ! [X1: $i,X2: $i] :
                                                                      ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                      = X1 )
                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                       => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                          ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                            = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                         => ( X1 = X3 ) )
                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                            ( ( ( kpair @ X1 @ X2 )
                                                                              = ( kpair @ X3 @ X4 ) )
                                                                           => ( X1 = X3 ) )
                                                                       => ( ! [X1: $i,X2: $i] :
                                                                              ( ( X1 = X2 )
                                                                             => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                = ( setadjoin @ X1 @ emptyset ) ) )
                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                ( ( X1 = X2 )
                                                                               => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                  = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                  ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                    = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                 => ( ( X3 = X4 )
                                                                                   => ( X2 = X4 ) ) )
                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                    ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                      = ( setadjoin @ X3 @ emptyset ) )
                                                                                   => ( X1 = X2 ) )
                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                      ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                        = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                     => ( X2 = X4 ) )
                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                        ( ( ( kpair @ X1 @ X2 )
                                                                                          = ( kpair @ X3 @ X4 ) )
                                                                                       => ( X2 = X4 ) )
                                                                                   => ( ! [X1: $i] :
                                                                                          ( ( iskpair @ X1 )
                                                                                         => ~ ! [X2: $i] :
                                                                                                ( ( in @ X2
                                                                                                  @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                    @ ^ [X3: $i] :
                                                                                                        ( X1
                                                                                                        = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                               => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                    @ ^ [X3: $i] :
                                                                                                        ( X1
                                                                                                        = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                 != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                            ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                            = X2 )
                                                                                       => ( sP8
                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                               => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                  ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                 => ( in @ X3 @ X1 ) )
                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                    ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                   => ( in @ X4 @ X2 ) )
                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                     => ! [X4: $i] :
                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                         => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                            = X3 ) ) )
                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                       => ! [X4: $i] :
                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                           => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                              = X4 ) ) )
                                                                                                   => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                       => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                          = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h235,assumption,
    ! [X1: $i,X2: $i,X3: $i] :
      ( ~ ( in @ X3 @ X1 )
     => ( ~ ( in @ X3 @ X2 )
       => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) ),
    introduced(assumption,[]) ).

thf(h236,assumption,
    ~ ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
     => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
       => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
         => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
           => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
             => ( ! [X1: $i,X2: $i] :
                    ( ( in @ X2 @ X1 )
                   => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
               => ( ! [X1: $i,X2: $i] :
                      ( ( in @ X2 @ X1 )
                     => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                 => ( ! [X1: $i,X2: $i,X3: $i] :
                        ( ( in @ X3 @ X1 )
                       => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                   => ( ! [X1: $i,X2: $i,X3: $i] :
                          ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                         => ( ( X3 != X1 )
                           => ( X3 = X2 ) ) )
                     => ( ! [X1: $i,X2: $i,X3: $i] :
                            ( ( in @ X3 @ X1 )
                           => ! [X4: $i] :
                                ( ( in @ X4 @ X2 )
                               => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                       => ( ! [X1: $i,X2: $i,X3: $i] :
                              ( ( in @ X3 @ X1 )
                             => ! [X4: $i] :
                                  ( ( in @ X4 @ X2 )
                                 => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                ( ( in @ X3 @ X1 )
                               => ! [X4: $i] :
                                    ( ( in @ X4 @ X2 )
                                   => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                  ( ( in @ X3 @ X1 )
                                 => ! [X4: $i] :
                                      ( ( in @ X4 @ X2 )
                                     => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                    ( ( in @ X3 @ X1 )
                                   => ! [X4: $i] :
                                        ( ( in @ X4 @ X2 )
                                       => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                      ( ( in @ X3 @ X1 )
                                     => ! [X4: $i] :
                                          ( ( in @ X4 @ X2 )
                                         => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                       => ~ ! [X4: $i] :
                                              ( ( in @ X4 @ X1 )
                                             => ! [X5: $i] :
                                                  ( ( in @ X5 @ X2 )
                                                 => ( X3
                                                   != ( kpair @ X4 @ X5 ) ) ) ) )
                                   => ( sP5
                                     => ( ! [X1: $i,X2: $i] :
                                            ( ( in @ X2 @ ( setunion @ X1 ) )
                                           => ~ ! [X3: $i] :
                                                  ( ( in @ X3 @ X1 )
                                                 => ~ ( in @ X2 @ X3 ) ) )
                                       => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                         => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                           => ( ! [X1: $i] :
                                                  ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                  = X1 )
                                             => ( ! [X1: $i,X2: $i > $o] :
                                                    ( ! [X3: $i] :
                                                        ( ( in @ X3 @ X1 )
                                                       => ! [X4: $i] :
                                                            ( ( in @ X4 @ X1 )
                                                           => ( ( X2 @ X3 )
                                                             => ( ( X2 @ X4 )
                                                               => ( X3 = X4 ) ) ) ) )
                                                   => ( ~ ! [X3: $i] :
                                                            ( ( in @ X3 @ X1 )
                                                           => ~ ( X2 @ X3 ) )
                                                     => ~ ! [X3: $i] :
                                                            ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                           => ( ( dsetconstr @ X1 @ X2 )
                                                             != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                               => ( ! [X1: $i,X2: $i > $o] :
                                                      ( ~ ! [X3: $i] :
                                                            ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                           => ( ( dsetconstr @ X1 @ X2 )
                                                             != ( setadjoin @ X3 @ emptyset ) ) )
                                                     => ~ ! [X3: $i] :
                                                            ( ( in @ X3 @ X1 )
                                                           => ~ ( X2 @ X3 ) ) )
                                                 => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                        ( ( in @ X3 @ X1 )
                                                       => ( ( X2 @ X3 )
                                                         => ( ! [X4: $i] :
                                                                ( ( in @ X4 @ X1 )
                                                               => ( ( X2 @ X4 )
                                                                 => ( X4 = X3 ) ) )
                                                           => ~ ! [X4: $i] :
                                                                  ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                 => ( ( dsetconstr @ X1 @ X2 )
                                                                   != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                          ( ! [X3: $i] :
                                                              ( ( in @ X3 @ X1 )
                                                             => ! [X4: $i] :
                                                                  ( ( in @ X4 @ X1 )
                                                                 => ( ( X2 @ X3 )
                                                                   => ( ( X2 @ X4 )
                                                                     => ( X3 = X4 ) ) ) ) )
                                                         => ( ~ ! [X3: $i] :
                                                                  ( ( in @ X3 @ X1 )
                                                                 => ~ ( X2 @ X3 ) )
                                                           => ~ ! [X3: $i] :
                                                                  ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                 => ( ( dsetconstr @ X1 @ X2 )
                                                                   != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                     => ( ! [X1: $i,X2: $i] :
                                                            ( ( ( setadjoin @ X1 @ emptyset )
                                                              = ( setadjoin @ X2 @ emptyset ) )
                                                           => ( X1 = X2 ) )
                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                              ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                             => ( X1 = X3 ) )
                                                         => ( ! [X1: $i] :
                                                                ( ( iskpair @ X1 )
                                                               => ~ ! [X2: $i] :
                                                                      ( ( in @ X2
                                                                        @ ( dsetconstr @ ( setunion @ X1 )
                                                                          @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                     => ( ( dsetconstr @ ( setunion @ X1 )
                                                                          @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                       != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                           => ( ! [X1: $i] :
                                                                  ( ~ ! [X2: $i] :
                                                                        ( ( in @ X2 @ X1 )
                                                                       => ( X1
                                                                         != ( setadjoin @ X2 @ emptyset ) ) )
                                                                 => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                             => ( ! [X1: $i,X2: $i] :
                                                                    ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                    = X1 )
                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                      ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                     => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                        ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                          = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                       => ( X1 = X3 ) )
                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                          ( ( ( kpair @ X1 @ X2 )
                                                                            = ( kpair @ X3 @ X4 ) )
                                                                         => ( X1 = X3 ) )
                                                                     => ( ! [X1: $i,X2: $i] :
                                                                            ( ( X1 = X2 )
                                                                           => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                              = ( setadjoin @ X1 @ emptyset ) ) )
                                                                       => ( ! [X1: $i,X2: $i] :
                                                                              ( ( X1 = X2 )
                                                                             => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                  = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                               => ( ( X3 = X4 )
                                                                                 => ( X2 = X4 ) ) )
                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                  ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                    = ( setadjoin @ X3 @ emptyset ) )
                                                                                 => ( X1 = X2 ) )
                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                    ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                      = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                   => ( X2 = X4 ) )
                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                      ( ( ( kpair @ X1 @ X2 )
                                                                                        = ( kpair @ X3 @ X4 ) )
                                                                                     => ( X2 = X4 ) )
                                                                                 => ( ! [X1: $i] :
                                                                                        ( ( iskpair @ X1 )
                                                                                       => ~ ! [X2: $i] :
                                                                                              ( ( in @ X2
                                                                                                @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                  @ ^ [X3: $i] :
                                                                                                      ( X1
                                                                                                      = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                             => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                  @ ^ [X3: $i] :
                                                                                                      ( X1
                                                                                                      = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                               != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                          ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                          = X2 )
                                                                                     => ( sP8
                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                              ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                             => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                               => ( in @ X3 @ X1 ) )
                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                  ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                 => ( in @ X4 @ X2 ) )
                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                   => ! [X4: $i] :
                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                       => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                          = X3 ) ) )
                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                     => ! [X4: $i] :
                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                         => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                            = X4 ) ) )
                                                                                                 => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                      ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                     => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                        = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h237,assumption,
    ~ ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
     => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
       => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
         => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
           => ( ! [X1: $i,X2: $i] :
                  ( ( in @ X2 @ X1 )
                 => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
             => ( ! [X1: $i,X2: $i] :
                    ( ( in @ X2 @ X1 )
                   => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
               => ( ! [X1: $i,X2: $i,X3: $i] :
                      ( ( in @ X3 @ X1 )
                     => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                 => ( ! [X1: $i,X2: $i,X3: $i] :
                        ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                       => ( ( X3 != X1 )
                         => ( X3 = X2 ) ) )
                   => ( ! [X1: $i,X2: $i,X3: $i] :
                          ( ( in @ X3 @ X1 )
                         => ! [X4: $i] :
                              ( ( in @ X4 @ X2 )
                             => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                     => ( ! [X1: $i,X2: $i,X3: $i] :
                            ( ( in @ X3 @ X1 )
                           => ! [X4: $i] :
                                ( ( in @ X4 @ X2 )
                               => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                       => ( ! [X1: $i,X2: $i,X3: $i] :
                              ( ( in @ X3 @ X1 )
                             => ! [X4: $i] :
                                  ( ( in @ X4 @ X2 )
                                 => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                ( ( in @ X3 @ X1 )
                               => ! [X4: $i] :
                                    ( ( in @ X4 @ X2 )
                                   => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                  ( ( in @ X3 @ X1 )
                                 => ! [X4: $i] :
                                      ( ( in @ X4 @ X2 )
                                     => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                    ( ( in @ X3 @ X1 )
                                   => ! [X4: $i] :
                                        ( ( in @ X4 @ X2 )
                                       => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                      ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                     => ~ ! [X4: $i] :
                                            ( ( in @ X4 @ X1 )
                                           => ! [X5: $i] :
                                                ( ( in @ X5 @ X2 )
                                               => ( X3
                                                 != ( kpair @ X4 @ X5 ) ) ) ) )
                                 => ( sP5
                                   => ( ! [X1: $i,X2: $i] :
                                          ( ( in @ X2 @ ( setunion @ X1 ) )
                                         => ~ ! [X3: $i] :
                                                ( ( in @ X3 @ X1 )
                                               => ~ ( in @ X2 @ X3 ) ) )
                                     => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                       => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                         => ( ! [X1: $i] :
                                                ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                = X1 )
                                           => ( ! [X1: $i,X2: $i > $o] :
                                                  ( ! [X3: $i] :
                                                      ( ( in @ X3 @ X1 )
                                                     => ! [X4: $i] :
                                                          ( ( in @ X4 @ X1 )
                                                         => ( ( X2 @ X3 )
                                                           => ( ( X2 @ X4 )
                                                             => ( X3 = X4 ) ) ) ) )
                                                 => ( ~ ! [X3: $i] :
                                                          ( ( in @ X3 @ X1 )
                                                         => ~ ( X2 @ X3 ) )
                                                   => ~ ! [X3: $i] :
                                                          ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                         => ( ( dsetconstr @ X1 @ X2 )
                                                           != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                             => ( ! [X1: $i,X2: $i > $o] :
                                                    ( ~ ! [X3: $i] :
                                                          ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                         => ( ( dsetconstr @ X1 @ X2 )
                                                           != ( setadjoin @ X3 @ emptyset ) ) )
                                                   => ~ ! [X3: $i] :
                                                          ( ( in @ X3 @ X1 )
                                                         => ~ ( X2 @ X3 ) ) )
                                               => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                      ( ( in @ X3 @ X1 )
                                                     => ( ( X2 @ X3 )
                                                       => ( ! [X4: $i] :
                                                              ( ( in @ X4 @ X1 )
                                                             => ( ( X2 @ X4 )
                                                               => ( X4 = X3 ) ) )
                                                         => ~ ! [X4: $i] :
                                                                ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                               => ( ( dsetconstr @ X1 @ X2 )
                                                                 != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                        ( ! [X3: $i] :
                                                            ( ( in @ X3 @ X1 )
                                                           => ! [X4: $i] :
                                                                ( ( in @ X4 @ X1 )
                                                               => ( ( X2 @ X3 )
                                                                 => ( ( X2 @ X4 )
                                                                   => ( X3 = X4 ) ) ) ) )
                                                       => ( ~ ! [X3: $i] :
                                                                ( ( in @ X3 @ X1 )
                                                               => ~ ( X2 @ X3 ) )
                                                         => ~ ! [X3: $i] :
                                                                ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                               => ( ( dsetconstr @ X1 @ X2 )
                                                                 != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                   => ( ! [X1: $i,X2: $i] :
                                                          ( ( ( setadjoin @ X1 @ emptyset )
                                                            = ( setadjoin @ X2 @ emptyset ) )
                                                         => ( X1 = X2 ) )
                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                            ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                           => ( X1 = X3 ) )
                                                       => ( ! [X1: $i] :
                                                              ( ( iskpair @ X1 )
                                                             => ~ ! [X2: $i] :
                                                                    ( ( in @ X2
                                                                      @ ( dsetconstr @ ( setunion @ X1 )
                                                                        @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                   => ( ( dsetconstr @ ( setunion @ X1 )
                                                                        @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                     != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                         => ( ! [X1: $i] :
                                                                ( ~ ! [X2: $i] :
                                                                      ( ( in @ X2 @ X1 )
                                                                     => ( X1
                                                                       != ( setadjoin @ X2 @ emptyset ) ) )
                                                               => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                           => ( ! [X1: $i,X2: $i] :
                                                                  ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                  = X1 )
                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                    ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                   => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                      ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                        = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                     => ( X1 = X3 ) )
                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                        ( ( ( kpair @ X1 @ X2 )
                                                                          = ( kpair @ X3 @ X4 ) )
                                                                       => ( X1 = X3 ) )
                                                                   => ( ! [X1: $i,X2: $i] :
                                                                          ( ( X1 = X2 )
                                                                         => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                            = ( setadjoin @ X1 @ emptyset ) ) )
                                                                     => ( ! [X1: $i,X2: $i] :
                                                                            ( ( X1 = X2 )
                                                                           => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                              = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                              ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                             => ( ( X3 = X4 )
                                                                               => ( X2 = X4 ) ) )
                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                  = ( setadjoin @ X3 @ emptyset ) )
                                                                               => ( X1 = X2 ) )
                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                  ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                    = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                 => ( X2 = X4 ) )
                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                    ( ( ( kpair @ X1 @ X2 )
                                                                                      = ( kpair @ X3 @ X4 ) )
                                                                                   => ( X2 = X4 ) )
                                                                               => ( ! [X1: $i] :
                                                                                      ( ( iskpair @ X1 )
                                                                                     => ~ ! [X2: $i] :
                                                                                            ( ( in @ X2
                                                                                              @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                @ ^ [X3: $i] :
                                                                                                    ( X1
                                                                                                    = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                           => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                @ ^ [X3: $i] :
                                                                                                    ( X1
                                                                                                    = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                             != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                        ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                        = X2 )
                                                                                   => ( sP8
                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                            ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                           => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                              ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                             => ( in @ X3 @ X1 ) )
                                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                               => ( in @ X4 @ X2 ) )
                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                 => ! [X4: $i] :
                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                     => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                        = X3 ) ) )
                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                   => ! [X4: $i] :
                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                       => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                          = X4 ) ) )
                                                                                               => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                    ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                   => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                      = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h238,assumption,
    ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) ),
    introduced(assumption,[]) ).

thf(h239,assumption,
    ~ ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
     => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
       => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
         => ( ! [X1: $i,X2: $i] :
                ( ( in @ X2 @ X1 )
               => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
           => ( ! [X1: $i,X2: $i] :
                  ( ( in @ X2 @ X1 )
                 => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
             => ( ! [X1: $i,X2: $i,X3: $i] :
                    ( ( in @ X3 @ X1 )
                   => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
               => ( ! [X1: $i,X2: $i,X3: $i] :
                      ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                     => ( ( X3 != X1 )
                       => ( X3 = X2 ) ) )
                 => ( ! [X1: $i,X2: $i,X3: $i] :
                        ( ( in @ X3 @ X1 )
                       => ! [X4: $i] :
                            ( ( in @ X4 @ X2 )
                           => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                   => ( ! [X1: $i,X2: $i,X3: $i] :
                          ( ( in @ X3 @ X1 )
                         => ! [X4: $i] :
                              ( ( in @ X4 @ X2 )
                             => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                     => ( ! [X1: $i,X2: $i,X3: $i] :
                            ( ( in @ X3 @ X1 )
                           => ! [X4: $i] :
                                ( ( in @ X4 @ X2 )
                               => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                       => ( ! [X1: $i,X2: $i,X3: $i] :
                              ( ( in @ X3 @ X1 )
                             => ! [X4: $i] :
                                  ( ( in @ X4 @ X2 )
                                 => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                ( ( in @ X3 @ X1 )
                               => ! [X4: $i] :
                                    ( ( in @ X4 @ X2 )
                                   => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                  ( ( in @ X3 @ X1 )
                                 => ! [X4: $i] :
                                      ( ( in @ X4 @ X2 )
                                     => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                    ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                   => ~ ! [X4: $i] :
                                          ( ( in @ X4 @ X1 )
                                         => ! [X5: $i] :
                                              ( ( in @ X5 @ X2 )
                                             => ( X3
                                               != ( kpair @ X4 @ X5 ) ) ) ) )
                               => ( sP5
                                 => ( ! [X1: $i,X2: $i] :
                                        ( ( in @ X2 @ ( setunion @ X1 ) )
                                       => ~ ! [X3: $i] :
                                              ( ( in @ X3 @ X1 )
                                             => ~ ( in @ X2 @ X3 ) ) )
                                   => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                     => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                       => ( ! [X1: $i] :
                                              ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                              = X1 )
                                         => ( ! [X1: $i,X2: $i > $o] :
                                                ( ! [X3: $i] :
                                                    ( ( in @ X3 @ X1 )
                                                   => ! [X4: $i] :
                                                        ( ( in @ X4 @ X1 )
                                                       => ( ( X2 @ X3 )
                                                         => ( ( X2 @ X4 )
                                                           => ( X3 = X4 ) ) ) ) )
                                               => ( ~ ! [X3: $i] :
                                                        ( ( in @ X3 @ X1 )
                                                       => ~ ( X2 @ X3 ) )
                                                 => ~ ! [X3: $i] :
                                                        ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                       => ( ( dsetconstr @ X1 @ X2 )
                                                         != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                           => ( ! [X1: $i,X2: $i > $o] :
                                                  ( ~ ! [X3: $i] :
                                                        ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                       => ( ( dsetconstr @ X1 @ X2 )
                                                         != ( setadjoin @ X3 @ emptyset ) ) )
                                                 => ~ ! [X3: $i] :
                                                        ( ( in @ X3 @ X1 )
                                                       => ~ ( X2 @ X3 ) ) )
                                             => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                    ( ( in @ X3 @ X1 )
                                                   => ( ( X2 @ X3 )
                                                     => ( ! [X4: $i] :
                                                            ( ( in @ X4 @ X1 )
                                                           => ( ( X2 @ X4 )
                                                             => ( X4 = X3 ) ) )
                                                       => ~ ! [X4: $i] :
                                                              ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                             => ( ( dsetconstr @ X1 @ X2 )
                                                               != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                               => ( ! [X1: $i,X2: $i > $o] :
                                                      ( ! [X3: $i] :
                                                          ( ( in @ X3 @ X1 )
                                                         => ! [X4: $i] :
                                                              ( ( in @ X4 @ X1 )
                                                             => ( ( X2 @ X3 )
                                                               => ( ( X2 @ X4 )
                                                                 => ( X3 = X4 ) ) ) ) )
                                                     => ( ~ ! [X3: $i] :
                                                              ( ( in @ X3 @ X1 )
                                                             => ~ ( X2 @ X3 ) )
                                                       => ~ ! [X3: $i] :
                                                              ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                             => ( ( dsetconstr @ X1 @ X2 )
                                                               != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                 => ( ! [X1: $i,X2: $i] :
                                                        ( ( ( setadjoin @ X1 @ emptyset )
                                                          = ( setadjoin @ X2 @ emptyset ) )
                                                       => ( X1 = X2 ) )
                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                          ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                         => ( X1 = X3 ) )
                                                     => ( ! [X1: $i] :
                                                            ( ( iskpair @ X1 )
                                                           => ~ ! [X2: $i] :
                                                                  ( ( in @ X2
                                                                    @ ( dsetconstr @ ( setunion @ X1 )
                                                                      @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                 => ( ( dsetconstr @ ( setunion @ X1 )
                                                                      @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                   != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                       => ( ! [X1: $i] :
                                                              ( ~ ! [X2: $i] :
                                                                    ( ( in @ X2 @ X1 )
                                                                   => ( X1
                                                                     != ( setadjoin @ X2 @ emptyset ) ) )
                                                             => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                         => ( ! [X1: $i,X2: $i] :
                                                                ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                = X1 )
                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                  ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                 => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                    ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                      = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                   => ( X1 = X3 ) )
                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                      ( ( ( kpair @ X1 @ X2 )
                                                                        = ( kpair @ X3 @ X4 ) )
                                                                     => ( X1 = X3 ) )
                                                                 => ( ! [X1: $i,X2: $i] :
                                                                        ( ( X1 = X2 )
                                                                       => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                          = ( setadjoin @ X1 @ emptyset ) ) )
                                                                   => ( ! [X1: $i,X2: $i] :
                                                                          ( ( X1 = X2 )
                                                                         => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                            = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                            ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                              = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                           => ( ( X3 = X4 )
                                                                             => ( X2 = X4 ) ) )
                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                              ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                = ( setadjoin @ X3 @ emptyset ) )
                                                                             => ( X1 = X2 ) )
                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                  = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                               => ( X2 = X4 ) )
                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                  ( ( ( kpair @ X1 @ X2 )
                                                                                    = ( kpair @ X3 @ X4 ) )
                                                                                 => ( X2 = X4 ) )
                                                                             => ( ! [X1: $i] :
                                                                                    ( ( iskpair @ X1 )
                                                                                   => ~ ! [X2: $i] :
                                                                                          ( ( in @ X2
                                                                                            @ ( dsetconstr @ ( setunion @ X1 )
                                                                                              @ ^ [X3: $i] :
                                                                                                  ( X1
                                                                                                  = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                         => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                              @ ^ [X3: $i] :
                                                                                                  ( X1
                                                                                                  = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                           != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                      ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                      = X2 )
                                                                                 => ( sP8
                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                         => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                            ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                           => ( in @ X3 @ X1 ) )
                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                              ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                             => ( in @ X4 @ X2 ) )
                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                ( ( in @ X3 @ X1 )
                                                                                               => ! [X4: $i] :
                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                   => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                      = X3 ) ) )
                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                 => ! [X4: $i] :
                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                     => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                        = X4 ) ) )
                                                                                             => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                  ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                 => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                    = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h240,assumption,
    ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) ),
    introduced(assumption,[]) ).

thf(h241,assumption,
    ~ ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
     => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
       => ( ! [X1: $i,X2: $i] :
              ( ( in @ X2 @ X1 )
             => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
         => ( ! [X1: $i,X2: $i] :
                ( ( in @ X2 @ X1 )
               => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
           => ( ! [X1: $i,X2: $i,X3: $i] :
                  ( ( in @ X3 @ X1 )
                 => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
             => ( ! [X1: $i,X2: $i,X3: $i] :
                    ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                   => ( ( X3 != X1 )
                     => ( X3 = X2 ) ) )
               => ( ! [X1: $i,X2: $i,X3: $i] :
                      ( ( in @ X3 @ X1 )
                     => ! [X4: $i] :
                          ( ( in @ X4 @ X2 )
                         => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                 => ( ! [X1: $i,X2: $i,X3: $i] :
                        ( ( in @ X3 @ X1 )
                       => ! [X4: $i] :
                            ( ( in @ X4 @ X2 )
                           => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                   => ( ! [X1: $i,X2: $i,X3: $i] :
                          ( ( in @ X3 @ X1 )
                         => ! [X4: $i] :
                              ( ( in @ X4 @ X2 )
                             => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                     => ( ! [X1: $i,X2: $i,X3: $i] :
                            ( ( in @ X3 @ X1 )
                           => ! [X4: $i] :
                                ( ( in @ X4 @ X2 )
                               => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                       => ( ! [X1: $i,X2: $i,X3: $i] :
                              ( ( in @ X3 @ X1 )
                             => ! [X4: $i] :
                                  ( ( in @ X4 @ X2 )
                                 => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                ( ( in @ X3 @ X1 )
                               => ! [X4: $i] :
                                    ( ( in @ X4 @ X2 )
                                   => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                  ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                 => ~ ! [X4: $i] :
                                        ( ( in @ X4 @ X1 )
                                       => ! [X5: $i] :
                                            ( ( in @ X5 @ X2 )
                                           => ( X3
                                             != ( kpair @ X4 @ X5 ) ) ) ) )
                             => ( sP5
                               => ( ! [X1: $i,X2: $i] :
                                      ( ( in @ X2 @ ( setunion @ X1 ) )
                                     => ~ ! [X3: $i] :
                                            ( ( in @ X3 @ X1 )
                                           => ~ ( in @ X2 @ X3 ) ) )
                                 => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                   => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                     => ( ! [X1: $i] :
                                            ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                            = X1 )
                                       => ( ! [X1: $i,X2: $i > $o] :
                                              ( ! [X3: $i] :
                                                  ( ( in @ X3 @ X1 )
                                                 => ! [X4: $i] :
                                                      ( ( in @ X4 @ X1 )
                                                     => ( ( X2 @ X3 )
                                                       => ( ( X2 @ X4 )
                                                         => ( X3 = X4 ) ) ) ) )
                                             => ( ~ ! [X3: $i] :
                                                      ( ( in @ X3 @ X1 )
                                                     => ~ ( X2 @ X3 ) )
                                               => ~ ! [X3: $i] :
                                                      ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                     => ( ( dsetconstr @ X1 @ X2 )
                                                       != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                         => ( ! [X1: $i,X2: $i > $o] :
                                                ( ~ ! [X3: $i] :
                                                      ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                     => ( ( dsetconstr @ X1 @ X2 )
                                                       != ( setadjoin @ X3 @ emptyset ) ) )
                                               => ~ ! [X3: $i] :
                                                      ( ( in @ X3 @ X1 )
                                                     => ~ ( X2 @ X3 ) ) )
                                           => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                  ( ( in @ X3 @ X1 )
                                                 => ( ( X2 @ X3 )
                                                   => ( ! [X4: $i] :
                                                          ( ( in @ X4 @ X1 )
                                                         => ( ( X2 @ X4 )
                                                           => ( X4 = X3 ) ) )
                                                     => ~ ! [X4: $i] :
                                                            ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                           => ( ( dsetconstr @ X1 @ X2 )
                                                             != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                             => ( ! [X1: $i,X2: $i > $o] :
                                                    ( ! [X3: $i] :
                                                        ( ( in @ X3 @ X1 )
                                                       => ! [X4: $i] :
                                                            ( ( in @ X4 @ X1 )
                                                           => ( ( X2 @ X3 )
                                                             => ( ( X2 @ X4 )
                                                               => ( X3 = X4 ) ) ) ) )
                                                   => ( ~ ! [X3: $i] :
                                                            ( ( in @ X3 @ X1 )
                                                           => ~ ( X2 @ X3 ) )
                                                     => ~ ! [X3: $i] :
                                                            ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                           => ( ( dsetconstr @ X1 @ X2 )
                                                             != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                               => ( ! [X1: $i,X2: $i] :
                                                      ( ( ( setadjoin @ X1 @ emptyset )
                                                        = ( setadjoin @ X2 @ emptyset ) )
                                                     => ( X1 = X2 ) )
                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                        ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                       => ( X1 = X3 ) )
                                                   => ( ! [X1: $i] :
                                                          ( ( iskpair @ X1 )
                                                         => ~ ! [X2: $i] :
                                                                ( ( in @ X2
                                                                  @ ( dsetconstr @ ( setunion @ X1 )
                                                                    @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                               => ( ( dsetconstr @ ( setunion @ X1 )
                                                                    @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                 != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                     => ( ! [X1: $i] :
                                                            ( ~ ! [X2: $i] :
                                                                  ( ( in @ X2 @ X1 )
                                                                 => ( X1
                                                                   != ( setadjoin @ X2 @ emptyset ) ) )
                                                           => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                       => ( ! [X1: $i,X2: $i] :
                                                              ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                              = X1 )
                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                               => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                  ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                    = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                 => ( X1 = X3 ) )
                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                    ( ( ( kpair @ X1 @ X2 )
                                                                      = ( kpair @ X3 @ X4 ) )
                                                                   => ( X1 = X3 ) )
                                                               => ( ! [X1: $i,X2: $i] :
                                                                      ( ( X1 = X2 )
                                                                     => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                        = ( setadjoin @ X1 @ emptyset ) ) )
                                                                 => ( ! [X1: $i,X2: $i] :
                                                                        ( ( X1 = X2 )
                                                                       => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                          = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                          ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                            = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                         => ( ( X3 = X4 )
                                                                           => ( X2 = X4 ) ) )
                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                            ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                              = ( setadjoin @ X3 @ emptyset ) )
                                                                           => ( X1 = X2 ) )
                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                              ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                             => ( X2 = X4 ) )
                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                ( ( ( kpair @ X1 @ X2 )
                                                                                  = ( kpair @ X3 @ X4 ) )
                                                                               => ( X2 = X4 ) )
                                                                           => ( ! [X1: $i] :
                                                                                  ( ( iskpair @ X1 )
                                                                                 => ~ ! [X2: $i] :
                                                                                        ( ( in @ X2
                                                                                          @ ( dsetconstr @ ( setunion @ X1 )
                                                                                            @ ^ [X3: $i] :
                                                                                                ( X1
                                                                                                = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                       => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                            @ ^ [X3: $i] :
                                                                                                ( X1
                                                                                                = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                         != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                    ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                    = X2 )
                                                                               => ( sP8
                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                       => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                          ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                         => ( in @ X3 @ X1 ) )
                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                            ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                           => ( in @ X4 @ X2 ) )
                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                              ( ( in @ X3 @ X1 )
                                                                                             => ! [X4: $i] :
                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                 => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                    = X3 ) ) )
                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                ( ( in @ X3 @ X1 )
                                                                                               => ! [X4: $i] :
                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                   => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                      = X4 ) ) )
                                                                                           => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                               => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                  = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h242,assumption,
    ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ),
    introduced(assumption,[]) ).

thf(h243,assumption,
    ~ ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
     => ( ! [X1: $i,X2: $i] :
            ( ( in @ X2 @ X1 )
           => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
       => ( ! [X1: $i,X2: $i] :
              ( ( in @ X2 @ X1 )
             => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
         => ( ! [X1: $i,X2: $i,X3: $i] :
                ( ( in @ X3 @ X1 )
               => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
           => ( ! [X1: $i,X2: $i,X3: $i] :
                  ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                 => ( ( X3 != X1 )
                   => ( X3 = X2 ) ) )
             => ( ! [X1: $i,X2: $i,X3: $i] :
                    ( ( in @ X3 @ X1 )
                   => ! [X4: $i] :
                        ( ( in @ X4 @ X2 )
                       => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
               => ( ! [X1: $i,X2: $i,X3: $i] :
                      ( ( in @ X3 @ X1 )
                     => ! [X4: $i] :
                          ( ( in @ X4 @ X2 )
                         => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                 => ( ! [X1: $i,X2: $i,X3: $i] :
                        ( ( in @ X3 @ X1 )
                       => ! [X4: $i] :
                            ( ( in @ X4 @ X2 )
                           => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                   => ( ! [X1: $i,X2: $i,X3: $i] :
                          ( ( in @ X3 @ X1 )
                         => ! [X4: $i] :
                              ( ( in @ X4 @ X2 )
                             => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                     => ( ! [X1: $i,X2: $i,X3: $i] :
                            ( ( in @ X3 @ X1 )
                           => ! [X4: $i] :
                                ( ( in @ X4 @ X2 )
                               => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                       => ( ! [X1: $i,X2: $i,X3: $i] :
                              ( ( in @ X3 @ X1 )
                             => ! [X4: $i] :
                                  ( ( in @ X4 @ X2 )
                                 => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                               => ~ ! [X4: $i] :
                                      ( ( in @ X4 @ X1 )
                                     => ! [X5: $i] :
                                          ( ( in @ X5 @ X2 )
                                         => ( X3
                                           != ( kpair @ X4 @ X5 ) ) ) ) )
                           => ( sP5
                             => ( ! [X1: $i,X2: $i] :
                                    ( ( in @ X2 @ ( setunion @ X1 ) )
                                   => ~ ! [X3: $i] :
                                          ( ( in @ X3 @ X1 )
                                         => ~ ( in @ X2 @ X3 ) ) )
                               => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                 => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                   => ( ! [X1: $i] :
                                          ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                          = X1 )
                                     => ( ! [X1: $i,X2: $i > $o] :
                                            ( ! [X3: $i] :
                                                ( ( in @ X3 @ X1 )
                                               => ! [X4: $i] :
                                                    ( ( in @ X4 @ X1 )
                                                   => ( ( X2 @ X3 )
                                                     => ( ( X2 @ X4 )
                                                       => ( X3 = X4 ) ) ) ) )
                                           => ( ~ ! [X3: $i] :
                                                    ( ( in @ X3 @ X1 )
                                                   => ~ ( X2 @ X3 ) )
                                             => ~ ! [X3: $i] :
                                                    ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                   => ( ( dsetconstr @ X1 @ X2 )
                                                     != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                       => ( ! [X1: $i,X2: $i > $o] :
                                              ( ~ ! [X3: $i] :
                                                    ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                   => ( ( dsetconstr @ X1 @ X2 )
                                                     != ( setadjoin @ X3 @ emptyset ) ) )
                                             => ~ ! [X3: $i] :
                                                    ( ( in @ X3 @ X1 )
                                                   => ~ ( X2 @ X3 ) ) )
                                         => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                ( ( in @ X3 @ X1 )
                                               => ( ( X2 @ X3 )
                                                 => ( ! [X4: $i] :
                                                        ( ( in @ X4 @ X1 )
                                                       => ( ( X2 @ X4 )
                                                         => ( X4 = X3 ) ) )
                                                   => ~ ! [X4: $i] :
                                                          ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                         => ( ( dsetconstr @ X1 @ X2 )
                                                           != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                           => ( ! [X1: $i,X2: $i > $o] :
                                                  ( ! [X3: $i] :
                                                      ( ( in @ X3 @ X1 )
                                                     => ! [X4: $i] :
                                                          ( ( in @ X4 @ X1 )
                                                         => ( ( X2 @ X3 )
                                                           => ( ( X2 @ X4 )
                                                             => ( X3 = X4 ) ) ) ) )
                                                 => ( ~ ! [X3: $i] :
                                                          ( ( in @ X3 @ X1 )
                                                         => ~ ( X2 @ X3 ) )
                                                   => ~ ! [X3: $i] :
                                                          ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                         => ( ( dsetconstr @ X1 @ X2 )
                                                           != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                             => ( ! [X1: $i,X2: $i] :
                                                    ( ( ( setadjoin @ X1 @ emptyset )
                                                      = ( setadjoin @ X2 @ emptyset ) )
                                                   => ( X1 = X2 ) )
                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                      ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                     => ( X1 = X3 ) )
                                                 => ( ! [X1: $i] :
                                                        ( ( iskpair @ X1 )
                                                       => ~ ! [X2: $i] :
                                                              ( ( in @ X2
                                                                @ ( dsetconstr @ ( setunion @ X1 )
                                                                  @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                             => ( ( dsetconstr @ ( setunion @ X1 )
                                                                  @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                               != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                   => ( ! [X1: $i] :
                                                          ( ~ ! [X2: $i] :
                                                                ( ( in @ X2 @ X1 )
                                                               => ( X1
                                                                 != ( setadjoin @ X2 @ emptyset ) ) )
                                                         => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                     => ( ! [X1: $i,X2: $i] :
                                                            ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                            = X1 )
                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                              ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                             => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                  = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                               => ( X1 = X3 ) )
                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                  ( ( ( kpair @ X1 @ X2 )
                                                                    = ( kpair @ X3 @ X4 ) )
                                                                 => ( X1 = X3 ) )
                                                             => ( ! [X1: $i,X2: $i] :
                                                                    ( ( X1 = X2 )
                                                                   => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                      = ( setadjoin @ X1 @ emptyset ) ) )
                                                               => ( ! [X1: $i,X2: $i] :
                                                                      ( ( X1 = X2 )
                                                                     => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                        = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                        ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                          = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                       => ( ( X3 = X4 )
                                                                         => ( X2 = X4 ) ) )
                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                          ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                            = ( setadjoin @ X3 @ emptyset ) )
                                                                         => ( X1 = X2 ) )
                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                            ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                              = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                           => ( X2 = X4 ) )
                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                              ( ( ( kpair @ X1 @ X2 )
                                                                                = ( kpair @ X3 @ X4 ) )
                                                                             => ( X2 = X4 ) )
                                                                         => ( ! [X1: $i] :
                                                                                ( ( iskpair @ X1 )
                                                                               => ~ ! [X2: $i] :
                                                                                      ( ( in @ X2
                                                                                        @ ( dsetconstr @ ( setunion @ X1 )
                                                                                          @ ^ [X3: $i] :
                                                                                              ( X1
                                                                                              = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                     => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                          @ ^ [X3: $i] :
                                                                                              ( X1
                                                                                              = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                       != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                  ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                  = X2 )
                                                                             => ( sP8
                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                      ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                     => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                        ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                       => ( in @ X3 @ X1 ) )
                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                          ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                         => ( in @ X4 @ X2 ) )
                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                            ( ( in @ X3 @ X1 )
                                                                                           => ! [X4: $i] :
                                                                                                ( ( in @ X4 @ X2 )
                                                                                               => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                  = X3 ) ) )
                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                              ( ( in @ X3 @ X1 )
                                                                                             => ! [X4: $i] :
                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                 => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                    = X4 ) ) )
                                                                                         => ! [X1: $i,X2: $i,X3: $i] :
                                                                                              ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                             => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h244,assumption,
    ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) ),
    introduced(assumption,[]) ).

thf(h245,assumption,
    ~ ( ! [X1: $i,X2: $i] :
          ( ( in @ X2 @ X1 )
         => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
     => ( ! [X1: $i,X2: $i] :
            ( ( in @ X2 @ X1 )
           => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
       => ( ! [X1: $i,X2: $i,X3: $i] :
              ( ( in @ X3 @ X1 )
             => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
         => ( ! [X1: $i,X2: $i,X3: $i] :
                ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
               => ( ( X3 != X1 )
                 => ( X3 = X2 ) ) )
           => ( ! [X1: $i,X2: $i,X3: $i] :
                  ( ( in @ X3 @ X1 )
                 => ! [X4: $i] :
                      ( ( in @ X4 @ X2 )
                     => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
             => ( ! [X1: $i,X2: $i,X3: $i] :
                    ( ( in @ X3 @ X1 )
                   => ! [X4: $i] :
                        ( ( in @ X4 @ X2 )
                       => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
               => ( ! [X1: $i,X2: $i,X3: $i] :
                      ( ( in @ X3 @ X1 )
                     => ! [X4: $i] :
                          ( ( in @ X4 @ X2 )
                         => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                 => ( ! [X1: $i,X2: $i,X3: $i] :
                        ( ( in @ X3 @ X1 )
                       => ! [X4: $i] :
                            ( ( in @ X4 @ X2 )
                           => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                   => ( ! [X1: $i,X2: $i,X3: $i] :
                          ( ( in @ X3 @ X1 )
                         => ! [X4: $i] :
                              ( ( in @ X4 @ X2 )
                             => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                     => ( ! [X1: $i,X2: $i,X3: $i] :
                            ( ( in @ X3 @ X1 )
                           => ! [X4: $i] :
                                ( ( in @ X4 @ X2 )
                               => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                       => ( ! [X1: $i,X2: $i,X3: $i] :
                              ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                             => ~ ! [X4: $i] :
                                    ( ( in @ X4 @ X1 )
                                   => ! [X5: $i] :
                                        ( ( in @ X5 @ X2 )
                                       => ( X3
                                         != ( kpair @ X4 @ X5 ) ) ) ) )
                         => ( sP5
                           => ( ! [X1: $i,X2: $i] :
                                  ( ( in @ X2 @ ( setunion @ X1 ) )
                                 => ~ ! [X3: $i] :
                                        ( ( in @ X3 @ X1 )
                                       => ~ ( in @ X2 @ X3 ) ) )
                             => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                               => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                 => ( ! [X1: $i] :
                                        ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                        = X1 )
                                   => ( ! [X1: $i,X2: $i > $o] :
                                          ( ! [X3: $i] :
                                              ( ( in @ X3 @ X1 )
                                             => ! [X4: $i] :
                                                  ( ( in @ X4 @ X1 )
                                                 => ( ( X2 @ X3 )
                                                   => ( ( X2 @ X4 )
                                                     => ( X3 = X4 ) ) ) ) )
                                         => ( ~ ! [X3: $i] :
                                                  ( ( in @ X3 @ X1 )
                                                 => ~ ( X2 @ X3 ) )
                                           => ~ ! [X3: $i] :
                                                  ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                 => ( ( dsetconstr @ X1 @ X2 )
                                                   != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                     => ( ! [X1: $i,X2: $i > $o] :
                                            ( ~ ! [X3: $i] :
                                                  ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                 => ( ( dsetconstr @ X1 @ X2 )
                                                   != ( setadjoin @ X3 @ emptyset ) ) )
                                           => ~ ! [X3: $i] :
                                                  ( ( in @ X3 @ X1 )
                                                 => ~ ( X2 @ X3 ) ) )
                                       => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                              ( ( in @ X3 @ X1 )
                                             => ( ( X2 @ X3 )
                                               => ( ! [X4: $i] :
                                                      ( ( in @ X4 @ X1 )
                                                     => ( ( X2 @ X4 )
                                                       => ( X4 = X3 ) ) )
                                                 => ~ ! [X4: $i] :
                                                        ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                       => ( ( dsetconstr @ X1 @ X2 )
                                                         != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                         => ( ! [X1: $i,X2: $i > $o] :
                                                ( ! [X3: $i] :
                                                    ( ( in @ X3 @ X1 )
                                                   => ! [X4: $i] :
                                                        ( ( in @ X4 @ X1 )
                                                       => ( ( X2 @ X3 )
                                                         => ( ( X2 @ X4 )
                                                           => ( X3 = X4 ) ) ) ) )
                                               => ( ~ ! [X3: $i] :
                                                        ( ( in @ X3 @ X1 )
                                                       => ~ ( X2 @ X3 ) )
                                                 => ~ ! [X3: $i] :
                                                        ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                       => ( ( dsetconstr @ X1 @ X2 )
                                                         != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                           => ( ! [X1: $i,X2: $i] :
                                                  ( ( ( setadjoin @ X1 @ emptyset )
                                                    = ( setadjoin @ X2 @ emptyset ) )
                                                 => ( X1 = X2 ) )
                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                    ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                   => ( X1 = X3 ) )
                                               => ( ! [X1: $i] :
                                                      ( ( iskpair @ X1 )
                                                     => ~ ! [X2: $i] :
                                                            ( ( in @ X2
                                                              @ ( dsetconstr @ ( setunion @ X1 )
                                                                @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                           => ( ( dsetconstr @ ( setunion @ X1 )
                                                                @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                             != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                 => ( ! [X1: $i] :
                                                        ( ~ ! [X2: $i] :
                                                              ( ( in @ X2 @ X1 )
                                                             => ( X1
                                                               != ( setadjoin @ X2 @ emptyset ) ) )
                                                       => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                   => ( ! [X1: $i,X2: $i] :
                                                          ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                          = X1 )
                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                            ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                           => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                              ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                             => ( X1 = X3 ) )
                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                ( ( ( kpair @ X1 @ X2 )
                                                                  = ( kpair @ X3 @ X4 ) )
                                                               => ( X1 = X3 ) )
                                                           => ( ! [X1: $i,X2: $i] :
                                                                  ( ( X1 = X2 )
                                                                 => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                    = ( setadjoin @ X1 @ emptyset ) ) )
                                                             => ( ! [X1: $i,X2: $i] :
                                                                    ( ( X1 = X2 )
                                                                   => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                      = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                      ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                        = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                     => ( ( X3 = X4 )
                                                                       => ( X2 = X4 ) ) )
                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                        ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                          = ( setadjoin @ X3 @ emptyset ) )
                                                                       => ( X1 = X2 ) )
                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                          ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                            = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                         => ( X2 = X4 ) )
                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                            ( ( ( kpair @ X1 @ X2 )
                                                                              = ( kpair @ X3 @ X4 ) )
                                                                           => ( X2 = X4 ) )
                                                                       => ( ! [X1: $i] :
                                                                              ( ( iskpair @ X1 )
                                                                             => ~ ! [X2: $i] :
                                                                                    ( ( in @ X2
                                                                                      @ ( dsetconstr @ ( setunion @ X1 )
                                                                                        @ ^ [X3: $i] :
                                                                                            ( X1
                                                                                            = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                   => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                        @ ^ [X3: $i] :
                                                                                            ( X1
                                                                                            = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                     != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                = X2 )
                                                                           => ( sP8
                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                    ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                   => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                      ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                     => ( in @ X3 @ X1 ) )
                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                        ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                       => ( in @ X4 @ X2 ) )
                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                          ( ( in @ X3 @ X1 )
                                                                                         => ! [X4: $i] :
                                                                                              ( ( in @ X4 @ X2 )
                                                                                             => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                = X3 ) ) )
                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                            ( ( in @ X3 @ X1 )
                                                                                           => ! [X4: $i] :
                                                                                                ( ( in @ X4 @ X2 )
                                                                                               => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                  = X4 ) ) )
                                                                                       => ! [X1: $i,X2: $i,X3: $i] :
                                                                                            ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                           => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                              = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h246,assumption,
    ! [X1: $i,X2: $i] :
      ( ( in @ X2 @ X1 )
     => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) ),
    introduced(assumption,[]) ).

thf(h247,assumption,
    ~ ( ! [X1: $i,X2: $i] :
          ( ( in @ X2 @ X1 )
         => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
     => ( ! [X1: $i,X2: $i,X3: $i] :
            ( ( in @ X3 @ X1 )
           => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
       => ( ! [X1: $i,X2: $i,X3: $i] :
              ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
             => ( ( X3 != X1 )
               => ( X3 = X2 ) ) )
         => ( ! [X1: $i,X2: $i,X3: $i] :
                ( ( in @ X3 @ X1 )
               => ! [X4: $i] :
                    ( ( in @ X4 @ X2 )
                   => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
           => ( ! [X1: $i,X2: $i,X3: $i] :
                  ( ( in @ X3 @ X1 )
                 => ! [X4: $i] :
                      ( ( in @ X4 @ X2 )
                     => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
             => ( ! [X1: $i,X2: $i,X3: $i] :
                    ( ( in @ X3 @ X1 )
                   => ! [X4: $i] :
                        ( ( in @ X4 @ X2 )
                       => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
               => ( ! [X1: $i,X2: $i,X3: $i] :
                      ( ( in @ X3 @ X1 )
                     => ! [X4: $i] :
                          ( ( in @ X4 @ X2 )
                         => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                 => ( ! [X1: $i,X2: $i,X3: $i] :
                        ( ( in @ X3 @ X1 )
                       => ! [X4: $i] :
                            ( ( in @ X4 @ X2 )
                           => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                   => ( ! [X1: $i,X2: $i,X3: $i] :
                          ( ( in @ X3 @ X1 )
                         => ! [X4: $i] :
                              ( ( in @ X4 @ X2 )
                             => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                     => ( ! [X1: $i,X2: $i,X3: $i] :
                            ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                           => ~ ! [X4: $i] :
                                  ( ( in @ X4 @ X1 )
                                 => ! [X5: $i] :
                                      ( ( in @ X5 @ X2 )
                                     => ( X3
                                       != ( kpair @ X4 @ X5 ) ) ) ) )
                       => ( sP5
                         => ( ! [X1: $i,X2: $i] :
                                ( ( in @ X2 @ ( setunion @ X1 ) )
                               => ~ ! [X3: $i] :
                                      ( ( in @ X3 @ X1 )
                                     => ~ ( in @ X2 @ X3 ) ) )
                           => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                             => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                               => ( ! [X1: $i] :
                                      ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                      = X1 )
                                 => ( ! [X1: $i,X2: $i > $o] :
                                        ( ! [X3: $i] :
                                            ( ( in @ X3 @ X1 )
                                           => ! [X4: $i] :
                                                ( ( in @ X4 @ X1 )
                                               => ( ( X2 @ X3 )
                                                 => ( ( X2 @ X4 )
                                                   => ( X3 = X4 ) ) ) ) )
                                       => ( ~ ! [X3: $i] :
                                                ( ( in @ X3 @ X1 )
                                               => ~ ( X2 @ X3 ) )
                                         => ~ ! [X3: $i] :
                                                ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                               => ( ( dsetconstr @ X1 @ X2 )
                                                 != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                   => ( ! [X1: $i,X2: $i > $o] :
                                          ( ~ ! [X3: $i] :
                                                ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                               => ( ( dsetconstr @ X1 @ X2 )
                                                 != ( setadjoin @ X3 @ emptyset ) ) )
                                         => ~ ! [X3: $i] :
                                                ( ( in @ X3 @ X1 )
                                               => ~ ( X2 @ X3 ) ) )
                                     => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                            ( ( in @ X3 @ X1 )
                                           => ( ( X2 @ X3 )
                                             => ( ! [X4: $i] :
                                                    ( ( in @ X4 @ X1 )
                                                   => ( ( X2 @ X4 )
                                                     => ( X4 = X3 ) ) )
                                               => ~ ! [X4: $i] :
                                                      ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                     => ( ( dsetconstr @ X1 @ X2 )
                                                       != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                       => ( ! [X1: $i,X2: $i > $o] :
                                              ( ! [X3: $i] :
                                                  ( ( in @ X3 @ X1 )
                                                 => ! [X4: $i] :
                                                      ( ( in @ X4 @ X1 )
                                                     => ( ( X2 @ X3 )
                                                       => ( ( X2 @ X4 )
                                                         => ( X3 = X4 ) ) ) ) )
                                             => ( ~ ! [X3: $i] :
                                                      ( ( in @ X3 @ X1 )
                                                     => ~ ( X2 @ X3 ) )
                                               => ~ ! [X3: $i] :
                                                      ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                     => ( ( dsetconstr @ X1 @ X2 )
                                                       != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                         => ( ! [X1: $i,X2: $i] :
                                                ( ( ( setadjoin @ X1 @ emptyset )
                                                  = ( setadjoin @ X2 @ emptyset ) )
                                               => ( X1 = X2 ) )
                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                  ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                 => ( X1 = X3 ) )
                                             => ( ! [X1: $i] :
                                                    ( ( iskpair @ X1 )
                                                   => ~ ! [X2: $i] :
                                                          ( ( in @ X2
                                                            @ ( dsetconstr @ ( setunion @ X1 )
                                                              @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                         => ( ( dsetconstr @ ( setunion @ X1 )
                                                              @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                           != ( setadjoin @ X2 @ emptyset ) ) ) )
                                               => ( ! [X1: $i] :
                                                      ( ~ ! [X2: $i] :
                                                            ( ( in @ X2 @ X1 )
                                                           => ( X1
                                                             != ( setadjoin @ X2 @ emptyset ) ) )
                                                     => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                 => ( ! [X1: $i,X2: $i] :
                                                        ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                        = X1 )
                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                         => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                            ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                              = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                           => ( X1 = X3 ) )
                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                              ( ( ( kpair @ X1 @ X2 )
                                                                = ( kpair @ X3 @ X4 ) )
                                                             => ( X1 = X3 ) )
                                                         => ( ! [X1: $i,X2: $i] :
                                                                ( ( X1 = X2 )
                                                               => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                  = ( setadjoin @ X1 @ emptyset ) ) )
                                                           => ( ! [X1: $i,X2: $i] :
                                                                  ( ( X1 = X2 )
                                                                 => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                    = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                    ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                      = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                   => ( ( X3 = X4 )
                                                                     => ( X2 = X4 ) ) )
                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                      ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                        = ( setadjoin @ X3 @ emptyset ) )
                                                                     => ( X1 = X2 ) )
                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                        ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                          = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                       => ( X2 = X4 ) )
                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                          ( ( ( kpair @ X1 @ X2 )
                                                                            = ( kpair @ X3 @ X4 ) )
                                                                         => ( X2 = X4 ) )
                                                                     => ( ! [X1: $i] :
                                                                            ( ( iskpair @ X1 )
                                                                           => ~ ! [X2: $i] :
                                                                                  ( ( in @ X2
                                                                                    @ ( dsetconstr @ ( setunion @ X1 )
                                                                                      @ ^ [X3: $i] :
                                                                                          ( X1
                                                                                          = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                 => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                      @ ^ [X3: $i] :
                                                                                          ( X1
                                                                                          = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                   != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                       => ( ! [X1: $i,X2: $i] :
                                                                              ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                              = X2 )
                                                                         => ( sP8
                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                  ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                 => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                    ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                   => ( in @ X3 @ X1 ) )
                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                      ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                     => ( in @ X4 @ X2 ) )
                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                        ( ( in @ X3 @ X1 )
                                                                                       => ! [X4: $i] :
                                                                                            ( ( in @ X4 @ X2 )
                                                                                           => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                              = X3 ) ) )
                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                          ( ( in @ X3 @ X1 )
                                                                                         => ! [X4: $i] :
                                                                                              ( ( in @ X4 @ X2 )
                                                                                             => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                = X4 ) ) )
                                                                                     => ! [X1: $i,X2: $i,X3: $i] :
                                                                                          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                         => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                            = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h248,assumption,
    ! [X1: $i,X2: $i] :
      ( ( in @ X2 @ X1 )
     => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) ),
    introduced(assumption,[]) ).

thf(h249,assumption,
    ~ ( ! [X1: $i,X2: $i,X3: $i] :
          ( ( in @ X3 @ X1 )
         => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
     => ( ! [X1: $i,X2: $i,X3: $i] :
            ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
           => ( ( X3 != X1 )
             => ( X3 = X2 ) ) )
       => ( ! [X1: $i,X2: $i,X3: $i] :
              ( ( in @ X3 @ X1 )
             => ! [X4: $i] :
                  ( ( in @ X4 @ X2 )
                 => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
         => ( ! [X1: $i,X2: $i,X3: $i] :
                ( ( in @ X3 @ X1 )
               => ! [X4: $i] :
                    ( ( in @ X4 @ X2 )
                   => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
           => ( ! [X1: $i,X2: $i,X3: $i] :
                  ( ( in @ X3 @ X1 )
                 => ! [X4: $i] :
                      ( ( in @ X4 @ X2 )
                     => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
             => ( ! [X1: $i,X2: $i,X3: $i] :
                    ( ( in @ X3 @ X1 )
                   => ! [X4: $i] :
                        ( ( in @ X4 @ X2 )
                       => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
               => ( ! [X1: $i,X2: $i,X3: $i] :
                      ( ( in @ X3 @ X1 )
                     => ! [X4: $i] :
                          ( ( in @ X4 @ X2 )
                         => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                 => ( ! [X1: $i,X2: $i,X3: $i] :
                        ( ( in @ X3 @ X1 )
                       => ! [X4: $i] :
                            ( ( in @ X4 @ X2 )
                           => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                   => ( ! [X1: $i,X2: $i,X3: $i] :
                          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                         => ~ ! [X4: $i] :
                                ( ( in @ X4 @ X1 )
                               => ! [X5: $i] :
                                    ( ( in @ X5 @ X2 )
                                   => ( X3
                                     != ( kpair @ X4 @ X5 ) ) ) ) )
                     => ( sP5
                       => ( ! [X1: $i,X2: $i] :
                              ( ( in @ X2 @ ( setunion @ X1 ) )
                             => ~ ! [X3: $i] :
                                    ( ( in @ X3 @ X1 )
                                   => ~ ( in @ X2 @ X3 ) ) )
                         => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                           => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                             => ( ! [X1: $i] :
                                    ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                    = X1 )
                               => ( ! [X1: $i,X2: $i > $o] :
                                      ( ! [X3: $i] :
                                          ( ( in @ X3 @ X1 )
                                         => ! [X4: $i] :
                                              ( ( in @ X4 @ X1 )
                                             => ( ( X2 @ X3 )
                                               => ( ( X2 @ X4 )
                                                 => ( X3 = X4 ) ) ) ) )
                                     => ( ~ ! [X3: $i] :
                                              ( ( in @ X3 @ X1 )
                                             => ~ ( X2 @ X3 ) )
                                       => ~ ! [X3: $i] :
                                              ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                             => ( ( dsetconstr @ X1 @ X2 )
                                               != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                 => ( ! [X1: $i,X2: $i > $o] :
                                        ( ~ ! [X3: $i] :
                                              ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                             => ( ( dsetconstr @ X1 @ X2 )
                                               != ( setadjoin @ X3 @ emptyset ) ) )
                                       => ~ ! [X3: $i] :
                                              ( ( in @ X3 @ X1 )
                                             => ~ ( X2 @ X3 ) ) )
                                   => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                          ( ( in @ X3 @ X1 )
                                         => ( ( X2 @ X3 )
                                           => ( ! [X4: $i] :
                                                  ( ( in @ X4 @ X1 )
                                                 => ( ( X2 @ X4 )
                                                   => ( X4 = X3 ) ) )
                                             => ~ ! [X4: $i] :
                                                    ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                   => ( ( dsetconstr @ X1 @ X2 )
                                                     != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                     => ( ! [X1: $i,X2: $i > $o] :
                                            ( ! [X3: $i] :
                                                ( ( in @ X3 @ X1 )
                                               => ! [X4: $i] :
                                                    ( ( in @ X4 @ X1 )
                                                   => ( ( X2 @ X3 )
                                                     => ( ( X2 @ X4 )
                                                       => ( X3 = X4 ) ) ) ) )
                                           => ( ~ ! [X3: $i] :
                                                    ( ( in @ X3 @ X1 )
                                                   => ~ ( X2 @ X3 ) )
                                             => ~ ! [X3: $i] :
                                                    ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                   => ( ( dsetconstr @ X1 @ X2 )
                                                     != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                       => ( ! [X1: $i,X2: $i] :
                                              ( ( ( setadjoin @ X1 @ emptyset )
                                                = ( setadjoin @ X2 @ emptyset ) )
                                             => ( X1 = X2 ) )
                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                               => ( X1 = X3 ) )
                                           => ( ! [X1: $i] :
                                                  ( ( iskpair @ X1 )
                                                 => ~ ! [X2: $i] :
                                                        ( ( in @ X2
                                                          @ ( dsetconstr @ ( setunion @ X1 )
                                                            @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                       => ( ( dsetconstr @ ( setunion @ X1 )
                                                            @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                         != ( setadjoin @ X2 @ emptyset ) ) ) )
                                             => ( ! [X1: $i] :
                                                    ( ~ ! [X2: $i] :
                                                          ( ( in @ X2 @ X1 )
                                                         => ( X1
                                                           != ( setadjoin @ X2 @ emptyset ) ) )
                                                   => ( in @ ( setunion @ X1 ) @ X1 ) )
                                               => ( ! [X1: $i,X2: $i] :
                                                      ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                      = X1 )
                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                       => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                          ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                            = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                         => ( X1 = X3 ) )
                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                            ( ( ( kpair @ X1 @ X2 )
                                                              = ( kpair @ X3 @ X4 ) )
                                                           => ( X1 = X3 ) )
                                                       => ( ! [X1: $i,X2: $i] :
                                                              ( ( X1 = X2 )
                                                             => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                = ( setadjoin @ X1 @ emptyset ) ) )
                                                         => ( ! [X1: $i,X2: $i] :
                                                                ( ( X1 = X2 )
                                                               => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                  = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                  ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                    = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                 => ( ( X3 = X4 )
                                                                   => ( X2 = X4 ) ) )
                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                    ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                      = ( setadjoin @ X3 @ emptyset ) )
                                                                   => ( X1 = X2 ) )
                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                      ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                        = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                     => ( X2 = X4 ) )
                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                        ( ( ( kpair @ X1 @ X2 )
                                                                          = ( kpair @ X3 @ X4 ) )
                                                                       => ( X2 = X4 ) )
                                                                   => ( ! [X1: $i] :
                                                                          ( ( iskpair @ X1 )
                                                                         => ~ ! [X2: $i] :
                                                                                ( ( in @ X2
                                                                                  @ ( dsetconstr @ ( setunion @ X1 )
                                                                                    @ ^ [X3: $i] :
                                                                                        ( X1
                                                                                        = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                               => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                    @ ^ [X3: $i] :
                                                                                        ( X1
                                                                                        = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                 != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                     => ( ! [X1: $i,X2: $i] :
                                                                            ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                            = X2 )
                                                                       => ( sP8
                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                               => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                  ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                 => ( in @ X3 @ X1 ) )
                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                    ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                   => ( in @ X4 @ X2 ) )
                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                      ( ( in @ X3 @ X1 )
                                                                                     => ! [X4: $i] :
                                                                                          ( ( in @ X4 @ X2 )
                                                                                         => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                            = X3 ) ) )
                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                        ( ( in @ X3 @ X1 )
                                                                                       => ! [X4: $i] :
                                                                                            ( ( in @ X4 @ X2 )
                                                                                           => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                              = X4 ) ) )
                                                                                   => ! [X1: $i,X2: $i,X3: $i] :
                                                                                        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                       => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                          = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h250,assumption,
    ! [X1: $i,X2: $i,X3: $i] :
      ( ( in @ X3 @ X1 )
     => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ),
    introduced(assumption,[]) ).

thf(h251,assumption,
    ~ ( ! [X1: $i,X2: $i,X3: $i] :
          ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
         => ( ( X3 != X1 )
           => ( X3 = X2 ) ) )
     => ( ! [X1: $i,X2: $i,X3: $i] :
            ( ( in @ X3 @ X1 )
           => ! [X4: $i] :
                ( ( in @ X4 @ X2 )
               => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
       => ( ! [X1: $i,X2: $i,X3: $i] :
              ( ( in @ X3 @ X1 )
             => ! [X4: $i] :
                  ( ( in @ X4 @ X2 )
                 => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
         => ( ! [X1: $i,X2: $i,X3: $i] :
                ( ( in @ X3 @ X1 )
               => ! [X4: $i] :
                    ( ( in @ X4 @ X2 )
                   => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
           => ( ! [X1: $i,X2: $i,X3: $i] :
                  ( ( in @ X3 @ X1 )
                 => ! [X4: $i] :
                      ( ( in @ X4 @ X2 )
                     => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
             => ( ! [X1: $i,X2: $i,X3: $i] :
                    ( ( in @ X3 @ X1 )
                   => ! [X4: $i] :
                        ( ( in @ X4 @ X2 )
                       => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
               => ( ! [X1: $i,X2: $i,X3: $i] :
                      ( ( in @ X3 @ X1 )
                     => ! [X4: $i] :
                          ( ( in @ X4 @ X2 )
                         => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                 => ( ! [X1: $i,X2: $i,X3: $i] :
                        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                       => ~ ! [X4: $i] :
                              ( ( in @ X4 @ X1 )
                             => ! [X5: $i] :
                                  ( ( in @ X5 @ X2 )
                                 => ( X3
                                   != ( kpair @ X4 @ X5 ) ) ) ) )
                   => ( sP5
                     => ( ! [X1: $i,X2: $i] :
                            ( ( in @ X2 @ ( setunion @ X1 ) )
                           => ~ ! [X3: $i] :
                                  ( ( in @ X3 @ X1 )
                                 => ~ ( in @ X2 @ X3 ) ) )
                       => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                         => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                           => ( ! [X1: $i] :
                                  ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                  = X1 )
                             => ( ! [X1: $i,X2: $i > $o] :
                                    ( ! [X3: $i] :
                                        ( ( in @ X3 @ X1 )
                                       => ! [X4: $i] :
                                            ( ( in @ X4 @ X1 )
                                           => ( ( X2 @ X3 )
                                             => ( ( X2 @ X4 )
                                               => ( X3 = X4 ) ) ) ) )
                                   => ( ~ ! [X3: $i] :
                                            ( ( in @ X3 @ X1 )
                                           => ~ ( X2 @ X3 ) )
                                     => ~ ! [X3: $i] :
                                            ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                           => ( ( dsetconstr @ X1 @ X2 )
                                             != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                               => ( ! [X1: $i,X2: $i > $o] :
                                      ( ~ ! [X3: $i] :
                                            ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                           => ( ( dsetconstr @ X1 @ X2 )
                                             != ( setadjoin @ X3 @ emptyset ) ) )
                                     => ~ ! [X3: $i] :
                                            ( ( in @ X3 @ X1 )
                                           => ~ ( X2 @ X3 ) ) )
                                 => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                        ( ( in @ X3 @ X1 )
                                       => ( ( X2 @ X3 )
                                         => ( ! [X4: $i] :
                                                ( ( in @ X4 @ X1 )
                                               => ( ( X2 @ X4 )
                                                 => ( X4 = X3 ) ) )
                                           => ~ ! [X4: $i] :
                                                  ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                 => ( ( dsetconstr @ X1 @ X2 )
                                                   != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                   => ( ! [X1: $i,X2: $i > $o] :
                                          ( ! [X3: $i] :
                                              ( ( in @ X3 @ X1 )
                                             => ! [X4: $i] :
                                                  ( ( in @ X4 @ X1 )
                                                 => ( ( X2 @ X3 )
                                                   => ( ( X2 @ X4 )
                                                     => ( X3 = X4 ) ) ) ) )
                                         => ( ~ ! [X3: $i] :
                                                  ( ( in @ X3 @ X1 )
                                                 => ~ ( X2 @ X3 ) )
                                           => ~ ! [X3: $i] :
                                                  ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                 => ( ( dsetconstr @ X1 @ X2 )
                                                   != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                     => ( ! [X1: $i,X2: $i] :
                                            ( ( ( setadjoin @ X1 @ emptyset )
                                              = ( setadjoin @ X2 @ emptyset ) )
                                           => ( X1 = X2 ) )
                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                              ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                             => ( X1 = X3 ) )
                                         => ( ! [X1: $i] :
                                                ( ( iskpair @ X1 )
                                               => ~ ! [X2: $i] :
                                                      ( ( in @ X2
                                                        @ ( dsetconstr @ ( setunion @ X1 )
                                                          @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                     => ( ( dsetconstr @ ( setunion @ X1 )
                                                          @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                       != ( setadjoin @ X2 @ emptyset ) ) ) )
                                           => ( ! [X1: $i] :
                                                  ( ~ ! [X2: $i] :
                                                        ( ( in @ X2 @ X1 )
                                                       => ( X1
                                                         != ( setadjoin @ X2 @ emptyset ) ) )
                                                 => ( in @ ( setunion @ X1 ) @ X1 ) )
                                             => ( ! [X1: $i,X2: $i] :
                                                    ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                    = X1 )
                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                      ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                     => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                        ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                          = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                       => ( X1 = X3 ) )
                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                          ( ( ( kpair @ X1 @ X2 )
                                                            = ( kpair @ X3 @ X4 ) )
                                                         => ( X1 = X3 ) )
                                                     => ( ! [X1: $i,X2: $i] :
                                                            ( ( X1 = X2 )
                                                           => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                              = ( setadjoin @ X1 @ emptyset ) ) )
                                                       => ( ! [X1: $i,X2: $i] :
                                                              ( ( X1 = X2 )
                                                             => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                  = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                               => ( ( X3 = X4 )
                                                                 => ( X2 = X4 ) ) )
                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                  ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                    = ( setadjoin @ X3 @ emptyset ) )
                                                                 => ( X1 = X2 ) )
                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                    ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                      = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                   => ( X2 = X4 ) )
                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                      ( ( ( kpair @ X1 @ X2 )
                                                                        = ( kpair @ X3 @ X4 ) )
                                                                     => ( X2 = X4 ) )
                                                                 => ( ! [X1: $i] :
                                                                        ( ( iskpair @ X1 )
                                                                       => ~ ! [X2: $i] :
                                                                              ( ( in @ X2
                                                                                @ ( dsetconstr @ ( setunion @ X1 )
                                                                                  @ ^ [X3: $i] :
                                                                                      ( X1
                                                                                      = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                             => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                  @ ^ [X3: $i] :
                                                                                      ( X1
                                                                                      = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                               != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                   => ( ! [X1: $i,X2: $i] :
                                                                          ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                          = X2 )
                                                                     => ( sP8
                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                              ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                             => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                               => ( in @ X3 @ X1 ) )
                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                  ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                 => ( in @ X4 @ X2 ) )
                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                    ( ( in @ X3 @ X1 )
                                                                                   => ! [X4: $i] :
                                                                                        ( ( in @ X4 @ X2 )
                                                                                       => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                          = X3 ) ) )
                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                      ( ( in @ X3 @ X1 )
                                                                                     => ! [X4: $i] :
                                                                                          ( ( in @ X4 @ X2 )
                                                                                         => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                            = X4 ) ) )
                                                                                 => ! [X1: $i,X2: $i,X3: $i] :
                                                                                      ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                     => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                        = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h252,assumption,
    ~ ( ! [X1: $i,X2: $i,X3: $i] :
          ( ( in @ X3 @ X1 )
         => ! [X4: $i] :
              ( ( in @ X4 @ X2 )
             => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
     => ( ! [X1: $i,X2: $i,X3: $i] :
            ( ( in @ X3 @ X1 )
           => ! [X4: $i] :
                ( ( in @ X4 @ X2 )
               => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
       => ( ! [X1: $i,X2: $i,X3: $i] :
              ( ( in @ X3 @ X1 )
             => ! [X4: $i] :
                  ( ( in @ X4 @ X2 )
                 => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
         => ( ! [X1: $i,X2: $i,X3: $i] :
                ( ( in @ X3 @ X1 )
               => ! [X4: $i] :
                    ( ( in @ X4 @ X2 )
                   => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
           => ( ! [X1: $i,X2: $i,X3: $i] :
                  ( ( in @ X3 @ X1 )
                 => ! [X4: $i] :
                      ( ( in @ X4 @ X2 )
                     => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
             => ( ! [X1: $i,X2: $i,X3: $i] :
                    ( ( in @ X3 @ X1 )
                   => ! [X4: $i] :
                        ( ( in @ X4 @ X2 )
                       => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
               => ( ! [X1: $i,X2: $i,X3: $i] :
                      ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                     => ~ ! [X4: $i] :
                            ( ( in @ X4 @ X1 )
                           => ! [X5: $i] :
                                ( ( in @ X5 @ X2 )
                               => ( X3
                                 != ( kpair @ X4 @ X5 ) ) ) ) )
                 => ( sP5
                   => ( ! [X1: $i,X2: $i] :
                          ( ( in @ X2 @ ( setunion @ X1 ) )
                         => ~ ! [X3: $i] :
                                ( ( in @ X3 @ X1 )
                               => ~ ( in @ X2 @ X3 ) ) )
                     => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                       => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                         => ( ! [X1: $i] :
                                ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                = X1 )
                           => ( ! [X1: $i,X2: $i > $o] :
                                  ( ! [X3: $i] :
                                      ( ( in @ X3 @ X1 )
                                     => ! [X4: $i] :
                                          ( ( in @ X4 @ X1 )
                                         => ( ( X2 @ X3 )
                                           => ( ( X2 @ X4 )
                                             => ( X3 = X4 ) ) ) ) )
                                 => ( ~ ! [X3: $i] :
                                          ( ( in @ X3 @ X1 )
                                         => ~ ( X2 @ X3 ) )
                                   => ~ ! [X3: $i] :
                                          ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                         => ( ( dsetconstr @ X1 @ X2 )
                                           != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                             => ( ! [X1: $i,X2: $i > $o] :
                                    ( ~ ! [X3: $i] :
                                          ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                         => ( ( dsetconstr @ X1 @ X2 )
                                           != ( setadjoin @ X3 @ emptyset ) ) )
                                   => ~ ! [X3: $i] :
                                          ( ( in @ X3 @ X1 )
                                         => ~ ( X2 @ X3 ) ) )
                               => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                      ( ( in @ X3 @ X1 )
                                     => ( ( X2 @ X3 )
                                       => ( ! [X4: $i] :
                                              ( ( in @ X4 @ X1 )
                                             => ( ( X2 @ X4 )
                                               => ( X4 = X3 ) ) )
                                         => ~ ! [X4: $i] :
                                                ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                               => ( ( dsetconstr @ X1 @ X2 )
                                                 != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                 => ( ! [X1: $i,X2: $i > $o] :
                                        ( ! [X3: $i] :
                                            ( ( in @ X3 @ X1 )
                                           => ! [X4: $i] :
                                                ( ( in @ X4 @ X1 )
                                               => ( ( X2 @ X3 )
                                                 => ( ( X2 @ X4 )
                                                   => ( X3 = X4 ) ) ) ) )
                                       => ( ~ ! [X3: $i] :
                                                ( ( in @ X3 @ X1 )
                                               => ~ ( X2 @ X3 ) )
                                         => ~ ! [X3: $i] :
                                                ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                               => ( ( dsetconstr @ X1 @ X2 )
                                                 != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                   => ( ! [X1: $i,X2: $i] :
                                          ( ( ( setadjoin @ X1 @ emptyset )
                                            = ( setadjoin @ X2 @ emptyset ) )
                                         => ( X1 = X2 ) )
                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                            ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                           => ( X1 = X3 ) )
                                       => ( ! [X1: $i] :
                                              ( ( iskpair @ X1 )
                                             => ~ ! [X2: $i] :
                                                    ( ( in @ X2
                                                      @ ( dsetconstr @ ( setunion @ X1 )
                                                        @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                   => ( ( dsetconstr @ ( setunion @ X1 )
                                                        @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                     != ( setadjoin @ X2 @ emptyset ) ) ) )
                                         => ( ! [X1: $i] :
                                                ( ~ ! [X2: $i] :
                                                      ( ( in @ X2 @ X1 )
                                                     => ( X1
                                                       != ( setadjoin @ X2 @ emptyset ) ) )
                                               => ( in @ ( setunion @ X1 ) @ X1 ) )
                                           => ( ! [X1: $i,X2: $i] :
                                                  ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                  = X1 )
                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                    ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                   => ( in @ ( kfst @ X3 ) @ X1 ) )
                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                      ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                        = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                     => ( X1 = X3 ) )
                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                        ( ( ( kpair @ X1 @ X2 )
                                                          = ( kpair @ X3 @ X4 ) )
                                                       => ( X1 = X3 ) )
                                                   => ( ! [X1: $i,X2: $i] :
                                                          ( ( X1 = X2 )
                                                         => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                            = ( setadjoin @ X1 @ emptyset ) ) )
                                                     => ( ! [X1: $i,X2: $i] :
                                                            ( ( X1 = X2 )
                                                           => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                              = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                              ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                             => ( ( X3 = X4 )
                                                               => ( X2 = X4 ) ) )
                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                  = ( setadjoin @ X3 @ emptyset ) )
                                                               => ( X1 = X2 ) )
                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                  ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                    = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                 => ( X2 = X4 ) )
                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                    ( ( ( kpair @ X1 @ X2 )
                                                                      = ( kpair @ X3 @ X4 ) )
                                                                   => ( X2 = X4 ) )
                                                               => ( ! [X1: $i] :
                                                                      ( ( iskpair @ X1 )
                                                                     => ~ ! [X2: $i] :
                                                                            ( ( in @ X2
                                                                              @ ( dsetconstr @ ( setunion @ X1 )
                                                                                @ ^ [X3: $i] :
                                                                                    ( X1
                                                                                    = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                           => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                @ ^ [X3: $i] :
                                                                                    ( X1
                                                                                    = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                             != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                 => ( ! [X1: $i,X2: $i] :
                                                                        ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                        = X2 )
                                                                   => ( sP8
                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                            ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                           => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                              ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                             => ( in @ X3 @ X1 ) )
                                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                               => ( in @ X4 @ X2 ) )
                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                  ( ( in @ X3 @ X1 )
                                                                                 => ! [X4: $i] :
                                                                                      ( ( in @ X4 @ X2 )
                                                                                     => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                        = X3 ) ) )
                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                    ( ( in @ X3 @ X1 )
                                                                                   => ! [X4: $i] :
                                                                                        ( ( in @ X4 @ X2 )
                                                                                       => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                          = X4 ) ) )
                                                                               => ! [X1: $i,X2: $i,X3: $i] :
                                                                                    ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                   => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                      = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h253,assumption,
    ! [X1: $i,X2: $i,X3: $i] :
      ( ( in @ X3 @ X1 )
     => ! [X4: $i] :
          ( ( in @ X4 @ X2 )
         => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) ),
    introduced(assumption,[]) ).

thf(h254,assumption,
    ~ ( ! [X1: $i,X2: $i,X3: $i] :
          ( ( in @ X3 @ X1 )
         => ! [X4: $i] :
              ( ( in @ X4 @ X2 )
             => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
     => ( ! [X1: $i,X2: $i,X3: $i] :
            ( ( in @ X3 @ X1 )
           => ! [X4: $i] :
                ( ( in @ X4 @ X2 )
               => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
       => ( ! [X1: $i,X2: $i,X3: $i] :
              ( ( in @ X3 @ X1 )
             => ! [X4: $i] :
                  ( ( in @ X4 @ X2 )
                 => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
         => ( ! [X1: $i,X2: $i,X3: $i] :
                ( ( in @ X3 @ X1 )
               => ! [X4: $i] :
                    ( ( in @ X4 @ X2 )
                   => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
           => ( ! [X1: $i,X2: $i,X3: $i] :
                  ( ( in @ X3 @ X1 )
                 => ! [X4: $i] :
                      ( ( in @ X4 @ X2 )
                     => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
             => ( ! [X1: $i,X2: $i,X3: $i] :
                    ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                   => ~ ! [X4: $i] :
                          ( ( in @ X4 @ X1 )
                         => ! [X5: $i] :
                              ( ( in @ X5 @ X2 )
                             => ( X3
                               != ( kpair @ X4 @ X5 ) ) ) ) )
               => ( sP5
                 => ( ! [X1: $i,X2: $i] :
                        ( ( in @ X2 @ ( setunion @ X1 ) )
                       => ~ ! [X3: $i] :
                              ( ( in @ X3 @ X1 )
                             => ~ ( in @ X2 @ X3 ) ) )
                   => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                     => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                       => ( ! [X1: $i] :
                              ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                              = X1 )
                         => ( ! [X1: $i,X2: $i > $o] :
                                ( ! [X3: $i] :
                                    ( ( in @ X3 @ X1 )
                                   => ! [X4: $i] :
                                        ( ( in @ X4 @ X1 )
                                       => ( ( X2 @ X3 )
                                         => ( ( X2 @ X4 )
                                           => ( X3 = X4 ) ) ) ) )
                               => ( ~ ! [X3: $i] :
                                        ( ( in @ X3 @ X1 )
                                       => ~ ( X2 @ X3 ) )
                                 => ~ ! [X3: $i] :
                                        ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                       => ( ( dsetconstr @ X1 @ X2 )
                                         != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                           => ( ! [X1: $i,X2: $i > $o] :
                                  ( ~ ! [X3: $i] :
                                        ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                       => ( ( dsetconstr @ X1 @ X2 )
                                         != ( setadjoin @ X3 @ emptyset ) ) )
                                 => ~ ! [X3: $i] :
                                        ( ( in @ X3 @ X1 )
                                       => ~ ( X2 @ X3 ) ) )
                             => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                    ( ( in @ X3 @ X1 )
                                   => ( ( X2 @ X3 )
                                     => ( ! [X4: $i] :
                                            ( ( in @ X4 @ X1 )
                                           => ( ( X2 @ X4 )
                                             => ( X4 = X3 ) ) )
                                       => ~ ! [X4: $i] :
                                              ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                             => ( ( dsetconstr @ X1 @ X2 )
                                               != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                               => ( ! [X1: $i,X2: $i > $o] :
                                      ( ! [X3: $i] :
                                          ( ( in @ X3 @ X1 )
                                         => ! [X4: $i] :
                                              ( ( in @ X4 @ X1 )
                                             => ( ( X2 @ X3 )
                                               => ( ( X2 @ X4 )
                                                 => ( X3 = X4 ) ) ) ) )
                                     => ( ~ ! [X3: $i] :
                                              ( ( in @ X3 @ X1 )
                                             => ~ ( X2 @ X3 ) )
                                       => ~ ! [X3: $i] :
                                              ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                             => ( ( dsetconstr @ X1 @ X2 )
                                               != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                 => ( ! [X1: $i,X2: $i] :
                                        ( ( ( setadjoin @ X1 @ emptyset )
                                          = ( setadjoin @ X2 @ emptyset ) )
                                       => ( X1 = X2 ) )
                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                          ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                         => ( X1 = X3 ) )
                                     => ( ! [X1: $i] :
                                            ( ( iskpair @ X1 )
                                           => ~ ! [X2: $i] :
                                                  ( ( in @ X2
                                                    @ ( dsetconstr @ ( setunion @ X1 )
                                                      @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                 => ( ( dsetconstr @ ( setunion @ X1 )
                                                      @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                   != ( setadjoin @ X2 @ emptyset ) ) ) )
                                       => ( ! [X1: $i] :
                                              ( ~ ! [X2: $i] :
                                                    ( ( in @ X2 @ X1 )
                                                   => ( X1
                                                     != ( setadjoin @ X2 @ emptyset ) ) )
                                             => ( in @ ( setunion @ X1 ) @ X1 ) )
                                         => ( ! [X1: $i,X2: $i] :
                                                ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                = X1 )
                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                  ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                 => ( in @ ( kfst @ X3 ) @ X1 ) )
                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                    ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                      = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                   => ( X1 = X3 ) )
                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                      ( ( ( kpair @ X1 @ X2 )
                                                        = ( kpair @ X3 @ X4 ) )
                                                     => ( X1 = X3 ) )
                                                 => ( ! [X1: $i,X2: $i] :
                                                        ( ( X1 = X2 )
                                                       => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                          = ( setadjoin @ X1 @ emptyset ) ) )
                                                   => ( ! [X1: $i,X2: $i] :
                                                          ( ( X1 = X2 )
                                                         => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                            = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                            ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                              = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                           => ( ( X3 = X4 )
                                                             => ( X2 = X4 ) ) )
                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                              ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                = ( setadjoin @ X3 @ emptyset ) )
                                                             => ( X1 = X2 ) )
                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                  = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                               => ( X2 = X4 ) )
                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                  ( ( ( kpair @ X1 @ X2 )
                                                                    = ( kpair @ X3 @ X4 ) )
                                                                 => ( X2 = X4 ) )
                                                             => ( ! [X1: $i] :
                                                                    ( ( iskpair @ X1 )
                                                                   => ~ ! [X2: $i] :
                                                                          ( ( in @ X2
                                                                            @ ( dsetconstr @ ( setunion @ X1 )
                                                                              @ ^ [X3: $i] :
                                                                                  ( X1
                                                                                  = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                         => ( ( dsetconstr @ ( setunion @ X1 )
                                                                              @ ^ [X3: $i] :
                                                                                  ( X1
                                                                                  = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                           != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                               => ( ! [X1: $i,X2: $i] :
                                                                      ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                      = X2 )
                                                                 => ( sP8
                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                         => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                            ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                           => ( in @ X3 @ X1 ) )
                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                              ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                             => ( in @ X4 @ X2 ) )
                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                ( ( in @ X3 @ X1 )
                                                                               => ! [X4: $i] :
                                                                                    ( ( in @ X4 @ X2 )
                                                                                   => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                      = X3 ) ) )
                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                  ( ( in @ X3 @ X1 )
                                                                                 => ! [X4: $i] :
                                                                                      ( ( in @ X4 @ X2 )
                                                                                     => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                        = X4 ) ) )
                                                                             => ! [X1: $i,X2: $i,X3: $i] :
                                                                                  ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                 => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                    = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h255,assumption,
    ! [X1: $i,X2: $i,X3: $i] :
      ( ( in @ X3 @ X1 )
     => ! [X4: $i] :
          ( ( in @ X4 @ X2 )
         => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h256,assumption,
    ~ ( ! [X1: $i,X2: $i,X3: $i] :
          ( ( in @ X3 @ X1 )
         => ! [X4: $i] :
              ( ( in @ X4 @ X2 )
             => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
     => ( ! [X1: $i,X2: $i,X3: $i] :
            ( ( in @ X3 @ X1 )
           => ! [X4: $i] :
                ( ( in @ X4 @ X2 )
               => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
       => ( ! [X1: $i,X2: $i,X3: $i] :
              ( ( in @ X3 @ X1 )
             => ! [X4: $i] :
                  ( ( in @ X4 @ X2 )
                 => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
         => ( ! [X1: $i,X2: $i,X3: $i] :
                ( ( in @ X3 @ X1 )
               => ! [X4: $i] :
                    ( ( in @ X4 @ X2 )
                   => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
           => ( ! [X1: $i,X2: $i,X3: $i] :
                  ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                 => ~ ! [X4: $i] :
                        ( ( in @ X4 @ X1 )
                       => ! [X5: $i] :
                            ( ( in @ X5 @ X2 )
                           => ( X3
                             != ( kpair @ X4 @ X5 ) ) ) ) )
             => ( sP5
               => ( ! [X1: $i,X2: $i] :
                      ( ( in @ X2 @ ( setunion @ X1 ) )
                     => ~ ! [X3: $i] :
                            ( ( in @ X3 @ X1 )
                           => ~ ( in @ X2 @ X3 ) ) )
                 => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                   => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                     => ( ! [X1: $i] :
                            ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                            = X1 )
                       => ( ! [X1: $i,X2: $i > $o] :
                              ( ! [X3: $i] :
                                  ( ( in @ X3 @ X1 )
                                 => ! [X4: $i] :
                                      ( ( in @ X4 @ X1 )
                                     => ( ( X2 @ X3 )
                                       => ( ( X2 @ X4 )
                                         => ( X3 = X4 ) ) ) ) )
                             => ( ~ ! [X3: $i] :
                                      ( ( in @ X3 @ X1 )
                                     => ~ ( X2 @ X3 ) )
                               => ~ ! [X3: $i] :
                                      ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                     => ( ( dsetconstr @ X1 @ X2 )
                                       != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                         => ( ! [X1: $i,X2: $i > $o] :
                                ( ~ ! [X3: $i] :
                                      ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                     => ( ( dsetconstr @ X1 @ X2 )
                                       != ( setadjoin @ X3 @ emptyset ) ) )
                               => ~ ! [X3: $i] :
                                      ( ( in @ X3 @ X1 )
                                     => ~ ( X2 @ X3 ) ) )
                           => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                  ( ( in @ X3 @ X1 )
                                 => ( ( X2 @ X3 )
                                   => ( ! [X4: $i] :
                                          ( ( in @ X4 @ X1 )
                                         => ( ( X2 @ X4 )
                                           => ( X4 = X3 ) ) )
                                     => ~ ! [X4: $i] :
                                            ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                           => ( ( dsetconstr @ X1 @ X2 )
                                             != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                             => ( ! [X1: $i,X2: $i > $o] :
                                    ( ! [X3: $i] :
                                        ( ( in @ X3 @ X1 )
                                       => ! [X4: $i] :
                                            ( ( in @ X4 @ X1 )
                                           => ( ( X2 @ X3 )
                                             => ( ( X2 @ X4 )
                                               => ( X3 = X4 ) ) ) ) )
                                   => ( ~ ! [X3: $i] :
                                            ( ( in @ X3 @ X1 )
                                           => ~ ( X2 @ X3 ) )
                                     => ~ ! [X3: $i] :
                                            ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                           => ( ( dsetconstr @ X1 @ X2 )
                                             != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                               => ( ! [X1: $i,X2: $i] :
                                      ( ( ( setadjoin @ X1 @ emptyset )
                                        = ( setadjoin @ X2 @ emptyset ) )
                                     => ( X1 = X2 ) )
                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                        ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                       => ( X1 = X3 ) )
                                   => ( ! [X1: $i] :
                                          ( ( iskpair @ X1 )
                                         => ~ ! [X2: $i] :
                                                ( ( in @ X2
                                                  @ ( dsetconstr @ ( setunion @ X1 )
                                                    @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                               => ( ( dsetconstr @ ( setunion @ X1 )
                                                    @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                 != ( setadjoin @ X2 @ emptyset ) ) ) )
                                     => ( ! [X1: $i] :
                                            ( ~ ! [X2: $i] :
                                                  ( ( in @ X2 @ X1 )
                                                 => ( X1
                                                   != ( setadjoin @ X2 @ emptyset ) ) )
                                           => ( in @ ( setunion @ X1 ) @ X1 ) )
                                       => ( ! [X1: $i,X2: $i] :
                                              ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                              = X1 )
                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                               => ( in @ ( kfst @ X3 ) @ X1 ) )
                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                  ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                    = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                 => ( X1 = X3 ) )
                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                    ( ( ( kpair @ X1 @ X2 )
                                                      = ( kpair @ X3 @ X4 ) )
                                                   => ( X1 = X3 ) )
                                               => ( ! [X1: $i,X2: $i] :
                                                      ( ( X1 = X2 )
                                                     => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                        = ( setadjoin @ X1 @ emptyset ) ) )
                                                 => ( ! [X1: $i,X2: $i] :
                                                        ( ( X1 = X2 )
                                                       => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                          = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                          ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                            = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                         => ( ( X3 = X4 )
                                                           => ( X2 = X4 ) ) )
                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                            ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                              = ( setadjoin @ X3 @ emptyset ) )
                                                           => ( X1 = X2 ) )
                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                              ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                             => ( X2 = X4 ) )
                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                ( ( ( kpair @ X1 @ X2 )
                                                                  = ( kpair @ X3 @ X4 ) )
                                                               => ( X2 = X4 ) )
                                                           => ( ! [X1: $i] :
                                                                  ( ( iskpair @ X1 )
                                                                 => ~ ! [X2: $i] :
                                                                        ( ( in @ X2
                                                                          @ ( dsetconstr @ ( setunion @ X1 )
                                                                            @ ^ [X3: $i] :
                                                                                ( X1
                                                                                = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                       => ( ( dsetconstr @ ( setunion @ X1 )
                                                                            @ ^ [X3: $i] :
                                                                                ( X1
                                                                                = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                         != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                             => ( ! [X1: $i,X2: $i] :
                                                                    ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                    = X2 )
                                                               => ( sP8
                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                       => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                          ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                         => ( in @ X3 @ X1 ) )
                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                            ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                           => ( in @ X4 @ X2 ) )
                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                              ( ( in @ X3 @ X1 )
                                                                             => ! [X4: $i] :
                                                                                  ( ( in @ X4 @ X2 )
                                                                                 => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                    = X3 ) ) )
                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                ( ( in @ X3 @ X1 )
                                                                               => ! [X4: $i] :
                                                                                    ( ( in @ X4 @ X2 )
                                                                                   => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                      = X4 ) ) )
                                                                           => ! [X1: $i,X2: $i,X3: $i] :
                                                                                ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                               => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                  = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h257,assumption,
    ! [X1: $i,X2: $i,X3: $i] :
      ( ( in @ X3 @ X1 )
     => ! [X4: $i] :
          ( ( in @ X4 @ X2 )
         => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h258,assumption,
    ~ ( ! [X1: $i,X2: $i,X3: $i] :
          ( ( in @ X3 @ X1 )
         => ! [X4: $i] :
              ( ( in @ X4 @ X2 )
             => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
     => ( ! [X1: $i,X2: $i,X3: $i] :
            ( ( in @ X3 @ X1 )
           => ! [X4: $i] :
                ( ( in @ X4 @ X2 )
               => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
       => ( ! [X1: $i,X2: $i,X3: $i] :
              ( ( in @ X3 @ X1 )
             => ! [X4: $i] :
                  ( ( in @ X4 @ X2 )
                 => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
         => ( ! [X1: $i,X2: $i,X3: $i] :
                ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
               => ~ ! [X4: $i] :
                      ( ( in @ X4 @ X1 )
                     => ! [X5: $i] :
                          ( ( in @ X5 @ X2 )
                         => ( X3
                           != ( kpair @ X4 @ X5 ) ) ) ) )
           => ( sP5
             => ( ! [X1: $i,X2: $i] :
                    ( ( in @ X2 @ ( setunion @ X1 ) )
                   => ~ ! [X3: $i] :
                          ( ( in @ X3 @ X1 )
                         => ~ ( in @ X2 @ X3 ) ) )
               => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                 => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                   => ( ! [X1: $i] :
                          ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                          = X1 )
                     => ( ! [X1: $i,X2: $i > $o] :
                            ( ! [X3: $i] :
                                ( ( in @ X3 @ X1 )
                               => ! [X4: $i] :
                                    ( ( in @ X4 @ X1 )
                                   => ( ( X2 @ X3 )
                                     => ( ( X2 @ X4 )
                                       => ( X3 = X4 ) ) ) ) )
                           => ( ~ ! [X3: $i] :
                                    ( ( in @ X3 @ X1 )
                                   => ~ ( X2 @ X3 ) )
                             => ~ ! [X3: $i] :
                                    ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                   => ( ( dsetconstr @ X1 @ X2 )
                                     != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                       => ( ! [X1: $i,X2: $i > $o] :
                              ( ~ ! [X3: $i] :
                                    ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                   => ( ( dsetconstr @ X1 @ X2 )
                                     != ( setadjoin @ X3 @ emptyset ) ) )
                             => ~ ! [X3: $i] :
                                    ( ( in @ X3 @ X1 )
                                   => ~ ( X2 @ X3 ) ) )
                         => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                ( ( in @ X3 @ X1 )
                               => ( ( X2 @ X3 )
                                 => ( ! [X4: $i] :
                                        ( ( in @ X4 @ X1 )
                                       => ( ( X2 @ X4 )
                                         => ( X4 = X3 ) ) )
                                   => ~ ! [X4: $i] :
                                          ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                         => ( ( dsetconstr @ X1 @ X2 )
                                           != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                           => ( ! [X1: $i,X2: $i > $o] :
                                  ( ! [X3: $i] :
                                      ( ( in @ X3 @ X1 )
                                     => ! [X4: $i] :
                                          ( ( in @ X4 @ X1 )
                                         => ( ( X2 @ X3 )
                                           => ( ( X2 @ X4 )
                                             => ( X3 = X4 ) ) ) ) )
                                 => ( ~ ! [X3: $i] :
                                          ( ( in @ X3 @ X1 )
                                         => ~ ( X2 @ X3 ) )
                                   => ~ ! [X3: $i] :
                                          ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                         => ( ( dsetconstr @ X1 @ X2 )
                                           != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                             => ( ! [X1: $i,X2: $i] :
                                    ( ( ( setadjoin @ X1 @ emptyset )
                                      = ( setadjoin @ X2 @ emptyset ) )
                                   => ( X1 = X2 ) )
                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                      ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                     => ( X1 = X3 ) )
                                 => ( ! [X1: $i] :
                                        ( ( iskpair @ X1 )
                                       => ~ ! [X2: $i] :
                                              ( ( in @ X2
                                                @ ( dsetconstr @ ( setunion @ X1 )
                                                  @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                             => ( ( dsetconstr @ ( setunion @ X1 )
                                                  @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                               != ( setadjoin @ X2 @ emptyset ) ) ) )
                                   => ( ! [X1: $i] :
                                          ( ~ ! [X2: $i] :
                                                ( ( in @ X2 @ X1 )
                                               => ( X1
                                                 != ( setadjoin @ X2 @ emptyset ) ) )
                                         => ( in @ ( setunion @ X1 ) @ X1 ) )
                                     => ( ! [X1: $i,X2: $i] :
                                            ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                            = X1 )
                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                              ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                             => ( in @ ( kfst @ X3 ) @ X1 ) )
                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                  = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                               => ( X1 = X3 ) )
                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                  ( ( ( kpair @ X1 @ X2 )
                                                    = ( kpair @ X3 @ X4 ) )
                                                 => ( X1 = X3 ) )
                                             => ( ! [X1: $i,X2: $i] :
                                                    ( ( X1 = X2 )
                                                   => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                      = ( setadjoin @ X1 @ emptyset ) ) )
                                               => ( ! [X1: $i,X2: $i] :
                                                      ( ( X1 = X2 )
                                                     => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                        = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                        ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                          = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                       => ( ( X3 = X4 )
                                                         => ( X2 = X4 ) ) )
                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                          ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                            = ( setadjoin @ X3 @ emptyset ) )
                                                         => ( X1 = X2 ) )
                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                            ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                              = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                           => ( X2 = X4 ) )
                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                              ( ( ( kpair @ X1 @ X2 )
                                                                = ( kpair @ X3 @ X4 ) )
                                                             => ( X2 = X4 ) )
                                                         => ( ! [X1: $i] :
                                                                ( ( iskpair @ X1 )
                                                               => ~ ! [X2: $i] :
                                                                      ( ( in @ X2
                                                                        @ ( dsetconstr @ ( setunion @ X1 )
                                                                          @ ^ [X3: $i] :
                                                                              ( X1
                                                                              = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                     => ( ( dsetconstr @ ( setunion @ X1 )
                                                                          @ ^ [X3: $i] :
                                                                              ( X1
                                                                              = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                       != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                           => ( ! [X1: $i,X2: $i] :
                                                                  ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                  = X2 )
                                                             => ( sP8
                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                      ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                     => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                        ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                       => ( in @ X3 @ X1 ) )
                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                          ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                         => ( in @ X4 @ X2 ) )
                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                            ( ( in @ X3 @ X1 )
                                                                           => ! [X4: $i] :
                                                                                ( ( in @ X4 @ X2 )
                                                                               => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                  = X3 ) ) )
                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                              ( ( in @ X3 @ X1 )
                                                                             => ! [X4: $i] :
                                                                                  ( ( in @ X4 @ X2 )
                                                                                 => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                    = X4 ) ) )
                                                                         => ! [X1: $i,X2: $i,X3: $i] :
                                                                              ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                             => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h259,assumption,
    ! [X1: $i,X2: $i,X3: $i] :
      ( ( in @ X3 @ X1 )
     => ! [X4: $i] :
          ( ( in @ X4 @ X2 )
         => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h260,assumption,
    ~ ( ! [X1: $i,X2: $i,X3: $i] :
          ( ( in @ X3 @ X1 )
         => ! [X4: $i] :
              ( ( in @ X4 @ X2 )
             => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
     => ( ! [X1: $i,X2: $i,X3: $i] :
            ( ( in @ X3 @ X1 )
           => ! [X4: $i] :
                ( ( in @ X4 @ X2 )
               => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
       => ( ! [X1: $i,X2: $i,X3: $i] :
              ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
             => ~ ! [X4: $i] :
                    ( ( in @ X4 @ X1 )
                   => ! [X5: $i] :
                        ( ( in @ X5 @ X2 )
                       => ( X3
                         != ( kpair @ X4 @ X5 ) ) ) ) )
         => ( sP5
           => ( ! [X1: $i,X2: $i] :
                  ( ( in @ X2 @ ( setunion @ X1 ) )
                 => ~ ! [X3: $i] :
                        ( ( in @ X3 @ X1 )
                       => ~ ( in @ X2 @ X3 ) ) )
             => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
               => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                 => ( ! [X1: $i] :
                        ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                        = X1 )
                   => ( ! [X1: $i,X2: $i > $o] :
                          ( ! [X3: $i] :
                              ( ( in @ X3 @ X1 )
                             => ! [X4: $i] :
                                  ( ( in @ X4 @ X1 )
                                 => ( ( X2 @ X3 )
                                   => ( ( X2 @ X4 )
                                     => ( X3 = X4 ) ) ) ) )
                         => ( ~ ! [X3: $i] :
                                  ( ( in @ X3 @ X1 )
                                 => ~ ( X2 @ X3 ) )
                           => ~ ! [X3: $i] :
                                  ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                 => ( ( dsetconstr @ X1 @ X2 )
                                   != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                     => ( ! [X1: $i,X2: $i > $o] :
                            ( ~ ! [X3: $i] :
                                  ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                 => ( ( dsetconstr @ X1 @ X2 )
                                   != ( setadjoin @ X3 @ emptyset ) ) )
                           => ~ ! [X3: $i] :
                                  ( ( in @ X3 @ X1 )
                                 => ~ ( X2 @ X3 ) ) )
                       => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                              ( ( in @ X3 @ X1 )
                             => ( ( X2 @ X3 )
                               => ( ! [X4: $i] :
                                      ( ( in @ X4 @ X1 )
                                     => ( ( X2 @ X4 )
                                       => ( X4 = X3 ) ) )
                                 => ~ ! [X4: $i] :
                                        ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                       => ( ( dsetconstr @ X1 @ X2 )
                                         != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                         => ( ! [X1: $i,X2: $i > $o] :
                                ( ! [X3: $i] :
                                    ( ( in @ X3 @ X1 )
                                   => ! [X4: $i] :
                                        ( ( in @ X4 @ X1 )
                                       => ( ( X2 @ X3 )
                                         => ( ( X2 @ X4 )
                                           => ( X3 = X4 ) ) ) ) )
                               => ( ~ ! [X3: $i] :
                                        ( ( in @ X3 @ X1 )
                                       => ~ ( X2 @ X3 ) )
                                 => ~ ! [X3: $i] :
                                        ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                       => ( ( dsetconstr @ X1 @ X2 )
                                         != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                           => ( ! [X1: $i,X2: $i] :
                                  ( ( ( setadjoin @ X1 @ emptyset )
                                    = ( setadjoin @ X2 @ emptyset ) )
                                 => ( X1 = X2 ) )
                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                    ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                   => ( X1 = X3 ) )
                               => ( ! [X1: $i] :
                                      ( ( iskpair @ X1 )
                                     => ~ ! [X2: $i] :
                                            ( ( in @ X2
                                              @ ( dsetconstr @ ( setunion @ X1 )
                                                @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                           => ( ( dsetconstr @ ( setunion @ X1 )
                                                @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                             != ( setadjoin @ X2 @ emptyset ) ) ) )
                                 => ( ! [X1: $i] :
                                        ( ~ ! [X2: $i] :
                                              ( ( in @ X2 @ X1 )
                                             => ( X1
                                               != ( setadjoin @ X2 @ emptyset ) ) )
                                       => ( in @ ( setunion @ X1 ) @ X1 ) )
                                   => ( ! [X1: $i,X2: $i] :
                                          ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                          = X1 )
                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                            ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                           => ( in @ ( kfst @ X3 ) @ X1 ) )
                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                              ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                             => ( X1 = X3 ) )
                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                ( ( ( kpair @ X1 @ X2 )
                                                  = ( kpair @ X3 @ X4 ) )
                                               => ( X1 = X3 ) )
                                           => ( ! [X1: $i,X2: $i] :
                                                  ( ( X1 = X2 )
                                                 => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                    = ( setadjoin @ X1 @ emptyset ) ) )
                                             => ( ! [X1: $i,X2: $i] :
                                                    ( ( X1 = X2 )
                                                   => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                      = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                      ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                        = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                     => ( ( X3 = X4 )
                                                       => ( X2 = X4 ) ) )
                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                        ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                          = ( setadjoin @ X3 @ emptyset ) )
                                                       => ( X1 = X2 ) )
                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                          ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                            = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                         => ( X2 = X4 ) )
                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                            ( ( ( kpair @ X1 @ X2 )
                                                              = ( kpair @ X3 @ X4 ) )
                                                           => ( X2 = X4 ) )
                                                       => ( ! [X1: $i] :
                                                              ( ( iskpair @ X1 )
                                                             => ~ ! [X2: $i] :
                                                                    ( ( in @ X2
                                                                      @ ( dsetconstr @ ( setunion @ X1 )
                                                                        @ ^ [X3: $i] :
                                                                            ( X1
                                                                            = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                   => ( ( dsetconstr @ ( setunion @ X1 )
                                                                        @ ^ [X3: $i] :
                                                                            ( X1
                                                                            = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                     != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                         => ( ! [X1: $i,X2: $i] :
                                                                ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                = X2 )
                                                           => ( sP8
                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                    ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                   => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                      ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                     => ( in @ X3 @ X1 ) )
                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                        ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                       => ( in @ X4 @ X2 ) )
                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                          ( ( in @ X3 @ X1 )
                                                                         => ! [X4: $i] :
                                                                              ( ( in @ X4 @ X2 )
                                                                             => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                = X3 ) ) )
                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                            ( ( in @ X3 @ X1 )
                                                                           => ! [X4: $i] :
                                                                                ( ( in @ X4 @ X2 )
                                                                               => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                  = X4 ) ) )
                                                                       => ! [X1: $i,X2: $i,X3: $i] :
                                                                            ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                           => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                              = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h261,assumption,
    ! [X1: $i,X2: $i,X3: $i] :
      ( ( in @ X3 @ X1 )
     => ! [X4: $i] :
          ( ( in @ X4 @ X2 )
         => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h262,assumption,
    ~ ( ! [X1: $i,X2: $i,X3: $i] :
          ( ( in @ X3 @ X1 )
         => ! [X4: $i] :
              ( ( in @ X4 @ X2 )
             => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
     => ( ! [X1: $i,X2: $i,X3: $i] :
            ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
           => ~ ! [X4: $i] :
                  ( ( in @ X4 @ X1 )
                 => ! [X5: $i] :
                      ( ( in @ X5 @ X2 )
                     => ( X3
                       != ( kpair @ X4 @ X5 ) ) ) ) )
       => ( sP5
         => ( ! [X1: $i,X2: $i] :
                ( ( in @ X2 @ ( setunion @ X1 ) )
               => ~ ! [X3: $i] :
                      ( ( in @ X3 @ X1 )
                     => ~ ( in @ X2 @ X3 ) ) )
           => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
             => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
               => ( ! [X1: $i] :
                      ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                      = X1 )
                 => ( ! [X1: $i,X2: $i > $o] :
                        ( ! [X3: $i] :
                            ( ( in @ X3 @ X1 )
                           => ! [X4: $i] :
                                ( ( in @ X4 @ X1 )
                               => ( ( X2 @ X3 )
                                 => ( ( X2 @ X4 )
                                   => ( X3 = X4 ) ) ) ) )
                       => ( ~ ! [X3: $i] :
                                ( ( in @ X3 @ X1 )
                               => ~ ( X2 @ X3 ) )
                         => ~ ! [X3: $i] :
                                ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                               => ( ( dsetconstr @ X1 @ X2 )
                                 != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                   => ( ! [X1: $i,X2: $i > $o] :
                          ( ~ ! [X3: $i] :
                                ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                               => ( ( dsetconstr @ X1 @ X2 )
                                 != ( setadjoin @ X3 @ emptyset ) ) )
                         => ~ ! [X3: $i] :
                                ( ( in @ X3 @ X1 )
                               => ~ ( X2 @ X3 ) ) )
                     => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                            ( ( in @ X3 @ X1 )
                           => ( ( X2 @ X3 )
                             => ( ! [X4: $i] :
                                    ( ( in @ X4 @ X1 )
                                   => ( ( X2 @ X4 )
                                     => ( X4 = X3 ) ) )
                               => ~ ! [X4: $i] :
                                      ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                     => ( ( dsetconstr @ X1 @ X2 )
                                       != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                       => ( ! [X1: $i,X2: $i > $o] :
                              ( ! [X3: $i] :
                                  ( ( in @ X3 @ X1 )
                                 => ! [X4: $i] :
                                      ( ( in @ X4 @ X1 )
                                     => ( ( X2 @ X3 )
                                       => ( ( X2 @ X4 )
                                         => ( X3 = X4 ) ) ) ) )
                             => ( ~ ! [X3: $i] :
                                      ( ( in @ X3 @ X1 )
                                     => ~ ( X2 @ X3 ) )
                               => ~ ! [X3: $i] :
                                      ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                     => ( ( dsetconstr @ X1 @ X2 )
                                       != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                         => ( ! [X1: $i,X2: $i] :
                                ( ( ( setadjoin @ X1 @ emptyset )
                                  = ( setadjoin @ X2 @ emptyset ) )
                               => ( X1 = X2 ) )
                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                  ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                 => ( X1 = X3 ) )
                             => ( ! [X1: $i] :
                                    ( ( iskpair @ X1 )
                                   => ~ ! [X2: $i] :
                                          ( ( in @ X2
                                            @ ( dsetconstr @ ( setunion @ X1 )
                                              @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                         => ( ( dsetconstr @ ( setunion @ X1 )
                                              @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                           != ( setadjoin @ X2 @ emptyset ) ) ) )
                               => ( ! [X1: $i] :
                                      ( ~ ! [X2: $i] :
                                            ( ( in @ X2 @ X1 )
                                           => ( X1
                                             != ( setadjoin @ X2 @ emptyset ) ) )
                                     => ( in @ ( setunion @ X1 ) @ X1 ) )
                                 => ( ! [X1: $i,X2: $i] :
                                        ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                        = X1 )
                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                         => ( in @ ( kfst @ X3 ) @ X1 ) )
                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                            ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                              = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                           => ( X1 = X3 ) )
                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                              ( ( ( kpair @ X1 @ X2 )
                                                = ( kpair @ X3 @ X4 ) )
                                             => ( X1 = X3 ) )
                                         => ( ! [X1: $i,X2: $i] :
                                                ( ( X1 = X2 )
                                               => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                  = ( setadjoin @ X1 @ emptyset ) ) )
                                           => ( ! [X1: $i,X2: $i] :
                                                  ( ( X1 = X2 )
                                                 => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                    = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                    ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                      = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                   => ( ( X3 = X4 )
                                                     => ( X2 = X4 ) ) )
                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                      ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                        = ( setadjoin @ X3 @ emptyset ) )
                                                     => ( X1 = X2 ) )
                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                        ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                          = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                       => ( X2 = X4 ) )
                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                          ( ( ( kpair @ X1 @ X2 )
                                                            = ( kpair @ X3 @ X4 ) )
                                                         => ( X2 = X4 ) )
                                                     => ( ! [X1: $i] :
                                                            ( ( iskpair @ X1 )
                                                           => ~ ! [X2: $i] :
                                                                  ( ( in @ X2
                                                                    @ ( dsetconstr @ ( setunion @ X1 )
                                                                      @ ^ [X3: $i] :
                                                                          ( X1
                                                                          = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                 => ( ( dsetconstr @ ( setunion @ X1 )
                                                                      @ ^ [X3: $i] :
                                                                          ( X1
                                                                          = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                   != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                       => ( ! [X1: $i,X2: $i] :
                                                              ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                              = X2 )
                                                         => ( sP8
                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                  ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                 => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                    ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                   => ( in @ X3 @ X1 ) )
                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                      ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                     => ( in @ X4 @ X2 ) )
                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                        ( ( in @ X3 @ X1 )
                                                                       => ! [X4: $i] :
                                                                            ( ( in @ X4 @ X2 )
                                                                           => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                              = X3 ) ) )
                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                          ( ( in @ X3 @ X1 )
                                                                         => ! [X4: $i] :
                                                                              ( ( in @ X4 @ X2 )
                                                                             => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                = X4 ) ) )
                                                                     => ! [X1: $i,X2: $i,X3: $i] :
                                                                          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                         => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                            = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h263,assumption,
    ! [X1: $i,X2: $i,X3: $i] :
      ( ( in @ X3 @ X1 )
     => ! [X4: $i] :
          ( ( in @ X4 @ X2 )
         => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) ),
    introduced(assumption,[]) ).

thf(h264,assumption,
    ~ ( ! [X1: $i,X2: $i,X3: $i] :
          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
         => ~ ! [X4: $i] :
                ( ( in @ X4 @ X1 )
               => ! [X5: $i] :
                    ( ( in @ X5 @ X2 )
                   => ( X3
                     != ( kpair @ X4 @ X5 ) ) ) ) )
     => ( sP5
       => ( ! [X1: $i,X2: $i] :
              ( ( in @ X2 @ ( setunion @ X1 ) )
             => ~ ! [X3: $i] :
                    ( ( in @ X3 @ X1 )
                   => ~ ( in @ X2 @ X3 ) ) )
         => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
           => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
             => ( ! [X1: $i] :
                    ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                    = X1 )
               => ( ! [X1: $i,X2: $i > $o] :
                      ( ! [X3: $i] :
                          ( ( in @ X3 @ X1 )
                         => ! [X4: $i] :
                              ( ( in @ X4 @ X1 )
                             => ( ( X2 @ X3 )
                               => ( ( X2 @ X4 )
                                 => ( X3 = X4 ) ) ) ) )
                     => ( ~ ! [X3: $i] :
                              ( ( in @ X3 @ X1 )
                             => ~ ( X2 @ X3 ) )
                       => ~ ! [X3: $i] :
                              ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                             => ( ( dsetconstr @ X1 @ X2 )
                               != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                 => ( ! [X1: $i,X2: $i > $o] :
                        ( ~ ! [X3: $i] :
                              ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                             => ( ( dsetconstr @ X1 @ X2 )
                               != ( setadjoin @ X3 @ emptyset ) ) )
                       => ~ ! [X3: $i] :
                              ( ( in @ X3 @ X1 )
                             => ~ ( X2 @ X3 ) ) )
                   => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                          ( ( in @ X3 @ X1 )
                         => ( ( X2 @ X3 )
                           => ( ! [X4: $i] :
                                  ( ( in @ X4 @ X1 )
                                 => ( ( X2 @ X4 )
                                   => ( X4 = X3 ) ) )
                             => ~ ! [X4: $i] :
                                    ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                   => ( ( dsetconstr @ X1 @ X2 )
                                     != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                     => ( ! [X1: $i,X2: $i > $o] :
                            ( ! [X3: $i] :
                                ( ( in @ X3 @ X1 )
                               => ! [X4: $i] :
                                    ( ( in @ X4 @ X1 )
                                   => ( ( X2 @ X3 )
                                     => ( ( X2 @ X4 )
                                       => ( X3 = X4 ) ) ) ) )
                           => ( ~ ! [X3: $i] :
                                    ( ( in @ X3 @ X1 )
                                   => ~ ( X2 @ X3 ) )
                             => ~ ! [X3: $i] :
                                    ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                   => ( ( dsetconstr @ X1 @ X2 )
                                     != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                       => ( ! [X1: $i,X2: $i] :
                              ( ( ( setadjoin @ X1 @ emptyset )
                                = ( setadjoin @ X2 @ emptyset ) )
                             => ( X1 = X2 ) )
                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                               => ( X1 = X3 ) )
                           => ( ! [X1: $i] :
                                  ( ( iskpair @ X1 )
                                 => ~ ! [X2: $i] :
                                        ( ( in @ X2
                                          @ ( dsetconstr @ ( setunion @ X1 )
                                            @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                       => ( ( dsetconstr @ ( setunion @ X1 )
                                            @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                         != ( setadjoin @ X2 @ emptyset ) ) ) )
                             => ( ! [X1: $i] :
                                    ( ~ ! [X2: $i] :
                                          ( ( in @ X2 @ X1 )
                                         => ( X1
                                           != ( setadjoin @ X2 @ emptyset ) ) )
                                   => ( in @ ( setunion @ X1 ) @ X1 ) )
                               => ( ! [X1: $i,X2: $i] :
                                      ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                      = X1 )
                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                       => ( in @ ( kfst @ X3 ) @ X1 ) )
                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                          ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                            = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                         => ( X1 = X3 ) )
                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                            ( ( ( kpair @ X1 @ X2 )
                                              = ( kpair @ X3 @ X4 ) )
                                           => ( X1 = X3 ) )
                                       => ( ! [X1: $i,X2: $i] :
                                              ( ( X1 = X2 )
                                             => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                = ( setadjoin @ X1 @ emptyset ) ) )
                                         => ( ! [X1: $i,X2: $i] :
                                                ( ( X1 = X2 )
                                               => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                  = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                  ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                    = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                 => ( ( X3 = X4 )
                                                   => ( X2 = X4 ) ) )
                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                    ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                      = ( setadjoin @ X3 @ emptyset ) )
                                                   => ( X1 = X2 ) )
                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                      ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                        = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                     => ( X2 = X4 ) )
                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                        ( ( ( kpair @ X1 @ X2 )
                                                          = ( kpair @ X3 @ X4 ) )
                                                       => ( X2 = X4 ) )
                                                   => ( ! [X1: $i] :
                                                          ( ( iskpair @ X1 )
                                                         => ~ ! [X2: $i] :
                                                                ( ( in @ X2
                                                                  @ ( dsetconstr @ ( setunion @ X1 )
                                                                    @ ^ [X3: $i] :
                                                                        ( X1
                                                                        = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                               => ( ( dsetconstr @ ( setunion @ X1 )
                                                                    @ ^ [X3: $i] :
                                                                        ( X1
                                                                        = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                 != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                     => ( ! [X1: $i,X2: $i] :
                                                            ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                            = X2 )
                                                       => ( sP8
                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                               => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                  ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                 => ( in @ X3 @ X1 ) )
                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                    ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                   => ( in @ X4 @ X2 ) )
                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                      ( ( in @ X3 @ X1 )
                                                                     => ! [X4: $i] :
                                                                          ( ( in @ X4 @ X2 )
                                                                         => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                            = X3 ) ) )
                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                        ( ( in @ X3 @ X1 )
                                                                       => ! [X4: $i] :
                                                                            ( ( in @ X4 @ X2 )
                                                                           => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                              = X4 ) ) )
                                                                   => ! [X1: $i,X2: $i,X3: $i] :
                                                                        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                       => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                          = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h265,assumption,
    ! [X1: $i,X2: $i,X3: $i] :
      ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
     => ~ ! [X4: $i] :
            ( ( in @ X4 @ X1 )
           => ! [X5: $i] :
                ( ( in @ X5 @ X2 )
               => ( X3
                 != ( kpair @ X4 @ X5 ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h266,assumption,
    ~ ( sP5
     => ( ! [X1: $i,X2: $i] :
            ( ( in @ X2 @ ( setunion @ X1 ) )
           => ~ ! [X3: $i] :
                  ( ( in @ X3 @ X1 )
                 => ~ ( in @ X2 @ X3 ) ) )
       => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
         => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
           => ( ! [X1: $i] :
                  ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                  = X1 )
             => ( ! [X1: $i,X2: $i > $o] :
                    ( ! [X3: $i] :
                        ( ( in @ X3 @ X1 )
                       => ! [X4: $i] :
                            ( ( in @ X4 @ X1 )
                           => ( ( X2 @ X3 )
                             => ( ( X2 @ X4 )
                               => ( X3 = X4 ) ) ) ) )
                   => ( ~ ! [X3: $i] :
                            ( ( in @ X3 @ X1 )
                           => ~ ( X2 @ X3 ) )
                     => ~ ! [X3: $i] :
                            ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                           => ( ( dsetconstr @ X1 @ X2 )
                             != ( setadjoin @ X3 @ emptyset ) ) ) ) )
               => ( ! [X1: $i,X2: $i > $o] :
                      ( ~ ! [X3: $i] :
                            ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                           => ( ( dsetconstr @ X1 @ X2 )
                             != ( setadjoin @ X3 @ emptyset ) ) )
                     => ~ ! [X3: $i] :
                            ( ( in @ X3 @ X1 )
                           => ~ ( X2 @ X3 ) ) )
                 => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                        ( ( in @ X3 @ X1 )
                       => ( ( X2 @ X3 )
                         => ( ! [X4: $i] :
                                ( ( in @ X4 @ X1 )
                               => ( ( X2 @ X4 )
                                 => ( X4 = X3 ) ) )
                           => ~ ! [X4: $i] :
                                  ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                 => ( ( dsetconstr @ X1 @ X2 )
                                   != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                   => ( ! [X1: $i,X2: $i > $o] :
                          ( ! [X3: $i] :
                              ( ( in @ X3 @ X1 )
                             => ! [X4: $i] :
                                  ( ( in @ X4 @ X1 )
                                 => ( ( X2 @ X3 )
                                   => ( ( X2 @ X4 )
                                     => ( X3 = X4 ) ) ) ) )
                         => ( ~ ! [X3: $i] :
                                  ( ( in @ X3 @ X1 )
                                 => ~ ( X2 @ X3 ) )
                           => ~ ! [X3: $i] :
                                  ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                 => ( ( dsetconstr @ X1 @ X2 )
                                   != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                     => ( ! [X1: $i,X2: $i] :
                            ( ( ( setadjoin @ X1 @ emptyset )
                              = ( setadjoin @ X2 @ emptyset ) )
                           => ( X1 = X2 ) )
                       => ( ! [X1: $i,X2: $i,X3: $i] :
                              ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                             => ( X1 = X3 ) )
                         => ( ! [X1: $i] :
                                ( ( iskpair @ X1 )
                               => ~ ! [X2: $i] :
                                      ( ( in @ X2
                                        @ ( dsetconstr @ ( setunion @ X1 )
                                          @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                     => ( ( dsetconstr @ ( setunion @ X1 )
                                          @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                       != ( setadjoin @ X2 @ emptyset ) ) ) )
                           => ( ! [X1: $i] :
                                  ( ~ ! [X2: $i] :
                                        ( ( in @ X2 @ X1 )
                                       => ( X1
                                         != ( setadjoin @ X2 @ emptyset ) ) )
                                 => ( in @ ( setunion @ X1 ) @ X1 ) )
                             => ( ! [X1: $i,X2: $i] :
                                    ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                    = X1 )
                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                      ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                     => ( in @ ( kfst @ X3 ) @ X1 ) )
                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                        ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                          = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                       => ( X1 = X3 ) )
                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                          ( ( ( kpair @ X1 @ X2 )
                                            = ( kpair @ X3 @ X4 ) )
                                         => ( X1 = X3 ) )
                                     => ( ! [X1: $i,X2: $i] :
                                            ( ( X1 = X2 )
                                           => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                              = ( setadjoin @ X1 @ emptyset ) ) )
                                       => ( ! [X1: $i,X2: $i] :
                                              ( ( X1 = X2 )
                                             => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                  = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                               => ( ( X3 = X4 )
                                                 => ( X2 = X4 ) ) )
                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                  ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                    = ( setadjoin @ X3 @ emptyset ) )
                                                 => ( X1 = X2 ) )
                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                    ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                      = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                   => ( X2 = X4 ) )
                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                      ( ( ( kpair @ X1 @ X2 )
                                                        = ( kpair @ X3 @ X4 ) )
                                                     => ( X2 = X4 ) )
                                                 => ( ! [X1: $i] :
                                                        ( ( iskpair @ X1 )
                                                       => ~ ! [X2: $i] :
                                                              ( ( in @ X2
                                                                @ ( dsetconstr @ ( setunion @ X1 )
                                                                  @ ^ [X3: $i] :
                                                                      ( X1
                                                                      = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                             => ( ( dsetconstr @ ( setunion @ X1 )
                                                                  @ ^ [X3: $i] :
                                                                      ( X1
                                                                      = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                               != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                   => ( ! [X1: $i,X2: $i] :
                                                          ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                          = X2 )
                                                     => ( sP8
                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                              ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                             => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                               => ( in @ X3 @ X1 ) )
                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                  ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                 => ( in @ X4 @ X2 ) )
                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                    ( ( in @ X3 @ X1 )
                                                                   => ! [X4: $i] :
                                                                        ( ( in @ X4 @ X2 )
                                                                       => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                          = X3 ) ) )
                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                      ( ( in @ X3 @ X1 )
                                                                     => ! [X4: $i] :
                                                                          ( ( in @ X4 @ X2 )
                                                                         => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                            = X4 ) ) )
                                                                 => ! [X1: $i,X2: $i,X3: $i] :
                                                                      ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                     => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                        = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h267,assumption,
    sP5,
    introduced(assumption,[]) ).

thf(h268,assumption,
    ~ ( ! [X1: $i,X2: $i] :
          ( ( in @ X2 @ ( setunion @ X1 ) )
         => ~ ! [X3: $i] :
                ( ( in @ X3 @ X1 )
               => ~ ( in @ X2 @ X3 ) ) )
     => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
       => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
         => ( ! [X1: $i] :
                ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                = X1 )
           => ( ! [X1: $i,X2: $i > $o] :
                  ( ! [X3: $i] :
                      ( ( in @ X3 @ X1 )
                     => ! [X4: $i] :
                          ( ( in @ X4 @ X1 )
                         => ( ( X2 @ X3 )
                           => ( ( X2 @ X4 )
                             => ( X3 = X4 ) ) ) ) )
                 => ( ~ ! [X3: $i] :
                          ( ( in @ X3 @ X1 )
                         => ~ ( X2 @ X3 ) )
                   => ~ ! [X3: $i] :
                          ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                         => ( ( dsetconstr @ X1 @ X2 )
                           != ( setadjoin @ X3 @ emptyset ) ) ) ) )
             => ( ! [X1: $i,X2: $i > $o] :
                    ( ~ ! [X3: $i] :
                          ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                         => ( ( dsetconstr @ X1 @ X2 )
                           != ( setadjoin @ X3 @ emptyset ) ) )
                   => ~ ! [X3: $i] :
                          ( ( in @ X3 @ X1 )
                         => ~ ( X2 @ X3 ) ) )
               => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                      ( ( in @ X3 @ X1 )
                     => ( ( X2 @ X3 )
                       => ( ! [X4: $i] :
                              ( ( in @ X4 @ X1 )
                             => ( ( X2 @ X4 )
                               => ( X4 = X3 ) ) )
                         => ~ ! [X4: $i] :
                                ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                               => ( ( dsetconstr @ X1 @ X2 )
                                 != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                 => ( ! [X1: $i,X2: $i > $o] :
                        ( ! [X3: $i] :
                            ( ( in @ X3 @ X1 )
                           => ! [X4: $i] :
                                ( ( in @ X4 @ X1 )
                               => ( ( X2 @ X3 )
                                 => ( ( X2 @ X4 )
                                   => ( X3 = X4 ) ) ) ) )
                       => ( ~ ! [X3: $i] :
                                ( ( in @ X3 @ X1 )
                               => ~ ( X2 @ X3 ) )
                         => ~ ! [X3: $i] :
                                ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                               => ( ( dsetconstr @ X1 @ X2 )
                                 != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                   => ( ! [X1: $i,X2: $i] :
                          ( ( ( setadjoin @ X1 @ emptyset )
                            = ( setadjoin @ X2 @ emptyset ) )
                         => ( X1 = X2 ) )
                     => ( ! [X1: $i,X2: $i,X3: $i] :
                            ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                           => ( X1 = X3 ) )
                       => ( ! [X1: $i] :
                              ( ( iskpair @ X1 )
                             => ~ ! [X2: $i] :
                                    ( ( in @ X2
                                      @ ( dsetconstr @ ( setunion @ X1 )
                                        @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                   => ( ( dsetconstr @ ( setunion @ X1 )
                                        @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                     != ( setadjoin @ X2 @ emptyset ) ) ) )
                         => ( ! [X1: $i] :
                                ( ~ ! [X2: $i] :
                                      ( ( in @ X2 @ X1 )
                                     => ( X1
                                       != ( setadjoin @ X2 @ emptyset ) ) )
                               => ( in @ ( setunion @ X1 ) @ X1 ) )
                           => ( ! [X1: $i,X2: $i] :
                                  ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                  = X1 )
                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                    ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                   => ( in @ ( kfst @ X3 ) @ X1 ) )
                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                      ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                        = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                     => ( X1 = X3 ) )
                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                        ( ( ( kpair @ X1 @ X2 )
                                          = ( kpair @ X3 @ X4 ) )
                                       => ( X1 = X3 ) )
                                   => ( ! [X1: $i,X2: $i] :
                                          ( ( X1 = X2 )
                                         => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                            = ( setadjoin @ X1 @ emptyset ) ) )
                                     => ( ! [X1: $i,X2: $i] :
                                            ( ( X1 = X2 )
                                           => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                              = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                              ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                             => ( ( X3 = X4 )
                                               => ( X2 = X4 ) ) )
                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                  = ( setadjoin @ X3 @ emptyset ) )
                                               => ( X1 = X2 ) )
                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                  ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                    = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                 => ( X2 = X4 ) )
                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                    ( ( ( kpair @ X1 @ X2 )
                                                      = ( kpair @ X3 @ X4 ) )
                                                   => ( X2 = X4 ) )
                                               => ( ! [X1: $i] :
                                                      ( ( iskpair @ X1 )
                                                     => ~ ! [X2: $i] :
                                                            ( ( in @ X2
                                                              @ ( dsetconstr @ ( setunion @ X1 )
                                                                @ ^ [X3: $i] :
                                                                    ( X1
                                                                    = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                           => ( ( dsetconstr @ ( setunion @ X1 )
                                                                @ ^ [X3: $i] :
                                                                    ( X1
                                                                    = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                             != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                 => ( ! [X1: $i,X2: $i] :
                                                        ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                        = X2 )
                                                   => ( sP8
                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                            ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                           => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                              ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                             => ( in @ X3 @ X1 ) )
                                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                               => ( in @ X4 @ X2 ) )
                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                  ( ( in @ X3 @ X1 )
                                                                 => ! [X4: $i] :
                                                                      ( ( in @ X4 @ X2 )
                                                                     => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                        = X3 ) ) )
                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                    ( ( in @ X3 @ X1 )
                                                                   => ! [X4: $i] :
                                                                        ( ( in @ X4 @ X2 )
                                                                       => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                          = X4 ) ) )
                                                               => ! [X1: $i,X2: $i,X3: $i] :
                                                                    ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                   => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                      = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h269,assumption,
    ! [X1: $i,X2: $i] :
      ( ( in @ X2 @ ( setunion @ X1 ) )
     => ~ ! [X3: $i] :
            ( ( in @ X3 @ X1 )
           => ~ ( in @ X2 @ X3 ) ) ),
    introduced(assumption,[]) ).

thf(h270,assumption,
    ~ ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
     => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
       => ( ! [X1: $i] :
              ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
              = X1 )
         => ( ! [X1: $i,X2: $i > $o] :
                ( ! [X3: $i] :
                    ( ( in @ X3 @ X1 )
                   => ! [X4: $i] :
                        ( ( in @ X4 @ X1 )
                       => ( ( X2 @ X3 )
                         => ( ( X2 @ X4 )
                           => ( X3 = X4 ) ) ) ) )
               => ( ~ ! [X3: $i] :
                        ( ( in @ X3 @ X1 )
                       => ~ ( X2 @ X3 ) )
                 => ~ ! [X3: $i] :
                        ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                       => ( ( dsetconstr @ X1 @ X2 )
                         != ( setadjoin @ X3 @ emptyset ) ) ) ) )
           => ( ! [X1: $i,X2: $i > $o] :
                  ( ~ ! [X3: $i] :
                        ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                       => ( ( dsetconstr @ X1 @ X2 )
                         != ( setadjoin @ X3 @ emptyset ) ) )
                 => ~ ! [X3: $i] :
                        ( ( in @ X3 @ X1 )
                       => ~ ( X2 @ X3 ) ) )
             => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                    ( ( in @ X3 @ X1 )
                   => ( ( X2 @ X3 )
                     => ( ! [X4: $i] :
                            ( ( in @ X4 @ X1 )
                           => ( ( X2 @ X4 )
                             => ( X4 = X3 ) ) )
                       => ~ ! [X4: $i] :
                              ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                             => ( ( dsetconstr @ X1 @ X2 )
                               != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
               => ( ! [X1: $i,X2: $i > $o] :
                      ( ! [X3: $i] :
                          ( ( in @ X3 @ X1 )
                         => ! [X4: $i] :
                              ( ( in @ X4 @ X1 )
                             => ( ( X2 @ X3 )
                               => ( ( X2 @ X4 )
                                 => ( X3 = X4 ) ) ) ) )
                     => ( ~ ! [X3: $i] :
                              ( ( in @ X3 @ X1 )
                             => ~ ( X2 @ X3 ) )
                       => ~ ! [X3: $i] :
                              ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                             => ( ( dsetconstr @ X1 @ X2 )
                               != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                 => ( ! [X1: $i,X2: $i] :
                        ( ( ( setadjoin @ X1 @ emptyset )
                          = ( setadjoin @ X2 @ emptyset ) )
                       => ( X1 = X2 ) )
                   => ( ! [X1: $i,X2: $i,X3: $i] :
                          ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                         => ( X1 = X3 ) )
                     => ( ! [X1: $i] :
                            ( ( iskpair @ X1 )
                           => ~ ! [X2: $i] :
                                  ( ( in @ X2
                                    @ ( dsetconstr @ ( setunion @ X1 )
                                      @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                 => ( ( dsetconstr @ ( setunion @ X1 )
                                      @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                   != ( setadjoin @ X2 @ emptyset ) ) ) )
                       => ( ! [X1: $i] :
                              ( ~ ! [X2: $i] :
                                    ( ( in @ X2 @ X1 )
                                   => ( X1
                                     != ( setadjoin @ X2 @ emptyset ) ) )
                             => ( in @ ( setunion @ X1 ) @ X1 ) )
                         => ( ! [X1: $i,X2: $i] :
                                ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                = X1 )
                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                  ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                 => ( in @ ( kfst @ X3 ) @ X1 ) )
                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                    ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                      = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                   => ( X1 = X3 ) )
                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                      ( ( ( kpair @ X1 @ X2 )
                                        = ( kpair @ X3 @ X4 ) )
                                     => ( X1 = X3 ) )
                                 => ( ! [X1: $i,X2: $i] :
                                        ( ( X1 = X2 )
                                       => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                          = ( setadjoin @ X1 @ emptyset ) ) )
                                   => ( ! [X1: $i,X2: $i] :
                                          ( ( X1 = X2 )
                                         => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                            = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                            ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                              = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                           => ( ( X3 = X4 )
                                             => ( X2 = X4 ) ) )
                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                              ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                = ( setadjoin @ X3 @ emptyset ) )
                                             => ( X1 = X2 ) )
                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                  = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                               => ( X2 = X4 ) )
                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                  ( ( ( kpair @ X1 @ X2 )
                                                    = ( kpair @ X3 @ X4 ) )
                                                 => ( X2 = X4 ) )
                                             => ( ! [X1: $i] :
                                                    ( ( iskpair @ X1 )
                                                   => ~ ! [X2: $i] :
                                                          ( ( in @ X2
                                                            @ ( dsetconstr @ ( setunion @ X1 )
                                                              @ ^ [X3: $i] :
                                                                  ( X1
                                                                  = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                         => ( ( dsetconstr @ ( setunion @ X1 )
                                                              @ ^ [X3: $i] :
                                                                  ( X1
                                                                  = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                           != ( setadjoin @ X2 @ emptyset ) ) ) )
                                               => ( ! [X1: $i,X2: $i] :
                                                      ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                      = X2 )
                                                 => ( sP8
                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                         => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                            ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                           => ( in @ X3 @ X1 ) )
                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                              ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                             => ( in @ X4 @ X2 ) )
                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                ( ( in @ X3 @ X1 )
                                                               => ! [X4: $i] :
                                                                    ( ( in @ X4 @ X2 )
                                                                   => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                      = X3 ) ) )
                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                  ( ( in @ X3 @ X1 )
                                                                 => ! [X4: $i] :
                                                                      ( ( in @ X4 @ X2 )
                                                                     => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                        = X4 ) ) )
                                                             => ! [X1: $i,X2: $i,X3: $i] :
                                                                  ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                 => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                    = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h271,assumption,
    ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 ),
    introduced(assumption,[]) ).

thf(h272,assumption,
    ~ ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
     => ( ! [X1: $i] :
            ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
            = X1 )
       => ( ! [X1: $i,X2: $i > $o] :
              ( ! [X3: $i] :
                  ( ( in @ X3 @ X1 )
                 => ! [X4: $i] :
                      ( ( in @ X4 @ X1 )
                     => ( ( X2 @ X3 )
                       => ( ( X2 @ X4 )
                         => ( X3 = X4 ) ) ) ) )
             => ( ~ ! [X3: $i] :
                      ( ( in @ X3 @ X1 )
                     => ~ ( X2 @ X3 ) )
               => ~ ! [X3: $i] :
                      ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                     => ( ( dsetconstr @ X1 @ X2 )
                       != ( setadjoin @ X3 @ emptyset ) ) ) ) )
         => ( ! [X1: $i,X2: $i > $o] :
                ( ~ ! [X3: $i] :
                      ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                     => ( ( dsetconstr @ X1 @ X2 )
                       != ( setadjoin @ X3 @ emptyset ) ) )
               => ~ ! [X3: $i] :
                      ( ( in @ X3 @ X1 )
                     => ~ ( X2 @ X3 ) ) )
           => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                  ( ( in @ X3 @ X1 )
                 => ( ( X2 @ X3 )
                   => ( ! [X4: $i] :
                          ( ( in @ X4 @ X1 )
                         => ( ( X2 @ X4 )
                           => ( X4 = X3 ) ) )
                     => ~ ! [X4: $i] :
                            ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                           => ( ( dsetconstr @ X1 @ X2 )
                             != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
             => ( ! [X1: $i,X2: $i > $o] :
                    ( ! [X3: $i] :
                        ( ( in @ X3 @ X1 )
                       => ! [X4: $i] :
                            ( ( in @ X4 @ X1 )
                           => ( ( X2 @ X3 )
                             => ( ( X2 @ X4 )
                               => ( X3 = X4 ) ) ) ) )
                   => ( ~ ! [X3: $i] :
                            ( ( in @ X3 @ X1 )
                           => ~ ( X2 @ X3 ) )
                     => ~ ! [X3: $i] :
                            ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                           => ( ( dsetconstr @ X1 @ X2 )
                             != ( setadjoin @ X3 @ emptyset ) ) ) ) )
               => ( ! [X1: $i,X2: $i] :
                      ( ( ( setadjoin @ X1 @ emptyset )
                        = ( setadjoin @ X2 @ emptyset ) )
                     => ( X1 = X2 ) )
                 => ( ! [X1: $i,X2: $i,X3: $i] :
                        ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                       => ( X1 = X3 ) )
                   => ( ! [X1: $i] :
                          ( ( iskpair @ X1 )
                         => ~ ! [X2: $i] :
                                ( ( in @ X2
                                  @ ( dsetconstr @ ( setunion @ X1 )
                                    @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                               => ( ( dsetconstr @ ( setunion @ X1 )
                                    @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                 != ( setadjoin @ X2 @ emptyset ) ) ) )
                     => ( ! [X1: $i] :
                            ( ~ ! [X2: $i] :
                                  ( ( in @ X2 @ X1 )
                                 => ( X1
                                   != ( setadjoin @ X2 @ emptyset ) ) )
                           => ( in @ ( setunion @ X1 ) @ X1 ) )
                       => ( ! [X1: $i,X2: $i] :
                              ( ( kfst @ ( kpair @ X1 @ X2 ) )
                              = X1 )
                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                               => ( in @ ( kfst @ X3 ) @ X1 ) )
                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                  ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                    = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                 => ( X1 = X3 ) )
                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                    ( ( ( kpair @ X1 @ X2 )
                                      = ( kpair @ X3 @ X4 ) )
                                   => ( X1 = X3 ) )
                               => ( ! [X1: $i,X2: $i] :
                                      ( ( X1 = X2 )
                                     => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                        = ( setadjoin @ X1 @ emptyset ) ) )
                                 => ( ! [X1: $i,X2: $i] :
                                        ( ( X1 = X2 )
                                       => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                          = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                          ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                            = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                         => ( ( X3 = X4 )
                                           => ( X2 = X4 ) ) )
                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                            ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                              = ( setadjoin @ X3 @ emptyset ) )
                                           => ( X1 = X2 ) )
                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                              ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                             => ( X2 = X4 ) )
                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                ( ( ( kpair @ X1 @ X2 )
                                                  = ( kpair @ X3 @ X4 ) )
                                               => ( X2 = X4 ) )
                                           => ( ! [X1: $i] :
                                                  ( ( iskpair @ X1 )
                                                 => ~ ! [X2: $i] :
                                                        ( ( in @ X2
                                                          @ ( dsetconstr @ ( setunion @ X1 )
                                                            @ ^ [X3: $i] :
                                                                ( X1
                                                                = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                       => ( ( dsetconstr @ ( setunion @ X1 )
                                                            @ ^ [X3: $i] :
                                                                ( X1
                                                                = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                         != ( setadjoin @ X2 @ emptyset ) ) ) )
                                             => ( ! [X1: $i,X2: $i] :
                                                    ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                    = X2 )
                                               => ( sP8
                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                       => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                          ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                         => ( in @ X3 @ X1 ) )
                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                            ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                           => ( in @ X4 @ X2 ) )
                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                              ( ( in @ X3 @ X1 )
                                                             => ! [X4: $i] :
                                                                  ( ( in @ X4 @ X2 )
                                                                 => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                    = X3 ) ) )
                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                ( ( in @ X3 @ X1 )
                                                               => ! [X4: $i] :
                                                                    ( ( in @ X4 @ X2 )
                                                                   => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                      = X4 ) ) )
                                                           => ! [X1: $i,X2: $i,X3: $i] :
                                                                ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                               => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                  = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h273,assumption,
    ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) ),
    introduced(assumption,[]) ).

thf(h274,assumption,
    ~ ( ! [X1: $i] :
          ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
          = X1 )
     => ( ! [X1: $i,X2: $i > $o] :
            ( ! [X3: $i] :
                ( ( in @ X3 @ X1 )
               => ! [X4: $i] :
                    ( ( in @ X4 @ X1 )
                   => ( ( X2 @ X3 )
                     => ( ( X2 @ X4 )
                       => ( X3 = X4 ) ) ) ) )
           => ( ~ ! [X3: $i] :
                    ( ( in @ X3 @ X1 )
                   => ~ ( X2 @ X3 ) )
             => ~ ! [X3: $i] :
                    ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                   => ( ( dsetconstr @ X1 @ X2 )
                     != ( setadjoin @ X3 @ emptyset ) ) ) ) )
       => ( ! [X1: $i,X2: $i > $o] :
              ( ~ ! [X3: $i] :
                    ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                   => ( ( dsetconstr @ X1 @ X2 )
                     != ( setadjoin @ X3 @ emptyset ) ) )
             => ~ ! [X3: $i] :
                    ( ( in @ X3 @ X1 )
                   => ~ ( X2 @ X3 ) ) )
         => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                ( ( in @ X3 @ X1 )
               => ( ( X2 @ X3 )
                 => ( ! [X4: $i] :
                        ( ( in @ X4 @ X1 )
                       => ( ( X2 @ X4 )
                         => ( X4 = X3 ) ) )
                   => ~ ! [X4: $i] :
                          ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                         => ( ( dsetconstr @ X1 @ X2 )
                           != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
           => ( ! [X1: $i,X2: $i > $o] :
                  ( ! [X3: $i] :
                      ( ( in @ X3 @ X1 )
                     => ! [X4: $i] :
                          ( ( in @ X4 @ X1 )
                         => ( ( X2 @ X3 )
                           => ( ( X2 @ X4 )
                             => ( X3 = X4 ) ) ) ) )
                 => ( ~ ! [X3: $i] :
                          ( ( in @ X3 @ X1 )
                         => ~ ( X2 @ X3 ) )
                   => ~ ! [X3: $i] :
                          ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                         => ( ( dsetconstr @ X1 @ X2 )
                           != ( setadjoin @ X3 @ emptyset ) ) ) ) )
             => ( ! [X1: $i,X2: $i] :
                    ( ( ( setadjoin @ X1 @ emptyset )
                      = ( setadjoin @ X2 @ emptyset ) )
                   => ( X1 = X2 ) )
               => ( ! [X1: $i,X2: $i,X3: $i] :
                      ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                     => ( X1 = X3 ) )
                 => ( ! [X1: $i] :
                        ( ( iskpair @ X1 )
                       => ~ ! [X2: $i] :
                              ( ( in @ X2
                                @ ( dsetconstr @ ( setunion @ X1 )
                                  @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                             => ( ( dsetconstr @ ( setunion @ X1 )
                                  @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                               != ( setadjoin @ X2 @ emptyset ) ) ) )
                   => ( ! [X1: $i] :
                          ( ~ ! [X2: $i] :
                                ( ( in @ X2 @ X1 )
                               => ( X1
                                 != ( setadjoin @ X2 @ emptyset ) ) )
                         => ( in @ ( setunion @ X1 ) @ X1 ) )
                     => ( ! [X1: $i,X2: $i] :
                            ( ( kfst @ ( kpair @ X1 @ X2 ) )
                            = X1 )
                       => ( ! [X1: $i,X2: $i,X3: $i] :
                              ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                             => ( in @ ( kfst @ X3 ) @ X1 ) )
                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                  = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                               => ( X1 = X3 ) )
                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                  ( ( ( kpair @ X1 @ X2 )
                                    = ( kpair @ X3 @ X4 ) )
                                 => ( X1 = X3 ) )
                             => ( ! [X1: $i,X2: $i] :
                                    ( ( X1 = X2 )
                                   => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                      = ( setadjoin @ X1 @ emptyset ) ) )
                               => ( ! [X1: $i,X2: $i] :
                                      ( ( X1 = X2 )
                                     => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                        = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                        ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                          = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                       => ( ( X3 = X4 )
                                         => ( X2 = X4 ) ) )
                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                          ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                            = ( setadjoin @ X3 @ emptyset ) )
                                         => ( X1 = X2 ) )
                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                            ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                              = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                           => ( X2 = X4 ) )
                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                              ( ( ( kpair @ X1 @ X2 )
                                                = ( kpair @ X3 @ X4 ) )
                                             => ( X2 = X4 ) )
                                         => ( ! [X1: $i] :
                                                ( ( iskpair @ X1 )
                                               => ~ ! [X2: $i] :
                                                      ( ( in @ X2
                                                        @ ( dsetconstr @ ( setunion @ X1 )
                                                          @ ^ [X3: $i] :
                                                              ( X1
                                                              = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                     => ( ( dsetconstr @ ( setunion @ X1 )
                                                          @ ^ [X3: $i] :
                                                              ( X1
                                                              = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                       != ( setadjoin @ X2 @ emptyset ) ) ) )
                                           => ( ! [X1: $i,X2: $i] :
                                                  ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                  = X2 )
                                             => ( sP8
                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                      ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                     => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                        ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                       => ( in @ X3 @ X1 ) )
                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                          ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                         => ( in @ X4 @ X2 ) )
                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                            ( ( in @ X3 @ X1 )
                                                           => ! [X4: $i] :
                                                                ( ( in @ X4 @ X2 )
                                                               => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                  = X3 ) ) )
                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                              ( ( in @ X3 @ X1 )
                                                             => ! [X4: $i] :
                                                                  ( ( in @ X4 @ X2 )
                                                                 => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                    = X4 ) ) )
                                                         => ! [X1: $i,X2: $i,X3: $i] :
                                                              ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                             => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h275,assumption,
    ! [X1: $i] :
      ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
      = X1 ),
    introduced(assumption,[]) ).

thf(h276,assumption,
    ~ ( ! [X1: $i,X2: $i > $o] :
          ( ! [X3: $i] :
              ( ( in @ X3 @ X1 )
             => ! [X4: $i] :
                  ( ( in @ X4 @ X1 )
                 => ( ( X2 @ X3 )
                   => ( ( X2 @ X4 )
                     => ( X3 = X4 ) ) ) ) )
         => ( ~ ! [X3: $i] :
                  ( ( in @ X3 @ X1 )
                 => ~ ( X2 @ X3 ) )
           => ~ ! [X3: $i] :
                  ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                 => ( ( dsetconstr @ X1 @ X2 )
                   != ( setadjoin @ X3 @ emptyset ) ) ) ) )
     => ( ! [X1: $i,X2: $i > $o] :
            ( ~ ! [X3: $i] :
                  ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                 => ( ( dsetconstr @ X1 @ X2 )
                   != ( setadjoin @ X3 @ emptyset ) ) )
           => ~ ! [X3: $i] :
                  ( ( in @ X3 @ X1 )
                 => ~ ( X2 @ X3 ) ) )
       => ( ! [X1: $i,X2: $i > $o,X3: $i] :
              ( ( in @ X3 @ X1 )
             => ( ( X2 @ X3 )
               => ( ! [X4: $i] :
                      ( ( in @ X4 @ X1 )
                     => ( ( X2 @ X4 )
                       => ( X4 = X3 ) ) )
                 => ~ ! [X4: $i] :
                        ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                       => ( ( dsetconstr @ X1 @ X2 )
                         != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
         => ( ! [X1: $i,X2: $i > $o] :
                ( ! [X3: $i] :
                    ( ( in @ X3 @ X1 )
                   => ! [X4: $i] :
                        ( ( in @ X4 @ X1 )
                       => ( ( X2 @ X3 )
                         => ( ( X2 @ X4 )
                           => ( X3 = X4 ) ) ) ) )
               => ( ~ ! [X3: $i] :
                        ( ( in @ X3 @ X1 )
                       => ~ ( X2 @ X3 ) )
                 => ~ ! [X3: $i] :
                        ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                       => ( ( dsetconstr @ X1 @ X2 )
                         != ( setadjoin @ X3 @ emptyset ) ) ) ) )
           => ( ! [X1: $i,X2: $i] :
                  ( ( ( setadjoin @ X1 @ emptyset )
                    = ( setadjoin @ X2 @ emptyset ) )
                 => ( X1 = X2 ) )
             => ( ! [X1: $i,X2: $i,X3: $i] :
                    ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                   => ( X1 = X3 ) )
               => ( ! [X1: $i] :
                      ( ( iskpair @ X1 )
                     => ~ ! [X2: $i] :
                            ( ( in @ X2
                              @ ( dsetconstr @ ( setunion @ X1 )
                                @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                           => ( ( dsetconstr @ ( setunion @ X1 )
                                @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                             != ( setadjoin @ X2 @ emptyset ) ) ) )
                 => ( ! [X1: $i] :
                        ( ~ ! [X2: $i] :
                              ( ( in @ X2 @ X1 )
                             => ( X1
                               != ( setadjoin @ X2 @ emptyset ) ) )
                       => ( in @ ( setunion @ X1 ) @ X1 ) )
                   => ( ! [X1: $i,X2: $i] :
                          ( ( kfst @ ( kpair @ X1 @ X2 ) )
                          = X1 )
                     => ( ! [X1: $i,X2: $i,X3: $i] :
                            ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                           => ( in @ ( kfst @ X3 ) @ X1 ) )
                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                              ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                             => ( X1 = X3 ) )
                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                ( ( ( kpair @ X1 @ X2 )
                                  = ( kpair @ X3 @ X4 ) )
                               => ( X1 = X3 ) )
                           => ( ! [X1: $i,X2: $i] :
                                  ( ( X1 = X2 )
                                 => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                    = ( setadjoin @ X1 @ emptyset ) ) )
                             => ( ! [X1: $i,X2: $i] :
                                    ( ( X1 = X2 )
                                   => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                      = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                      ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                        = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                     => ( ( X3 = X4 )
                                       => ( X2 = X4 ) ) )
                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                        ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                          = ( setadjoin @ X3 @ emptyset ) )
                                       => ( X1 = X2 ) )
                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                          ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                            = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                         => ( X2 = X4 ) )
                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                            ( ( ( kpair @ X1 @ X2 )
                                              = ( kpair @ X3 @ X4 ) )
                                           => ( X2 = X4 ) )
                                       => ( ! [X1: $i] :
                                              ( ( iskpair @ X1 )
                                             => ~ ! [X2: $i] :
                                                    ( ( in @ X2
                                                      @ ( dsetconstr @ ( setunion @ X1 )
                                                        @ ^ [X3: $i] :
                                                            ( X1
                                                            = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                   => ( ( dsetconstr @ ( setunion @ X1 )
                                                        @ ^ [X3: $i] :
                                                            ( X1
                                                            = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                     != ( setadjoin @ X2 @ emptyset ) ) ) )
                                         => ( ! [X1: $i,X2: $i] :
                                                ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                = X2 )
                                           => ( sP8
                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                    ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                   => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                      ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                     => ( in @ X3 @ X1 ) )
                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                        ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                       => ( in @ X4 @ X2 ) )
                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                          ( ( in @ X3 @ X1 )
                                                         => ! [X4: $i] :
                                                              ( ( in @ X4 @ X2 )
                                                             => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                = X3 ) ) )
                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                            ( ( in @ X3 @ X1 )
                                                           => ! [X4: $i] :
                                                                ( ( in @ X4 @ X2 )
                                                               => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                  = X4 ) ) )
                                                       => ! [X1: $i,X2: $i,X3: $i] :
                                                            ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                           => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                              = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h277,assumption,
    ! [X1: $i,X2: $i > $o] :
      ( ! [X3: $i] :
          ( ( in @ X3 @ X1 )
         => ! [X4: $i] :
              ( ( in @ X4 @ X1 )
             => ( ( X2 @ X3 )
               => ( ( X2 @ X4 )
                 => ( X3 = X4 ) ) ) ) )
     => ( ~ ! [X3: $i] :
              ( ( in @ X3 @ X1 )
             => ~ ( X2 @ X3 ) )
       => ~ ! [X3: $i] :
              ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
             => ( ( dsetconstr @ X1 @ X2 )
               != ( setadjoin @ X3 @ emptyset ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h278,assumption,
    ~ ( ! [X1: $i,X2: $i > $o] :
          ( ~ ! [X3: $i] :
                ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
               => ( ( dsetconstr @ X1 @ X2 )
                 != ( setadjoin @ X3 @ emptyset ) ) )
         => ~ ! [X3: $i] :
                ( ( in @ X3 @ X1 )
               => ~ ( X2 @ X3 ) ) )
     => ( ! [X1: $i,X2: $i > $o,X3: $i] :
            ( ( in @ X3 @ X1 )
           => ( ( X2 @ X3 )
             => ( ! [X4: $i] :
                    ( ( in @ X4 @ X1 )
                   => ( ( X2 @ X4 )
                     => ( X4 = X3 ) ) )
               => ~ ! [X4: $i] :
                      ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                     => ( ( dsetconstr @ X1 @ X2 )
                       != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
       => ( ! [X1: $i,X2: $i > $o] :
              ( ! [X3: $i] :
                  ( ( in @ X3 @ X1 )
                 => ! [X4: $i] :
                      ( ( in @ X4 @ X1 )
                     => ( ( X2 @ X3 )
                       => ( ( X2 @ X4 )
                         => ( X3 = X4 ) ) ) ) )
             => ( ~ ! [X3: $i] :
                      ( ( in @ X3 @ X1 )
                     => ~ ( X2 @ X3 ) )
               => ~ ! [X3: $i] :
                      ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                     => ( ( dsetconstr @ X1 @ X2 )
                       != ( setadjoin @ X3 @ emptyset ) ) ) ) )
         => ( ! [X1: $i,X2: $i] :
                ( ( ( setadjoin @ X1 @ emptyset )
                  = ( setadjoin @ X2 @ emptyset ) )
               => ( X1 = X2 ) )
           => ( ! [X1: $i,X2: $i,X3: $i] :
                  ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                 => ( X1 = X3 ) )
             => ( ! [X1: $i] :
                    ( ( iskpair @ X1 )
                   => ~ ! [X2: $i] :
                          ( ( in @ X2
                            @ ( dsetconstr @ ( setunion @ X1 )
                              @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                         => ( ( dsetconstr @ ( setunion @ X1 )
                              @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                           != ( setadjoin @ X2 @ emptyset ) ) ) )
               => ( ! [X1: $i] :
                      ( ~ ! [X2: $i] :
                            ( ( in @ X2 @ X1 )
                           => ( X1
                             != ( setadjoin @ X2 @ emptyset ) ) )
                     => ( in @ ( setunion @ X1 ) @ X1 ) )
                 => ( ! [X1: $i,X2: $i] :
                        ( ( kfst @ ( kpair @ X1 @ X2 ) )
                        = X1 )
                   => ( ! [X1: $i,X2: $i,X3: $i] :
                          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                         => ( in @ ( kfst @ X3 ) @ X1 ) )
                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                            ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                              = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                           => ( X1 = X3 ) )
                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                              ( ( ( kpair @ X1 @ X2 )
                                = ( kpair @ X3 @ X4 ) )
                             => ( X1 = X3 ) )
                         => ( ! [X1: $i,X2: $i] :
                                ( ( X1 = X2 )
                               => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                  = ( setadjoin @ X1 @ emptyset ) ) )
                           => ( ! [X1: $i,X2: $i] :
                                  ( ( X1 = X2 )
                                 => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                    = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                    ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                      = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                   => ( ( X3 = X4 )
                                     => ( X2 = X4 ) ) )
                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                      ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                        = ( setadjoin @ X3 @ emptyset ) )
                                     => ( X1 = X2 ) )
                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                        ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                          = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                       => ( X2 = X4 ) )
                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                          ( ( ( kpair @ X1 @ X2 )
                                            = ( kpair @ X3 @ X4 ) )
                                         => ( X2 = X4 ) )
                                     => ( ! [X1: $i] :
                                            ( ( iskpair @ X1 )
                                           => ~ ! [X2: $i] :
                                                  ( ( in @ X2
                                                    @ ( dsetconstr @ ( setunion @ X1 )
                                                      @ ^ [X3: $i] :
                                                          ( X1
                                                          = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                 => ( ( dsetconstr @ ( setunion @ X1 )
                                                      @ ^ [X3: $i] :
                                                          ( X1
                                                          = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                   != ( setadjoin @ X2 @ emptyset ) ) ) )
                                       => ( ! [X1: $i,X2: $i] :
                                              ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                              = X2 )
                                         => ( sP8
                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                  ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                 => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                    ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                   => ( in @ X3 @ X1 ) )
                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                      ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                     => ( in @ X4 @ X2 ) )
                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                        ( ( in @ X3 @ X1 )
                                                       => ! [X4: $i] :
                                                            ( ( in @ X4 @ X2 )
                                                           => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                              = X3 ) ) )
                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                          ( ( in @ X3 @ X1 )
                                                         => ! [X4: $i] :
                                                              ( ( in @ X4 @ X2 )
                                                             => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                = X4 ) ) )
                                                     => ! [X1: $i,X2: $i,X3: $i] :
                                                          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                         => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                            = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h279,assumption,
    ! [X1: $i,X2: $i > $o] :
      ( ~ ! [X3: $i] :
            ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
           => ( ( dsetconstr @ X1 @ X2 )
             != ( setadjoin @ X3 @ emptyset ) ) )
     => ~ ! [X3: $i] :
            ( ( in @ X3 @ X1 )
           => ~ ( X2 @ X3 ) ) ),
    introduced(assumption,[]) ).

thf(h280,assumption,
    ~ ( ! [X1: $i,X2: $i > $o,X3: $i] :
          ( ( in @ X3 @ X1 )
         => ( ( X2 @ X3 )
           => ( ! [X4: $i] :
                  ( ( in @ X4 @ X1 )
                 => ( ( X2 @ X4 )
                   => ( X4 = X3 ) ) )
             => ~ ! [X4: $i] :
                    ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                   => ( ( dsetconstr @ X1 @ X2 )
                     != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
     => ( ! [X1: $i,X2: $i > $o] :
            ( ! [X3: $i] :
                ( ( in @ X3 @ X1 )
               => ! [X4: $i] :
                    ( ( in @ X4 @ X1 )
                   => ( ( X2 @ X3 )
                     => ( ( X2 @ X4 )
                       => ( X3 = X4 ) ) ) ) )
           => ( ~ ! [X3: $i] :
                    ( ( in @ X3 @ X1 )
                   => ~ ( X2 @ X3 ) )
             => ~ ! [X3: $i] :
                    ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                   => ( ( dsetconstr @ X1 @ X2 )
                     != ( setadjoin @ X3 @ emptyset ) ) ) ) )
       => ( ! [X1: $i,X2: $i] :
              ( ( ( setadjoin @ X1 @ emptyset )
                = ( setadjoin @ X2 @ emptyset ) )
             => ( X1 = X2 ) )
         => ( ! [X1: $i,X2: $i,X3: $i] :
                ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
               => ( X1 = X3 ) )
           => ( ! [X1: $i] :
                  ( ( iskpair @ X1 )
                 => ~ ! [X2: $i] :
                        ( ( in @ X2
                          @ ( dsetconstr @ ( setunion @ X1 )
                            @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                       => ( ( dsetconstr @ ( setunion @ X1 )
                            @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                         != ( setadjoin @ X2 @ emptyset ) ) ) )
             => ( ! [X1: $i] :
                    ( ~ ! [X2: $i] :
                          ( ( in @ X2 @ X1 )
                         => ( X1
                           != ( setadjoin @ X2 @ emptyset ) ) )
                   => ( in @ ( setunion @ X1 ) @ X1 ) )
               => ( ! [X1: $i,X2: $i] :
                      ( ( kfst @ ( kpair @ X1 @ X2 ) )
                      = X1 )
                 => ( ! [X1: $i,X2: $i,X3: $i] :
                        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                       => ( in @ ( kfst @ X3 ) @ X1 ) )
                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                          ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                            = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                         => ( X1 = X3 ) )
                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                            ( ( ( kpair @ X1 @ X2 )
                              = ( kpair @ X3 @ X4 ) )
                           => ( X1 = X3 ) )
                       => ( ! [X1: $i,X2: $i] :
                              ( ( X1 = X2 )
                             => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                = ( setadjoin @ X1 @ emptyset ) ) )
                         => ( ! [X1: $i,X2: $i] :
                                ( ( X1 = X2 )
                               => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                  = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                  ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                    = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                 => ( ( X3 = X4 )
                                   => ( X2 = X4 ) ) )
                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                    ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                      = ( setadjoin @ X3 @ emptyset ) )
                                   => ( X1 = X2 ) )
                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                      ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                        = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                     => ( X2 = X4 ) )
                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                        ( ( ( kpair @ X1 @ X2 )
                                          = ( kpair @ X3 @ X4 ) )
                                       => ( X2 = X4 ) )
                                   => ( ! [X1: $i] :
                                          ( ( iskpair @ X1 )
                                         => ~ ! [X2: $i] :
                                                ( ( in @ X2
                                                  @ ( dsetconstr @ ( setunion @ X1 )
                                                    @ ^ [X3: $i] :
                                                        ( X1
                                                        = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                               => ( ( dsetconstr @ ( setunion @ X1 )
                                                    @ ^ [X3: $i] :
                                                        ( X1
                                                        = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                 != ( setadjoin @ X2 @ emptyset ) ) ) )
                                     => ( ! [X1: $i,X2: $i] :
                                            ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                            = X2 )
                                       => ( sP8
                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                               => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                  ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                 => ( in @ X3 @ X1 ) )
                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                    ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                   => ( in @ X4 @ X2 ) )
                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                      ( ( in @ X3 @ X1 )
                                                     => ! [X4: $i] :
                                                          ( ( in @ X4 @ X2 )
                                                         => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                            = X3 ) ) )
                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                        ( ( in @ X3 @ X1 )
                                                       => ! [X4: $i] :
                                                            ( ( in @ X4 @ X2 )
                                                           => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                              = X4 ) ) )
                                                   => ! [X1: $i,X2: $i,X3: $i] :
                                                        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                       => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                          = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h281,assumption,
    ! [X1: $i,X2: $i > $o,X3: $i] :
      ( ( in @ X3 @ X1 )
     => ( ( X2 @ X3 )
       => ( ! [X4: $i] :
              ( ( in @ X4 @ X1 )
             => ( ( X2 @ X4 )
               => ( X4 = X3 ) ) )
         => ~ ! [X4: $i] :
                ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
               => ( ( dsetconstr @ X1 @ X2 )
                 != ( setadjoin @ X4 @ emptyset ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h282,assumption,
    ~ ( ! [X1: $i,X2: $i > $o] :
          ( ! [X3: $i] :
              ( ( in @ X3 @ X1 )
             => ! [X4: $i] :
                  ( ( in @ X4 @ X1 )
                 => ( ( X2 @ X3 )
                   => ( ( X2 @ X4 )
                     => ( X3 = X4 ) ) ) ) )
         => ( ~ ! [X3: $i] :
                  ( ( in @ X3 @ X1 )
                 => ~ ( X2 @ X3 ) )
           => ~ ! [X3: $i] :
                  ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                 => ( ( dsetconstr @ X1 @ X2 )
                   != ( setadjoin @ X3 @ emptyset ) ) ) ) )
     => ( ! [X1: $i,X2: $i] :
            ( ( ( setadjoin @ X1 @ emptyset )
              = ( setadjoin @ X2 @ emptyset ) )
           => ( X1 = X2 ) )
       => ( ! [X1: $i,X2: $i,X3: $i] :
              ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
             => ( X1 = X3 ) )
         => ( ! [X1: $i] :
                ( ( iskpair @ X1 )
               => ~ ! [X2: $i] :
                      ( ( in @ X2
                        @ ( dsetconstr @ ( setunion @ X1 )
                          @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                     => ( ( dsetconstr @ ( setunion @ X1 )
                          @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                       != ( setadjoin @ X2 @ emptyset ) ) ) )
           => ( ! [X1: $i] :
                  ( ~ ! [X2: $i] :
                        ( ( in @ X2 @ X1 )
                       => ( X1
                         != ( setadjoin @ X2 @ emptyset ) ) )
                 => ( in @ ( setunion @ X1 ) @ X1 ) )
             => ( ! [X1: $i,X2: $i] :
                    ( ( kfst @ ( kpair @ X1 @ X2 ) )
                    = X1 )
               => ( ! [X1: $i,X2: $i,X3: $i] :
                      ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                     => ( in @ ( kfst @ X3 ) @ X1 ) )
                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                        ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                          = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                       => ( X1 = X3 ) )
                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                          ( ( ( kpair @ X1 @ X2 )
                            = ( kpair @ X3 @ X4 ) )
                         => ( X1 = X3 ) )
                     => ( ! [X1: $i,X2: $i] :
                            ( ( X1 = X2 )
                           => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                              = ( setadjoin @ X1 @ emptyset ) ) )
                       => ( ! [X1: $i,X2: $i] :
                              ( ( X1 = X2 )
                             => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                  = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                               => ( ( X3 = X4 )
                                 => ( X2 = X4 ) ) )
                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                  ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                    = ( setadjoin @ X3 @ emptyset ) )
                                 => ( X1 = X2 ) )
                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                    ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                      = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                   => ( X2 = X4 ) )
                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                      ( ( ( kpair @ X1 @ X2 )
                                        = ( kpair @ X3 @ X4 ) )
                                     => ( X2 = X4 ) )
                                 => ( ! [X1: $i] :
                                        ( ( iskpair @ X1 )
                                       => ~ ! [X2: $i] :
                                              ( ( in @ X2
                                                @ ( dsetconstr @ ( setunion @ X1 )
                                                  @ ^ [X3: $i] :
                                                      ( X1
                                                      = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                             => ( ( dsetconstr @ ( setunion @ X1 )
                                                  @ ^ [X3: $i] :
                                                      ( X1
                                                      = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                               != ( setadjoin @ X2 @ emptyset ) ) ) )
                                   => ( ! [X1: $i,X2: $i] :
                                          ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                          = X2 )
                                     => ( sP8
                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                              ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                             => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                               => ( in @ X3 @ X1 ) )
                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                  ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                 => ( in @ X4 @ X2 ) )
                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                    ( ( in @ X3 @ X1 )
                                                   => ! [X4: $i] :
                                                        ( ( in @ X4 @ X2 )
                                                       => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                          = X3 ) ) )
                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                      ( ( in @ X3 @ X1 )
                                                     => ! [X4: $i] :
                                                          ( ( in @ X4 @ X2 )
                                                         => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                            = X4 ) ) )
                                                 => ! [X1: $i,X2: $i,X3: $i] :
                                                      ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                     => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                        = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h283,assumption,
    ~ ( ! [X1: $i,X2: $i] :
          ( ( ( setadjoin @ X1 @ emptyset )
            = ( setadjoin @ X2 @ emptyset ) )
         => ( X1 = X2 ) )
     => ( ! [X1: $i,X2: $i,X3: $i] :
            ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
           => ( X1 = X3 ) )
       => ( ! [X1: $i] :
              ( ( iskpair @ X1 )
             => ~ ! [X2: $i] :
                    ( ( in @ X2
                      @ ( dsetconstr @ ( setunion @ X1 )
                        @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                   => ( ( dsetconstr @ ( setunion @ X1 )
                        @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                     != ( setadjoin @ X2 @ emptyset ) ) ) )
         => ( ! [X1: $i] :
                ( ~ ! [X2: $i] :
                      ( ( in @ X2 @ X1 )
                     => ( X1
                       != ( setadjoin @ X2 @ emptyset ) ) )
               => ( in @ ( setunion @ X1 ) @ X1 ) )
           => ( ! [X1: $i,X2: $i] :
                  ( ( kfst @ ( kpair @ X1 @ X2 ) )
                  = X1 )
             => ( ! [X1: $i,X2: $i,X3: $i] :
                    ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                   => ( in @ ( kfst @ X3 ) @ X1 ) )
               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                      ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                        = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                     => ( X1 = X3 ) )
                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                        ( ( ( kpair @ X1 @ X2 )
                          = ( kpair @ X3 @ X4 ) )
                       => ( X1 = X3 ) )
                   => ( ! [X1: $i,X2: $i] :
                          ( ( X1 = X2 )
                         => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                            = ( setadjoin @ X1 @ emptyset ) ) )
                     => ( ! [X1: $i,X2: $i] :
                            ( ( X1 = X2 )
                           => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                              = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                              ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                             => ( ( X3 = X4 )
                               => ( X2 = X4 ) ) )
                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                  = ( setadjoin @ X3 @ emptyset ) )
                               => ( X1 = X2 ) )
                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                  ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                    = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                 => ( X2 = X4 ) )
                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                    ( ( ( kpair @ X1 @ X2 )
                                      = ( kpair @ X3 @ X4 ) )
                                   => ( X2 = X4 ) )
                               => ( ! [X1: $i] :
                                      ( ( iskpair @ X1 )
                                     => ~ ! [X2: $i] :
                                            ( ( in @ X2
                                              @ ( dsetconstr @ ( setunion @ X1 )
                                                @ ^ [X3: $i] :
                                                    ( X1
                                                    = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                           => ( ( dsetconstr @ ( setunion @ X1 )
                                                @ ^ [X3: $i] :
                                                    ( X1
                                                    = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                             != ( setadjoin @ X2 @ emptyset ) ) ) )
                                 => ( ! [X1: $i,X2: $i] :
                                        ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                        = X2 )
                                   => ( sP8
                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                            ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                           => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                              ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                             => ( in @ X3 @ X1 ) )
                                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                               => ( in @ X4 @ X2 ) )
                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                  ( ( in @ X3 @ X1 )
                                                 => ! [X4: $i] :
                                                      ( ( in @ X4 @ X2 )
                                                     => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                        = X3 ) ) )
                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                    ( ( in @ X3 @ X1 )
                                                   => ! [X4: $i] :
                                                        ( ( in @ X4 @ X2 )
                                                       => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                          = X4 ) ) )
                                               => ! [X1: $i,X2: $i,X3: $i] :
                                                    ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                   => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                      = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h284,assumption,
    ! [X1: $i,X2: $i] :
      ( ( ( setadjoin @ X1 @ emptyset )
        = ( setadjoin @ X2 @ emptyset ) )
     => ( X1 = X2 ) ),
    introduced(assumption,[]) ).

thf(h285,assumption,
    ~ ( ! [X1: $i,X2: $i,X3: $i] :
          ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
         => ( X1 = X3 ) )
     => ( ! [X1: $i] :
            ( ( iskpair @ X1 )
           => ~ ! [X2: $i] :
                  ( ( in @ X2
                    @ ( dsetconstr @ ( setunion @ X1 )
                      @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                 => ( ( dsetconstr @ ( setunion @ X1 )
                      @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                   != ( setadjoin @ X2 @ emptyset ) ) ) )
       => ( ! [X1: $i] :
              ( ~ ! [X2: $i] :
                    ( ( in @ X2 @ X1 )
                   => ( X1
                     != ( setadjoin @ X2 @ emptyset ) ) )
             => ( in @ ( setunion @ X1 ) @ X1 ) )
         => ( ! [X1: $i,X2: $i] :
                ( ( kfst @ ( kpair @ X1 @ X2 ) )
                = X1 )
           => ( ! [X1: $i,X2: $i,X3: $i] :
                  ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                 => ( in @ ( kfst @ X3 ) @ X1 ) )
             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                    ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                      = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                   => ( X1 = X3 ) )
               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                      ( ( ( kpair @ X1 @ X2 )
                        = ( kpair @ X3 @ X4 ) )
                     => ( X1 = X3 ) )
                 => ( ! [X1: $i,X2: $i] :
                        ( ( X1 = X2 )
                       => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                          = ( setadjoin @ X1 @ emptyset ) ) )
                   => ( ! [X1: $i,X2: $i] :
                          ( ( X1 = X2 )
                         => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                            = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                            ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                              = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                           => ( ( X3 = X4 )
                             => ( X2 = X4 ) ) )
                       => ( ! [X1: $i,X2: $i,X3: $i] :
                              ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                = ( setadjoin @ X3 @ emptyset ) )
                             => ( X1 = X2 ) )
                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                  = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                               => ( X2 = X4 ) )
                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                  ( ( ( kpair @ X1 @ X2 )
                                    = ( kpair @ X3 @ X4 ) )
                                 => ( X2 = X4 ) )
                             => ( ! [X1: $i] :
                                    ( ( iskpair @ X1 )
                                   => ~ ! [X2: $i] :
                                          ( ( in @ X2
                                            @ ( dsetconstr @ ( setunion @ X1 )
                                              @ ^ [X3: $i] :
                                                  ( X1
                                                  = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                         => ( ( dsetconstr @ ( setunion @ X1 )
                                              @ ^ [X3: $i] :
                                                  ( X1
                                                  = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                           != ( setadjoin @ X2 @ emptyset ) ) ) )
                               => ( ! [X1: $i,X2: $i] :
                                      ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                      = X2 )
                                 => ( sP8
                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                         => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                            ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                           => ( in @ X3 @ X1 ) )
                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                              ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                             => ( in @ X4 @ X2 ) )
                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                ( ( in @ X3 @ X1 )
                                               => ! [X4: $i] :
                                                    ( ( in @ X4 @ X2 )
                                                   => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                      = X3 ) ) )
                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                  ( ( in @ X3 @ X1 )
                                                 => ! [X4: $i] :
                                                      ( ( in @ X4 @ X2 )
                                                     => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                        = X4 ) ) )
                                             => ! [X1: $i,X2: $i,X3: $i] :
                                                  ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                 => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                    = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h286,assumption,
    ! [X1: $i,X2: $i,X3: $i] :
      ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
     => ( X1 = X3 ) ),
    introduced(assumption,[]) ).

thf(h287,assumption,
    ~ ( ! [X1: $i] :
          ( ( iskpair @ X1 )
         => ~ ! [X2: $i] :
                ( ( in @ X2
                  @ ( dsetconstr @ ( setunion @ X1 )
                    @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
               => ( ( dsetconstr @ ( setunion @ X1 )
                    @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                 != ( setadjoin @ X2 @ emptyset ) ) ) )
     => ( ! [X1: $i] :
            ( ~ ! [X2: $i] :
                  ( ( in @ X2 @ X1 )
                 => ( X1
                   != ( setadjoin @ X2 @ emptyset ) ) )
           => ( in @ ( setunion @ X1 ) @ X1 ) )
       => ( ! [X1: $i,X2: $i] :
              ( ( kfst @ ( kpair @ X1 @ X2 ) )
              = X1 )
         => ( ! [X1: $i,X2: $i,X3: $i] :
                ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
               => ( in @ ( kfst @ X3 ) @ X1 ) )
           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                  ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                    = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                 => ( X1 = X3 ) )
             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                    ( ( ( kpair @ X1 @ X2 )
                      = ( kpair @ X3 @ X4 ) )
                   => ( X1 = X3 ) )
               => ( ! [X1: $i,X2: $i] :
                      ( ( X1 = X2 )
                     => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                        = ( setadjoin @ X1 @ emptyset ) ) )
                 => ( ! [X1: $i,X2: $i] :
                        ( ( X1 = X2 )
                       => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                          = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                          ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                            = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                         => ( ( X3 = X4 )
                           => ( X2 = X4 ) ) )
                     => ( ! [X1: $i,X2: $i,X3: $i] :
                            ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                              = ( setadjoin @ X3 @ emptyset ) )
                           => ( X1 = X2 ) )
                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                              ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                             => ( X2 = X4 ) )
                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                ( ( ( kpair @ X1 @ X2 )
                                  = ( kpair @ X3 @ X4 ) )
                               => ( X2 = X4 ) )
                           => ( ! [X1: $i] :
                                  ( ( iskpair @ X1 )
                                 => ~ ! [X2: $i] :
                                        ( ( in @ X2
                                          @ ( dsetconstr @ ( setunion @ X1 )
                                            @ ^ [X3: $i] :
                                                ( X1
                                                = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                       => ( ( dsetconstr @ ( setunion @ X1 )
                                            @ ^ [X3: $i] :
                                                ( X1
                                                = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                         != ( setadjoin @ X2 @ emptyset ) ) ) )
                             => ( ! [X1: $i,X2: $i] :
                                    ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                    = X2 )
                               => ( sP8
                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                       => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                          ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                         => ( in @ X3 @ X1 ) )
                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                            ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                           => ( in @ X4 @ X2 ) )
                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                              ( ( in @ X3 @ X1 )
                                             => ! [X4: $i] :
                                                  ( ( in @ X4 @ X2 )
                                                 => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                    = X3 ) ) )
                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                ( ( in @ X3 @ X1 )
                                               => ! [X4: $i] :
                                                    ( ( in @ X4 @ X2 )
                                                   => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                      = X4 ) ) )
                                           => ! [X1: $i,X2: $i,X3: $i] :
                                                ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                               => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                  = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h288,assumption,
    ! [X1: $i] :
      ( ( iskpair @ X1 )
     => ~ ! [X2: $i] :
            ( ( in @ X2
              @ ( dsetconstr @ ( setunion @ X1 )
                @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
           => ( ( dsetconstr @ ( setunion @ X1 )
                @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
             != ( setadjoin @ X2 @ emptyset ) ) ) ),
    introduced(assumption,[]) ).

thf(h289,assumption,
    ~ ( ! [X1: $i] :
          ( ~ ! [X2: $i] :
                ( ( in @ X2 @ X1 )
               => ( X1
                 != ( setadjoin @ X2 @ emptyset ) ) )
         => ( in @ ( setunion @ X1 ) @ X1 ) )
     => ( ! [X1: $i,X2: $i] :
            ( ( kfst @ ( kpair @ X1 @ X2 ) )
            = X1 )
       => ( ! [X1: $i,X2: $i,X3: $i] :
              ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
             => ( in @ ( kfst @ X3 ) @ X1 ) )
         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                  = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
               => ( X1 = X3 ) )
           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                  ( ( ( kpair @ X1 @ X2 )
                    = ( kpair @ X3 @ X4 ) )
                 => ( X1 = X3 ) )
             => ( ! [X1: $i,X2: $i] :
                    ( ( X1 = X2 )
                   => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                      = ( setadjoin @ X1 @ emptyset ) ) )
               => ( ! [X1: $i,X2: $i] :
                      ( ( X1 = X2 )
                     => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                        = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                        ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                          = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                       => ( ( X3 = X4 )
                         => ( X2 = X4 ) ) )
                   => ( ! [X1: $i,X2: $i,X3: $i] :
                          ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                            = ( setadjoin @ X3 @ emptyset ) )
                         => ( X1 = X2 ) )
                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                            ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                              = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                           => ( X2 = X4 ) )
                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                              ( ( ( kpair @ X1 @ X2 )
                                = ( kpair @ X3 @ X4 ) )
                             => ( X2 = X4 ) )
                         => ( ! [X1: $i] :
                                ( ( iskpair @ X1 )
                               => ~ ! [X2: $i] :
                                      ( ( in @ X2
                                        @ ( dsetconstr @ ( setunion @ X1 )
                                          @ ^ [X3: $i] :
                                              ( X1
                                              = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                     => ( ( dsetconstr @ ( setunion @ X1 )
                                          @ ^ [X3: $i] :
                                              ( X1
                                              = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                       != ( setadjoin @ X2 @ emptyset ) ) ) )
                           => ( ! [X1: $i,X2: $i] :
                                  ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                  = X2 )
                             => ( sP8
                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                      ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                     => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                        ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                       => ( in @ X3 @ X1 ) )
                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                          ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                         => ( in @ X4 @ X2 ) )
                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                            ( ( in @ X3 @ X1 )
                                           => ! [X4: $i] :
                                                ( ( in @ X4 @ X2 )
                                               => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                  = X3 ) ) )
                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                              ( ( in @ X3 @ X1 )
                                             => ! [X4: $i] :
                                                  ( ( in @ X4 @ X2 )
                                                 => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                    = X4 ) ) )
                                         => ! [X1: $i,X2: $i,X3: $i] :
                                              ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                             => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h290,assumption,
    ! [X1: $i] :
      ( ~ ! [X2: $i] :
            ( ( in @ X2 @ X1 )
           => ( X1
             != ( setadjoin @ X2 @ emptyset ) ) )
     => ( in @ ( setunion @ X1 ) @ X1 ) ),
    introduced(assumption,[]) ).

thf(h291,assumption,
    ~ ( ! [X1: $i,X2: $i] :
          ( ( kfst @ ( kpair @ X1 @ X2 ) )
          = X1 )
     => ( ! [X1: $i,X2: $i,X3: $i] :
            ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
           => ( in @ ( kfst @ X3 ) @ X1 ) )
       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
              ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
             => ( X1 = X3 ) )
         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                ( ( ( kpair @ X1 @ X2 )
                  = ( kpair @ X3 @ X4 ) )
               => ( X1 = X3 ) )
           => ( ! [X1: $i,X2: $i] :
                  ( ( X1 = X2 )
                 => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                    = ( setadjoin @ X1 @ emptyset ) ) )
             => ( ! [X1: $i,X2: $i] :
                    ( ( X1 = X2 )
                   => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                      = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                      ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                        = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                     => ( ( X3 = X4 )
                       => ( X2 = X4 ) ) )
                 => ( ! [X1: $i,X2: $i,X3: $i] :
                        ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                          = ( setadjoin @ X3 @ emptyset ) )
                       => ( X1 = X2 ) )
                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                          ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                            = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                         => ( X2 = X4 ) )
                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                            ( ( ( kpair @ X1 @ X2 )
                              = ( kpair @ X3 @ X4 ) )
                           => ( X2 = X4 ) )
                       => ( ! [X1: $i] :
                              ( ( iskpair @ X1 )
                             => ~ ! [X2: $i] :
                                    ( ( in @ X2
                                      @ ( dsetconstr @ ( setunion @ X1 )
                                        @ ^ [X3: $i] :
                                            ( X1
                                            = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                   => ( ( dsetconstr @ ( setunion @ X1 )
                                        @ ^ [X3: $i] :
                                            ( X1
                                            = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                     != ( setadjoin @ X2 @ emptyset ) ) ) )
                         => ( ! [X1: $i,X2: $i] :
                                ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                = X2 )
                           => ( sP8
                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                    ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                   => ( in @ ( ksnd @ X3 ) @ X2 ) )
                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                      ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                     => ( in @ X3 @ X1 ) )
                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                        ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                       => ( in @ X4 @ X2 ) )
                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                          ( ( in @ X3 @ X1 )
                                         => ! [X4: $i] :
                                              ( ( in @ X4 @ X2 )
                                             => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                = X3 ) ) )
                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                            ( ( in @ X3 @ X1 )
                                           => ! [X4: $i] :
                                                ( ( in @ X4 @ X2 )
                                               => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                  = X4 ) ) )
                                       => ! [X1: $i,X2: $i,X3: $i] :
                                            ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                           => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                              = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h292,assumption,
    ! [X1: $i,X2: $i] :
      ( ( kfst @ ( kpair @ X1 @ X2 ) )
      = X1 ),
    introduced(assumption,[]) ).

thf(h293,assumption,
    ~ ( ! [X1: $i,X2: $i,X3: $i] :
          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
         => ( in @ ( kfst @ X3 ) @ X1 ) )
     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
            ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
              = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
           => ( X1 = X3 ) )
       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
              ( ( ( kpair @ X1 @ X2 )
                = ( kpair @ X3 @ X4 ) )
             => ( X1 = X3 ) )
         => ( ! [X1: $i,X2: $i] :
                ( ( X1 = X2 )
               => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                  = ( setadjoin @ X1 @ emptyset ) ) )
           => ( ! [X1: $i,X2: $i] :
                  ( ( X1 = X2 )
                 => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                    = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                    ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                      = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                   => ( ( X3 = X4 )
                     => ( X2 = X4 ) ) )
               => ( ! [X1: $i,X2: $i,X3: $i] :
                      ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                        = ( setadjoin @ X3 @ emptyset ) )
                     => ( X1 = X2 ) )
                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                        ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                          = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                       => ( X2 = X4 ) )
                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                          ( ( ( kpair @ X1 @ X2 )
                            = ( kpair @ X3 @ X4 ) )
                         => ( X2 = X4 ) )
                     => ( ! [X1: $i] :
                            ( ( iskpair @ X1 )
                           => ~ ! [X2: $i] :
                                  ( ( in @ X2
                                    @ ( dsetconstr @ ( setunion @ X1 )
                                      @ ^ [X3: $i] :
                                          ( X1
                                          = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                 => ( ( dsetconstr @ ( setunion @ X1 )
                                      @ ^ [X3: $i] :
                                          ( X1
                                          = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                   != ( setadjoin @ X2 @ emptyset ) ) ) )
                       => ( ! [X1: $i,X2: $i] :
                              ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                              = X2 )
                         => ( sP8
                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                  ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                 => ( in @ ( ksnd @ X3 ) @ X2 ) )
                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                    ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                   => ( in @ X3 @ X1 ) )
                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                      ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                     => ( in @ X4 @ X2 ) )
                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                        ( ( in @ X3 @ X1 )
                                       => ! [X4: $i] :
                                            ( ( in @ X4 @ X2 )
                                           => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                              = X3 ) ) )
                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                          ( ( in @ X3 @ X1 )
                                         => ! [X4: $i] :
                                              ( ( in @ X4 @ X2 )
                                             => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                = X4 ) ) )
                                     => ! [X1: $i,X2: $i,X3: $i] :
                                          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                         => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                            = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h294,assumption,
    ! [X1: $i,X2: $i,X3: $i] :
      ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
     => ( in @ ( kfst @ X3 ) @ X1 ) ),
    introduced(assumption,[]) ).

thf(h295,assumption,
    ~ ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
          ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
            = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
         => ( X1 = X3 ) )
     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
            ( ( ( kpair @ X1 @ X2 )
              = ( kpair @ X3 @ X4 ) )
           => ( X1 = X3 ) )
       => ( ! [X1: $i,X2: $i] :
              ( ( X1 = X2 )
             => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                = ( setadjoin @ X1 @ emptyset ) ) )
         => ( ! [X1: $i,X2: $i] :
                ( ( X1 = X2 )
               => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                  = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                  ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                    = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                 => ( ( X3 = X4 )
                   => ( X2 = X4 ) ) )
             => ( ! [X1: $i,X2: $i,X3: $i] :
                    ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                      = ( setadjoin @ X3 @ emptyset ) )
                   => ( X1 = X2 ) )
               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                      ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                        = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                     => ( X2 = X4 ) )
                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                        ( ( ( kpair @ X1 @ X2 )
                          = ( kpair @ X3 @ X4 ) )
                       => ( X2 = X4 ) )
                   => ( ! [X1: $i] :
                          ( ( iskpair @ X1 )
                         => ~ ! [X2: $i] :
                                ( ( in @ X2
                                  @ ( dsetconstr @ ( setunion @ X1 )
                                    @ ^ [X3: $i] :
                                        ( X1
                                        = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                               => ( ( dsetconstr @ ( setunion @ X1 )
                                    @ ^ [X3: $i] :
                                        ( X1
                                        = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                 != ( setadjoin @ X2 @ emptyset ) ) ) )
                     => ( ! [X1: $i,X2: $i] :
                            ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                            = X2 )
                       => ( sP8
                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                               => ( in @ ( ksnd @ X3 ) @ X2 ) )
                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                  ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                 => ( in @ X3 @ X1 ) )
                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                    ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                   => ( in @ X4 @ X2 ) )
                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                      ( ( in @ X3 @ X1 )
                                     => ! [X4: $i] :
                                          ( ( in @ X4 @ X2 )
                                         => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                            = X3 ) ) )
                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                        ( ( in @ X3 @ X1 )
                                       => ! [X4: $i] :
                                            ( ( in @ X4 @ X2 )
                                           => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                              = X4 ) ) )
                                   => ! [X1: $i,X2: $i,X3: $i] :
                                        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                       => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                          = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h296,assumption,
    ! [X1: $i,X2: $i,X3: $i,X4: $i] :
      ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
        = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
     => ( X1 = X3 ) ),
    introduced(assumption,[]) ).

thf(h297,assumption,
    ~ ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
          ( ( ( kpair @ X1 @ X2 )
            = ( kpair @ X3 @ X4 ) )
         => ( X1 = X3 ) )
     => ( ! [X1: $i,X2: $i] :
            ( ( X1 = X2 )
           => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
              = ( setadjoin @ X1 @ emptyset ) ) )
       => ( ! [X1: $i,X2: $i] :
              ( ( X1 = X2 )
             => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                  = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
               => ( ( X3 = X4 )
                 => ( X2 = X4 ) ) )
           => ( ! [X1: $i,X2: $i,X3: $i] :
                  ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                    = ( setadjoin @ X3 @ emptyset ) )
                 => ( X1 = X2 ) )
             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                    ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                      = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                   => ( X2 = X4 ) )
               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                      ( ( ( kpair @ X1 @ X2 )
                        = ( kpair @ X3 @ X4 ) )
                     => ( X2 = X4 ) )
                 => ( ! [X1: $i] :
                        ( ( iskpair @ X1 )
                       => ~ ! [X2: $i] :
                              ( ( in @ X2
                                @ ( dsetconstr @ ( setunion @ X1 )
                                  @ ^ [X3: $i] :
                                      ( X1
                                      = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                             => ( ( dsetconstr @ ( setunion @ X1 )
                                  @ ^ [X3: $i] :
                                      ( X1
                                      = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                               != ( setadjoin @ X2 @ emptyset ) ) ) )
                   => ( ! [X1: $i,X2: $i] :
                          ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                          = X2 )
                     => ( sP8
                       => ( ! [X1: $i,X2: $i,X3: $i] :
                              ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                             => ( in @ ( ksnd @ X3 ) @ X2 ) )
                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                               => ( in @ X3 @ X1 ) )
                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                  ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                 => ( in @ X4 @ X2 ) )
                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                    ( ( in @ X3 @ X1 )
                                   => ! [X4: $i] :
                                        ( ( in @ X4 @ X2 )
                                       => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                          = X3 ) ) )
                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                      ( ( in @ X3 @ X1 )
                                     => ! [X4: $i] :
                                          ( ( in @ X4 @ X2 )
                                         => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                            = X4 ) ) )
                                 => ! [X1: $i,X2: $i,X3: $i] :
                                      ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                     => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                        = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h298,assumption,
    ! [X1: $i,X2: $i,X3: $i,X4: $i] :
      ( ( ( kpair @ X1 @ X2 )
        = ( kpair @ X3 @ X4 ) )
     => ( X1 = X3 ) ),
    introduced(assumption,[]) ).

thf(h299,assumption,
    ~ ( ! [X1: $i,X2: $i] :
          ( ( X1 = X2 )
         => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
            = ( setadjoin @ X1 @ emptyset ) ) )
     => ( ! [X1: $i,X2: $i] :
            ( ( X1 = X2 )
           => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
              = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
              ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
             => ( ( X3 = X4 )
               => ( X2 = X4 ) ) )
         => ( ! [X1: $i,X2: $i,X3: $i] :
                ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                  = ( setadjoin @ X3 @ emptyset ) )
               => ( X1 = X2 ) )
           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                  ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                    = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                 => ( X2 = X4 ) )
             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                    ( ( ( kpair @ X1 @ X2 )
                      = ( kpair @ X3 @ X4 ) )
                   => ( X2 = X4 ) )
               => ( ! [X1: $i] :
                      ( ( iskpair @ X1 )
                     => ~ ! [X2: $i] :
                            ( ( in @ X2
                              @ ( dsetconstr @ ( setunion @ X1 )
                                @ ^ [X3: $i] :
                                    ( X1
                                    = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                           => ( ( dsetconstr @ ( setunion @ X1 )
                                @ ^ [X3: $i] :
                                    ( X1
                                    = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                             != ( setadjoin @ X2 @ emptyset ) ) ) )
                 => ( ! [X1: $i,X2: $i] :
                        ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                        = X2 )
                   => ( sP8
                     => ( ! [X1: $i,X2: $i,X3: $i] :
                            ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                           => ( in @ ( ksnd @ X3 ) @ X2 ) )
                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                              ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                             => ( in @ X3 @ X1 ) )
                         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                               => ( in @ X4 @ X2 ) )
                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                  ( ( in @ X3 @ X1 )
                                 => ! [X4: $i] :
                                      ( ( in @ X4 @ X2 )
                                     => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                        = X3 ) ) )
                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                    ( ( in @ X3 @ X1 )
                                   => ! [X4: $i] :
                                        ( ( in @ X4 @ X2 )
                                       => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                          = X4 ) ) )
                               => ! [X1: $i,X2: $i,X3: $i] :
                                    ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                   => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                      = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h300,assumption,
    ! [X1: $i,X2: $i] :
      ( ( X1 = X2 )
     => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
        = ( setadjoin @ X1 @ emptyset ) ) ),
    introduced(assumption,[]) ).

thf(h301,assumption,
    ~ ( ! [X1: $i,X2: $i] :
          ( ( X1 = X2 )
         => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
            = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
            ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
              = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
           => ( ( X3 = X4 )
             => ( X2 = X4 ) ) )
       => ( ! [X1: $i,X2: $i,X3: $i] :
              ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                = ( setadjoin @ X3 @ emptyset ) )
             => ( X1 = X2 ) )
         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                  = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
               => ( X2 = X4 ) )
           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                  ( ( ( kpair @ X1 @ X2 )
                    = ( kpair @ X3 @ X4 ) )
                 => ( X2 = X4 ) )
             => ( ! [X1: $i] :
                    ( ( iskpair @ X1 )
                   => ~ ! [X2: $i] :
                          ( ( in @ X2
                            @ ( dsetconstr @ ( setunion @ X1 )
                              @ ^ [X3: $i] :
                                  ( X1
                                  = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                         => ( ( dsetconstr @ ( setunion @ X1 )
                              @ ^ [X3: $i] :
                                  ( X1
                                  = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                           != ( setadjoin @ X2 @ emptyset ) ) ) )
               => ( ! [X1: $i,X2: $i] :
                      ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                      = X2 )
                 => ( sP8
                   => ( ! [X1: $i,X2: $i,X3: $i] :
                          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                         => ( in @ ( ksnd @ X3 ) @ X2 ) )
                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                            ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                           => ( in @ X3 @ X1 ) )
                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                              ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                             => ( in @ X4 @ X2 ) )
                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                ( ( in @ X3 @ X1 )
                               => ! [X4: $i] :
                                    ( ( in @ X4 @ X2 )
                                   => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                      = X3 ) ) )
                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                  ( ( in @ X3 @ X1 )
                                 => ! [X4: $i] :
                                      ( ( in @ X4 @ X2 )
                                     => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                        = X4 ) ) )
                             => ! [X1: $i,X2: $i,X3: $i] :
                                  ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                 => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                    = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h302,assumption,
    ! [X1: $i,X2: $i] :
      ( ( X1 = X2 )
     => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
        = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) ),
    introduced(assumption,[]) ).

thf(h303,assumption,
    ~ ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
          ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
            = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
         => ( ( X3 = X4 )
           => ( X2 = X4 ) ) )
     => ( ! [X1: $i,X2: $i,X3: $i] :
            ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
              = ( setadjoin @ X3 @ emptyset ) )
           => ( X1 = X2 ) )
       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
              ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
             => ( X2 = X4 ) )
         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                ( ( ( kpair @ X1 @ X2 )
                  = ( kpair @ X3 @ X4 ) )
               => ( X2 = X4 ) )
           => ( ! [X1: $i] :
                  ( ( iskpair @ X1 )
                 => ~ ! [X2: $i] :
                        ( ( in @ X2
                          @ ( dsetconstr @ ( setunion @ X1 )
                            @ ^ [X3: $i] :
                                ( X1
                                = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                       => ( ( dsetconstr @ ( setunion @ X1 )
                            @ ^ [X3: $i] :
                                ( X1
                                = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                         != ( setadjoin @ X2 @ emptyset ) ) ) )
             => ( ! [X1: $i,X2: $i] :
                    ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                    = X2 )
               => ( sP8
                 => ( ! [X1: $i,X2: $i,X3: $i] :
                        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                       => ( in @ ( ksnd @ X3 ) @ X2 ) )
                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                          ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                         => ( in @ X3 @ X1 ) )
                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                            ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                           => ( in @ X4 @ X2 ) )
                       => ( ! [X1: $i,X2: $i,X3: $i] :
                              ( ( in @ X3 @ X1 )
                             => ! [X4: $i] :
                                  ( ( in @ X4 @ X2 )
                                 => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                    = X3 ) ) )
                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                ( ( in @ X3 @ X1 )
                               => ! [X4: $i] :
                                    ( ( in @ X4 @ X2 )
                                   => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                      = X4 ) ) )
                           => ! [X1: $i,X2: $i,X3: $i] :
                                ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                               => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                  = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h304,assumption,
    ! [X1: $i,X2: $i,X3: $i,X4: $i] :
      ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
        = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
     => ( ( X3 = X4 )
       => ( X2 = X4 ) ) ),
    introduced(assumption,[]) ).

thf(h305,assumption,
    ~ ( ! [X1: $i,X2: $i,X3: $i] :
          ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
            = ( setadjoin @ X3 @ emptyset ) )
         => ( X1 = X2 ) )
     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
            ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
              = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
           => ( X2 = X4 ) )
       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
              ( ( ( kpair @ X1 @ X2 )
                = ( kpair @ X3 @ X4 ) )
             => ( X2 = X4 ) )
         => ( ! [X1: $i] :
                ( ( iskpair @ X1 )
               => ~ ! [X2: $i] :
                      ( ( in @ X2
                        @ ( dsetconstr @ ( setunion @ X1 )
                          @ ^ [X3: $i] :
                              ( X1
                              = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                     => ( ( dsetconstr @ ( setunion @ X1 )
                          @ ^ [X3: $i] :
                              ( X1
                              = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                       != ( setadjoin @ X2 @ emptyset ) ) ) )
           => ( ! [X1: $i,X2: $i] :
                  ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                  = X2 )
             => ( sP8
               => ( ! [X1: $i,X2: $i,X3: $i] :
                      ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                     => ( in @ ( ksnd @ X3 ) @ X2 ) )
                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                        ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                       => ( in @ X3 @ X1 ) )
                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                          ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                         => ( in @ X4 @ X2 ) )
                     => ( ! [X1: $i,X2: $i,X3: $i] :
                            ( ( in @ X3 @ X1 )
                           => ! [X4: $i] :
                                ( ( in @ X4 @ X2 )
                               => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                  = X3 ) ) )
                       => ( ! [X1: $i,X2: $i,X3: $i] :
                              ( ( in @ X3 @ X1 )
                             => ! [X4: $i] :
                                  ( ( in @ X4 @ X2 )
                                 => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                    = X4 ) ) )
                         => ! [X1: $i,X2: $i,X3: $i] :
                              ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                             => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                = X3 ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h306,assumption,
    ! [X1: $i,X2: $i,X3: $i] :
      ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
        = ( setadjoin @ X3 @ emptyset ) )
     => ( X1 = X2 ) ),
    introduced(assumption,[]) ).

thf(h307,assumption,
    ~ ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
          ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
            = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
         => ( X2 = X4 ) )
     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
            ( ( ( kpair @ X1 @ X2 )
              = ( kpair @ X3 @ X4 ) )
           => ( X2 = X4 ) )
       => ( ! [X1: $i] :
              ( ( iskpair @ X1 )
             => ~ ! [X2: $i] :
                    ( ( in @ X2
                      @ ( dsetconstr @ ( setunion @ X1 )
                        @ ^ [X3: $i] :
                            ( X1
                            = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                   => ( ( dsetconstr @ ( setunion @ X1 )
                        @ ^ [X3: $i] :
                            ( X1
                            = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                     != ( setadjoin @ X2 @ emptyset ) ) ) )
         => ( ! [X1: $i,X2: $i] :
                ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                = X2 )
           => ( sP8
             => ( ! [X1: $i,X2: $i,X3: $i] :
                    ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                   => ( in @ ( ksnd @ X3 ) @ X2 ) )
               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                      ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                     => ( in @ X3 @ X1 ) )
                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                        ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                       => ( in @ X4 @ X2 ) )
                   => ( ! [X1: $i,X2: $i,X3: $i] :
                          ( ( in @ X3 @ X1 )
                         => ! [X4: $i] :
                              ( ( in @ X4 @ X2 )
                             => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                = X3 ) ) )
                     => ( ! [X1: $i,X2: $i,X3: $i] :
                            ( ( in @ X3 @ X1 )
                           => ! [X4: $i] :
                                ( ( in @ X4 @ X2 )
                               => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                  = X4 ) ) )
                       => ! [X1: $i,X2: $i,X3: $i] :
                            ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                           => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                              = X3 ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h308,assumption,
    ! [X1: $i,X2: $i,X3: $i,X4: $i] :
      ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
        = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
     => ( X2 = X4 ) ),
    introduced(assumption,[]) ).

thf(h309,assumption,
    ~ ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
          ( ( ( kpair @ X1 @ X2 )
            = ( kpair @ X3 @ X4 ) )
         => ( X2 = X4 ) )
     => ( ! [X1: $i] :
            ( ( iskpair @ X1 )
           => ~ ! [X2: $i] :
                  ( ( in @ X2
                    @ ( dsetconstr @ ( setunion @ X1 )
                      @ ^ [X3: $i] :
                          ( X1
                          = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                 => ( ( dsetconstr @ ( setunion @ X1 )
                      @ ^ [X3: $i] :
                          ( X1
                          = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                   != ( setadjoin @ X2 @ emptyset ) ) ) )
       => ( ! [X1: $i,X2: $i] :
              ( ( ksnd @ ( kpair @ X1 @ X2 ) )
              = X2 )
         => ( sP8
           => ( ! [X1: $i,X2: $i,X3: $i] :
                  ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                 => ( in @ ( ksnd @ X3 ) @ X2 ) )
             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                    ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                   => ( in @ X3 @ X1 ) )
               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                      ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                     => ( in @ X4 @ X2 ) )
                 => ( ! [X1: $i,X2: $i,X3: $i] :
                        ( ( in @ X3 @ X1 )
                       => ! [X4: $i] :
                            ( ( in @ X4 @ X2 )
                           => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                              = X3 ) ) )
                   => ( ! [X1: $i,X2: $i,X3: $i] :
                          ( ( in @ X3 @ X1 )
                         => ! [X4: $i] :
                              ( ( in @ X4 @ X2 )
                             => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                = X4 ) ) )
                     => ! [X1: $i,X2: $i,X3: $i] :
                          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                         => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                            = X3 ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h310,assumption,
    ! [X1: $i,X2: $i,X3: $i,X4: $i] :
      ( ( ( kpair @ X1 @ X2 )
        = ( kpair @ X3 @ X4 ) )
     => ( X2 = X4 ) ),
    introduced(assumption,[]) ).

thf(h311,assumption,
    ~ ( ! [X1: $i] :
          ( ( iskpair @ X1 )
         => ~ ! [X2: $i] :
                ( ( in @ X2
                  @ ( dsetconstr @ ( setunion @ X1 )
                    @ ^ [X3: $i] :
                        ( X1
                        = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
               => ( ( dsetconstr @ ( setunion @ X1 )
                    @ ^ [X3: $i] :
                        ( X1
                        = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                 != ( setadjoin @ X2 @ emptyset ) ) ) )
     => ( ! [X1: $i,X2: $i] :
            ( ( ksnd @ ( kpair @ X1 @ X2 ) )
            = X2 )
       => ( sP8
         => ( ! [X1: $i,X2: $i,X3: $i] :
                ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
               => ( in @ ( ksnd @ X3 ) @ X2 ) )
           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                  ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                 => ( in @ X3 @ X1 ) )
             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                    ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                   => ( in @ X4 @ X2 ) )
               => ( ! [X1: $i,X2: $i,X3: $i] :
                      ( ( in @ X3 @ X1 )
                     => ! [X4: $i] :
                          ( ( in @ X4 @ X2 )
                         => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                            = X3 ) ) )
                 => ( ! [X1: $i,X2: $i,X3: $i] :
                        ( ( in @ X3 @ X1 )
                       => ! [X4: $i] :
                            ( ( in @ X4 @ X2 )
                           => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                              = X4 ) ) )
                   => ! [X1: $i,X2: $i,X3: $i] :
                        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                       => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                          = X3 ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h312,assumption,
    ! [X1: $i] :
      ( ( iskpair @ X1 )
     => ~ ! [X2: $i] :
            ( ( in @ X2
              @ ( dsetconstr @ ( setunion @ X1 )
                @ ^ [X3: $i] :
                    ( X1
                    = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
           => ( ( dsetconstr @ ( setunion @ X1 )
                @ ^ [X3: $i] :
                    ( X1
                    = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
             != ( setadjoin @ X2 @ emptyset ) ) ) ),
    introduced(assumption,[]) ).

thf(h313,assumption,
    ~ ( ! [X1: $i,X2: $i] :
          ( ( ksnd @ ( kpair @ X1 @ X2 ) )
          = X2 )
     => ( sP8
       => ( ! [X1: $i,X2: $i,X3: $i] :
              ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
             => ( in @ ( ksnd @ X3 ) @ X2 ) )
         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
               => ( in @ X3 @ X1 ) )
           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                  ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                 => ( in @ X4 @ X2 ) )
             => ( ! [X1: $i,X2: $i,X3: $i] :
                    ( ( in @ X3 @ X1 )
                   => ! [X4: $i] :
                        ( ( in @ X4 @ X2 )
                       => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                          = X3 ) ) )
               => ( ! [X1: $i,X2: $i,X3: $i] :
                      ( ( in @ X3 @ X1 )
                     => ! [X4: $i] :
                          ( ( in @ X4 @ X2 )
                         => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                            = X4 ) ) )
                 => ! [X1: $i,X2: $i,X3: $i] :
                      ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                     => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                        = X3 ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h314,assumption,
    ! [X1: $i,X2: $i] :
      ( ( ksnd @ ( kpair @ X1 @ X2 ) )
      = X2 ),
    introduced(assumption,[]) ).

thf(h315,assumption,
    ~ ( sP8
     => ( ! [X1: $i,X2: $i,X3: $i] :
            ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
           => ( in @ ( ksnd @ X3 ) @ X2 ) )
       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
              ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
             => ( in @ X3 @ X1 ) )
         => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
               => ( in @ X4 @ X2 ) )
           => ( ! [X1: $i,X2: $i,X3: $i] :
                  ( ( in @ X3 @ X1 )
                 => ! [X4: $i] :
                      ( ( in @ X4 @ X2 )
                     => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                        = X3 ) ) )
             => ( ! [X1: $i,X2: $i,X3: $i] :
                    ( ( in @ X3 @ X1 )
                   => ! [X4: $i] :
                        ( ( in @ X4 @ X2 )
                       => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                          = X4 ) ) )
               => ! [X1: $i,X2: $i,X3: $i] :
                    ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                   => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                      = X3 ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h316,assumption,
    sP8,
    introduced(assumption,[]) ).

thf(h317,assumption,
    ~ ( ! [X1: $i,X2: $i,X3: $i] :
          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
         => ( in @ ( ksnd @ X3 ) @ X2 ) )
     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
            ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
           => ( in @ X3 @ X1 ) )
       => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
              ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
             => ( in @ X4 @ X2 ) )
         => ( ! [X1: $i,X2: $i,X3: $i] :
                ( ( in @ X3 @ X1 )
               => ! [X4: $i] :
                    ( ( in @ X4 @ X2 )
                   => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                      = X3 ) ) )
           => ( ! [X1: $i,X2: $i,X3: $i] :
                  ( ( in @ X3 @ X1 )
                 => ! [X4: $i] :
                      ( ( in @ X4 @ X2 )
                     => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                        = X4 ) ) )
             => ! [X1: $i,X2: $i,X3: $i] :
                  ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                 => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                    = X3 ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h318,assumption,
    ! [X1: $i,X2: $i,X3: $i] :
      ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
     => ( in @ ( ksnd @ X3 ) @ X2 ) ),
    introduced(assumption,[]) ).

thf(h319,assumption,
    ~ ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
          ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
         => ( in @ X3 @ X1 ) )
     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
            ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
           => ( in @ X4 @ X2 ) )
       => ( ! [X1: $i,X2: $i,X3: $i] :
              ( ( in @ X3 @ X1 )
             => ! [X4: $i] :
                  ( ( in @ X4 @ X2 )
                 => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                    = X3 ) ) )
         => ( ! [X1: $i,X2: $i,X3: $i] :
                ( ( in @ X3 @ X1 )
               => ! [X4: $i] :
                    ( ( in @ X4 @ X2 )
                   => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                      = X4 ) ) )
           => ! [X1: $i,X2: $i,X3: $i] :
                ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
               => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                  = X3 ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h320,assumption,
    ! [X1: $i,X2: $i,X3: $i,X4: $i] :
      ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
     => ( in @ X3 @ X1 ) ),
    introduced(assumption,[]) ).

thf(h321,assumption,
    ~ ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
          ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
         => ( in @ X4 @ X2 ) )
     => ( ! [X1: $i,X2: $i,X3: $i] :
            ( ( in @ X3 @ X1 )
           => ! [X4: $i] :
                ( ( in @ X4 @ X2 )
               => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                  = X3 ) ) )
       => ( ! [X1: $i,X2: $i,X3: $i] :
              ( ( in @ X3 @ X1 )
             => ! [X4: $i] :
                  ( ( in @ X4 @ X2 )
                 => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                    = X4 ) ) )
         => ! [X1: $i,X2: $i,X3: $i] :
              ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
             => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                = X3 ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h322,assumption,
    ! [X1: $i,X2: $i,X3: $i,X4: $i] :
      ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
     => ( in @ X4 @ X2 ) ),
    introduced(assumption,[]) ).

thf(h323,assumption,
    ~ ( ! [X1: $i,X2: $i,X3: $i] :
          ( ( in @ X3 @ X1 )
         => ! [X4: $i] :
              ( ( in @ X4 @ X2 )
             => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                = X3 ) ) )
     => ( ! [X1: $i,X2: $i,X3: $i] :
            ( ( in @ X3 @ X1 )
           => ! [X4: $i] :
                ( ( in @ X4 @ X2 )
               => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                  = X4 ) ) )
       => ! [X1: $i,X2: $i,X3: $i] :
            ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
           => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
              = X3 ) ) ) ),
    introduced(assumption,[]) ).

thf(h324,assumption,
    ! [X1: $i,X2: $i,X3: $i] :
      ( ( in @ X3 @ X1 )
     => ! [X4: $i] :
          ( ( in @ X4 @ X2 )
         => ( ( kfst @ ( kpair @ X3 @ X4 ) )
            = X3 ) ) ),
    introduced(assumption,[]) ).

thf(h325,assumption,
    ~ ( ! [X1: $i,X2: $i,X3: $i] :
          ( ( in @ X3 @ X1 )
         => ! [X4: $i] :
              ( ( in @ X4 @ X2 )
             => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                = X4 ) ) )
     => ! [X1: $i,X2: $i,X3: $i] :
          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
         => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
            = X3 ) ) ),
    introduced(assumption,[]) ).

thf(h326,assumption,
    ! [X1: $i,X2: $i,X3: $i] :
      ( ( in @ X3 @ X1 )
     => ! [X4: $i] :
          ( ( in @ X4 @ X2 )
         => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
            = X4 ) ) ),
    introduced(assumption,[]) ).

thf(h327,assumption,
    ~ ! [X1: $i,X2: $i,X3: $i] :
        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
       => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
          = X3 ) ),
    introduced(assumption,[]) ).

thf(h328,assumption,
    ~ ! [X1: $i,X2: $i] :
        ( ( in @ X2 @ ( cartprod @ eigen__0 @ X1 ) )
       => ( ( kpair @ ( kfst @ X2 ) @ ( ksnd @ X2 ) )
          = X2 ) ),
    introduced(assumption,[]) ).

thf(h329,assumption,
    ~ ! [X1: $i] :
        ( ( in @ X1 @ ( cartprod @ eigen__0 @ eigen__1 ) )
       => ( ( kpair @ ( kfst @ X1 ) @ ( ksnd @ X1 ) )
          = X1 ) ),
    introduced(assumption,[]) ).

thf(h330,assumption,
    ~ ( sP1
     => sP7 ),
    introduced(assumption,[]) ).

thf(h331,assumption,
    sP1,
    introduced(assumption,[]) ).

thf(h332,assumption,
    ~ sP7,
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP4
    | ~ sP1
    | sP2 ),
    inference(prop_rule,[status(thm)],[]) ).

thf(2,plain,
    ( ~ sP3
    | sP4 ),
    inference(all_rule,[status(thm)],[]) ).

thf(3,plain,
    ( ~ sP9
    | sP3 ),
    inference(all_rule,[status(thm)],[]) ).

thf(4,plain,
    ( ~ sP5
    | sP9 ),
    inference(all_rule,[status(thm)],[]) ).

thf(5,plain,
    ( ~ sP6
    | ~ sP2
    | sP7 ),
    inference(prop_rule,[status(thm)],[]) ).

thf(6,plain,
    ( ~ sP8
    | sP6 ),
    inference(all_rule,[status(thm)],[]) ).

thf(7,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h331,h332,h330,h329,h328,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h277,h283,h281,h282,h279,h280,h277,h278,h275,h276,h273,h274,h271,h272,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h88,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h92,h237,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0])],[1,2,3,4,5,6,h267,h316,h331,h332]) ).

thf(8,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h330,h329,h328,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h277,h283,h281,h282,h279,h280,h277,h278,h275,h276,h273,h274,h271,h272,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h88,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h92,h237,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h331,h332])],[h330,7,h331,h332]) ).

thf(9,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h329,h328,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h277,h283,h281,h282,h279,h280,h277,h278,h275,h276,h273,h274,h271,h272,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h88,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h92,h237,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h330]),tab_negall(eigenvar,eigen__2)],[h329,8,h330]) ).

thf(10,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h328,h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h277,h283,h281,h282,h279,h280,h277,h278,h275,h276,h273,h274,h271,h272,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h88,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h92,h237,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h329]),tab_negall(eigenvar,eigen__1)],[h328,9,h329]) ).

thf(11,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h326,h327,h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h277,h283,h281,h282,h279,h280,h277,h278,h275,h276,h273,h274,h271,h272,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h88,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h92,h237,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h328]),tab_negall(eigenvar,eigen__0)],[h327,10,h328]) ).

thf(12,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h324,h325,h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h277,h283,h281,h282,h279,h280,h277,h278,h275,h276,h273,h274,h271,h272,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h88,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h92,h237,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h326,h327])],[h325,11,h326,h327]) ).

thf(13,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h322,h323,h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h277,h283,h281,h282,h279,h280,h277,h278,h275,h276,h273,h274,h271,h272,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h88,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h92,h237,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h324,h325])],[h323,12,h324,h325]) ).

thf(14,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h320,h321,h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h277,h283,h281,h282,h279,h280,h277,h278,h275,h276,h273,h274,h271,h272,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h88,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h92,h237,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h322,h323])],[h321,13,h322,h323]) ).

thf(15,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h318,h319,h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h277,h283,h281,h282,h279,h280,h277,h278,h275,h276,h273,h274,h271,h272,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h88,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h92,h237,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h320,h321])],[h319,14,h320,h321]) ).

thf(16,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h316,h317,h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h277,h283,h281,h282,h279,h280,h277,h278,h275,h276,h273,h274,h271,h272,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h88,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h92,h237,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h318,h319])],[h317,15,h318,h319]) ).

thf(17,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h314,h315,h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h277,h283,h281,h282,h279,h280,h277,h278,h275,h276,h273,h274,h271,h272,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h88,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h92,h237,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h316,h317])],[h315,16,h316,h317]) ).

thf(18,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h312,h313,h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h277,h283,h281,h282,h279,h280,h277,h278,h275,h276,h273,h274,h271,h272,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h88,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h92,h237,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h314,h315])],[h313,17,h314,h315]) ).

thf(19,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h310,h311,h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h277,h283,h281,h282,h279,h280,h277,h278,h275,h276,h273,h274,h271,h272,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h88,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h92,h237,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h312,h313])],[h311,18,h312,h313]) ).

thf(20,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h308,h309,h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h277,h283,h281,h282,h279,h280,h277,h278,h275,h276,h273,h274,h271,h272,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h88,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h92,h237,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h310,h311])],[h309,19,h310,h311]) ).

thf(21,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h306,h307,h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h277,h283,h281,h282,h279,h280,h277,h278,h275,h276,h273,h274,h271,h272,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h88,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h92,h237,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h308,h309])],[h307,20,h308,h309]) ).

thf(22,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h304,h305,h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h277,h283,h281,h282,h279,h280,h277,h278,h275,h276,h273,h274,h271,h272,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h88,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h92,h237,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h306,h307])],[h305,21,h306,h307]) ).

thf(23,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h302,h303,h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h277,h283,h281,h282,h279,h280,h277,h278,h275,h276,h273,h274,h271,h272,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h88,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h92,h237,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h304,h305])],[h303,22,h304,h305]) ).

thf(24,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h300,h301,h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h277,h283,h281,h282,h279,h280,h277,h278,h275,h276,h273,h274,h271,h272,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h88,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h92,h237,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h302,h303])],[h301,23,h302,h303]) ).

thf(25,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h298,h299,h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h277,h283,h281,h282,h279,h280,h277,h278,h275,h276,h273,h274,h271,h272,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h88,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h92,h237,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h300,h301])],[h299,24,h300,h301]) ).

thf(26,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h296,h297,h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h277,h283,h281,h282,h279,h280,h277,h278,h275,h276,h273,h274,h271,h272,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h88,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h92,h237,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h298,h299])],[h297,25,h298,h299]) ).

thf(27,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h294,h295,h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h277,h283,h281,h282,h279,h280,h277,h278,h275,h276,h273,h274,h271,h272,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h88,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h92,h237,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h296,h297])],[h295,26,h296,h297]) ).

thf(28,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h292,h293,h290,h291,h288,h289,h286,h287,h284,h285,h277,h283,h281,h282,h279,h280,h277,h278,h275,h276,h273,h274,h271,h272,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h88,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h92,h237,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h294,h295])],[h293,27,h294,h295]) ).

thf(29,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h290,h291,h288,h289,h286,h287,h284,h285,h277,h283,h281,h282,h279,h280,h277,h278,h275,h276,h273,h274,h271,h272,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h88,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h92,h237,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h292,h293])],[h291,28,h292,h293]) ).

thf(30,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h288,h289,h286,h287,h284,h285,h277,h283,h281,h282,h279,h280,h277,h278,h275,h276,h273,h274,h271,h272,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h88,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h92,h237,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h290,h291])],[h289,29,h290,h291]) ).

thf(31,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h286,h287,h284,h285,h277,h283,h281,h282,h279,h280,h277,h278,h275,h276,h273,h274,h271,h272,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h88,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h92,h237,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h288,h289])],[h287,30,h288,h289]) ).

thf(32,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h284,h285,h277,h283,h281,h282,h279,h280,h277,h278,h275,h276,h273,h274,h271,h272,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h88,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h92,h237,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h286,h287])],[h285,31,h286,h287]) ).

thf(33,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h277,h283,h281,h282,h279,h280,h277,h278,h275,h276,h273,h274,h271,h272,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h88,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h92,h237,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h284,h285])],[h283,32,h284,h285]) ).

thf(34,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h281,h282,h279,h280,h277,h278,h275,h276,h273,h274,h271,h272,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h88,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h92,h237,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h277,h283])],[h282,33,h277,h283]) ).

thf(35,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h279,h280,h277,h278,h275,h276,h273,h274,h271,h272,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h88,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h92,h237,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h281,h282])],[h280,34,h281,h282]) ).

thf(36,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h277,h278,h275,h276,h273,h274,h271,h272,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h88,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h92,h237,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h279,h280])],[h278,35,h279,h280]) ).

thf(37,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h275,h276,h273,h274,h271,h272,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h88,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h92,h237,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h277,h278])],[h276,36,h277,h278]) ).

thf(38,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h273,h274,h271,h272,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h88,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h92,h237,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h275,h276])],[h274,37,h275,h276]) ).

thf(39,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h271,h272,h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h88,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h92,h237,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h273,h274])],[h272,38,h273,h274]) ).

thf(40,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h269,h270,h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h88,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h92,h237,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h271,h272])],[h270,39,h271,h272]) ).

thf(41,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h267,h268,h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h88,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h92,h237,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h269,h270])],[h268,40,h269,h270]) ).

thf(42,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h265,h266,h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h88,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h92,h237,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h267,h268])],[h266,41,h267,h268]) ).

thf(43,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h263,h264,h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h88,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h92,h237,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h265,h266])],[h264,42,h265,h266]) ).

thf(44,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h261,h262,h259,h260,h257,h258,h255,h256,h253,h254,h88,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h92,h237,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h263,h264])],[h262,43,h263,h264]) ).

thf(45,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h259,h260,h257,h258,h255,h256,h253,h254,h88,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h92,h237,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h261,h262])],[h260,44,h261,h262]) ).

thf(46,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h257,h258,h255,h256,h253,h254,h88,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h92,h237,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h259,h260])],[h258,45,h259,h260]) ).

thf(47,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h255,h256,h253,h254,h88,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h92,h237,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h257,h258])],[h256,46,h257,h258]) ).

thf(48,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h253,h254,h88,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h92,h237,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h255,h256])],[h254,47,h255,h256]) ).

thf(49,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h88,h252,h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h92,h237,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h253,h254])],[h252,48,h253,h254]) ).

thf(50,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h250,h251,h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h92,h237,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h88,h252])],[h251,49,h88,h252]) ).

thf(51,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h248,h249,h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h92,h237,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h250,h251])],[h249,50,h250,h251]) ).

thf(52,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h246,h247,h244,h245,h242,h243,h240,h241,h238,h239,h92,h237,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h248,h249])],[h247,51,h248,h249]) ).

thf(53,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h244,h245,h242,h243,h240,h241,h238,h239,h92,h237,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h246,h247])],[h245,52,h246,h247]) ).

thf(54,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h242,h243,h240,h241,h238,h239,h92,h237,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h244,h245])],[h243,53,h244,h245]) ).

thf(55,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h240,h241,h238,h239,h92,h237,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h242,h243])],[h241,54,h242,h243]) ).

thf(56,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h238,h239,h92,h237,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h240,h241])],[h239,55,h240,h241]) ).

thf(57,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h92,h237,h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h238,h239])],[h237,56,h238,h239]) ).

thf(58,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h235,h236,h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h92,h237])],[h236,57,h92,h237]) ).

thf(59,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h233,h234,h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h235,h236])],[h234,58,h235,h236]) ).

thf(60,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h231,h232,h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h233,h234])],[h232,59,h233,h234]) ).

thf(61,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h229,h230,h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h231,h232])],[h230,60,h231,h232]) ).

thf(62,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h227,h228,h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h229,h230])],[h228,61,h229,h230]) ).

thf(63,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h225,h226,h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h227,h228])],[h226,62,h227,h228]) ).

thf(64,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h223,h224,h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h225,h226])],[h224,63,h225,h226]) ).

thf(65,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h221,h222,h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h223,h224])],[h222,64,h223,h224]) ).

thf(66,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h219,h220,h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h221,h222])],[h220,65,h221,h222]) ).

thf(67,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h217,h218,h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h219,h220])],[h218,66,h219,h220]) ).

thf(68,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h215,h216,h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h217,h218])],[h216,67,h217,h218]) ).

thf(69,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h213,h214,h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h215,h216])],[h214,68,h215,h216]) ).

thf(70,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h211,h212,h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h213,h214])],[h212,69,h213,h214]) ).

thf(71,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h209,h210,h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h211,h212])],[h210,70,h211,h212]) ).

thf(72,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h207,h208,h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h209,h210])],[h208,71,h209,h210]) ).

thf(73,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h205,h206,h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h207,h208])],[h206,72,h207,h208]) ).

thf(74,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h203,h204,h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h205,h206])],[h204,73,h205,h206]) ).

thf(75,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h201,h202,h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h203,h204])],[h202,74,h203,h204]) ).

thf(76,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h199,h200,h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h201,h202])],[h200,75,h201,h202]) ).

thf(77,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h197,h198,h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h199,h200])],[h198,76,h199,h200]) ).

thf(78,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h195,h196,h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h197,h198])],[h196,77,h197,h198]) ).

thf(79,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h193,h194,h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h195,h196])],[h194,78,h195,h196]) ).

thf(80,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h191,h192,h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h193,h194])],[h192,79,h193,h194]) ).

thf(81,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h189,h190,h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h191,h192])],[h190,80,h191,h192]) ).

thf(82,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h187,h188,h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h189,h190])],[h188,81,h189,h190]) ).

thf(83,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h185,h186,h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h187,h188])],[h186,82,h187,h188]) ).

thf(84,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h183,h184,h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h185,h186])],[h184,83,h185,h186]) ).

thf(85,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h181,h182,h179,h180,h177,h178,h175,h176,h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h183,h184])],[h182,84,h183,h184]) ).

thf(86,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h179,h180,h177,h178,h175,h176,h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h181,h182])],[h180,85,h181,h182]) ).

thf(87,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h177,h178,h175,h176,h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h179,h180])],[h178,86,h179,h180]) ).

thf(88,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h175,h176,h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h177,h178])],[h176,87,h177,h178]) ).

thf(89,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h173,h174,h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h175,h176])],[h174,88,h175,h176]) ).

thf(90,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h92,h172,h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h173,h174])],[h172,89,h173,h174]) ).

thf(91,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h170,h171,h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h92,h172])],[h171,90,h92,h172]) ).

thf(92,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h168,h169,h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h170,h171])],[h169,91,h170,h171]) ).

thf(93,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h166,h167,h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h168,h169])],[h167,92,h168,h169]) ).

thf(94,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h164,h165,h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h166,h167])],[h165,93,h166,h167]) ).

thf(95,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h162,h163,h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h164,h165])],[h163,94,h164,h165]) ).

thf(96,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h160,h161,h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h162,h163])],[h161,95,h162,h163]) ).

thf(97,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h158,h159,h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h160,h161])],[h159,96,h160,h161]) ).

thf(98,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h156,h157,h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h158,h159])],[h157,97,h158,h159]) ).

thf(99,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h154,h155,h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h156,h157])],[h155,98,h156,h157]) ).

thf(100,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h152,h153,h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h154,h155])],[h153,99,h154,h155]) ).

thf(101,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h150,h151,h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h152,h153])],[h151,100,h152,h153]) ).

thf(102,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h148,h149,h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h150,h151])],[h149,101,h150,h151]) ).

thf(103,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h146,h147,h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h148,h149])],[h147,102,h148,h149]) ).

thf(104,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h144,h145,h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h146,h147])],[h145,103,h146,h147]) ).

thf(105,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h142,h143,h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h144,h145])],[h143,104,h144,h145]) ).

thf(106,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h140,h141,h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h142,h143])],[h141,105,h142,h143]) ).

thf(107,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h138,h139,h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h140,h141])],[h139,106,h140,h141]) ).

thf(108,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h136,h137,h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h138,h139])],[h137,107,h138,h139]) ).

thf(109,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h134,h135,h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h136,h137])],[h135,108,h136,h137]) ).

thf(110,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h132,h133,h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h134,h135])],[h133,109,h134,h135]) ).

thf(111,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h125,h131,h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h132,h133])],[h131,110,h132,h133]) ).

thf(112,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h129,h130,h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h125,h131])],[h130,111,h125,h131]) ).

thf(113,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h127,h128,h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h129,h130])],[h128,112,h129,h130]) ).

thf(114,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h125,h126,h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h127,h128])],[h126,113,h127,h128]) ).

thf(115,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h123,h124,h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h125,h126])],[h124,114,h125,h126]) ).

thf(116,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h121,h122,h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h123,h124])],[h122,115,h123,h124]) ).

thf(117,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h110,h120,h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h121,h122])],[h120,116,h121,h122]) ).

thf(118,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h118,h119,h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h110,h120])],[h119,117,h110,h120]) ).

thf(119,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h116,h117,h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h118,h119])],[h117,118,h118,h119]) ).

thf(120,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h114,h115,h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h116,h117])],[h115,119,h116,h117]) ).

thf(121,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h112,h113,h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h114,h115])],[h113,120,h114,h115]) ).

thf(122,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h110,h111,h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h112,h113])],[h111,121,h112,h113]) ).

thf(123,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h108,h109,h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h110,h111])],[h109,122,h110,h111]) ).

thf(124,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h106,h107,h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h108,h109])],[h107,123,h108,h109]) ).

thf(125,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h104,h105,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h106,h107])],[h105,124,h106,h107]) ).

thf(126,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h104,h105])],[h103,125,h104,h105]) ).

thf(127,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h102,h103])],[h101,126,h102,h103]) ).

thf(128,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h100,h101])],[h99,127,h100,h101]) ).

thf(129,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h98,h99])],[h97,128,h98,h99]) ).

thf(130,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h96,h97])],[h95,129,h96,h97]) ).

thf(131,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h94,h95])],[h93,130,h94,h95]) ).

thf(132,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h92,h93])],[h91,131,h92,h93]) ).

thf(133,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h88,h89,h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h90,h91])],[h89,132,h90,h91]) ).

thf(134,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h86,h87,h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h88,h89])],[h87,133,h88,h89]) ).

thf(135,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h84,h85,h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h86,h87])],[h85,134,h86,h87]) ).

thf(136,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h82,h83,h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h84,h85])],[h83,135,h84,h85]) ).

thf(137,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h80,h81,h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h82,h83])],[h81,136,h82,h83]) ).

thf(138,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h46,h79,h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h80,h81])],[h79,137,h80,h81]) ).

thf(139,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h77,h78,h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h46,h79])],[h78,138,h46,h79]) ).

thf(140,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h75,h76,h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h77,h78])],[h76,139,h77,h78]) ).

thf(141,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h73,h74,h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h75,h76])],[h74,140,h75,h76]) ).

thf(142,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h71,h72,h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h73,h74])],[h72,141,h73,h74]) ).

thf(143,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h69,h70,h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h71,h72])],[h70,142,h71,h72]) ).

thf(144,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h66,h68,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h69,h70])],[h68,143,h69,h70]) ).

thf(145,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h66,h68])],[h67,144,h66,h68]) ).

thf(146,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h66,h67])],[h65,145,h66,h67]) ).

thf(147,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h64,h65])],[h63,146,h64,h65]) ).

thf(148,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h62,h63])],[h61,147,h62,h63]) ).

thf(149,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h60,h61])],[h59,148,h60,h61]) ).

thf(150,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h58,h59])],[h57,149,h58,h59]) ).

thf(151,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h56,h57])],[h55,150,h56,h57]) ).

thf(152,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h52,h53,h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h54,h55])],[h53,151,h54,h55]) ).

thf(153,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h50,h51,h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h52,h53])],[h51,152,h52,h53]) ).

thf(154,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h48,h49,h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h50,h51])],[h49,153,h50,h51]) ).

thf(155,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h46,h47,h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h48,h49])],[h47,154,h48,h49]) ).

thf(156,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h44,h45,h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h46,h47])],[h45,155,h46,h47]) ).

thf(157,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h41,h43,h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h44,h45])],[h43,156,h44,h45]) ).

thf(158,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h41,h42,h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h41,h43])],[h42,157,h41,h43]) ).

thf(159,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h39,h40,h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h41,h42])],[h40,158,h41,h42]) ).

thf(160,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h37,h38,h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h39,h40])],[h38,159,h39,h40]) ).

thf(161,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h3,h36,h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h37,h38])],[h36,160,h37,h38]) ).

thf(162,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h3,h35,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h3,h36])],[h35,161,h3,h36]) ).

thf(163,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h3,h35])],[h34,162,h3,h35]) ).

thf(164,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h33,h34])],[h32,163,h33,h34]) ).

thf(165,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h31,h32])],[h30,164,h31,h32]) ).

thf(166,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h29,h30])],[h28,165,h29,h30]) ).

thf(167,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h27,h28])],[h26,166,h27,h28]) ).

thf(168,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h25,h26])],[h24,167,h25,h26]) ).

thf(169,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h23,h24])],[h22,168,h23,h24]) ).

thf(170,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h21,h22])],[h20,169,h21,h22]) ).

thf(171,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h19,h20])],[h18,170,h19,h20]) ).

thf(172,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h17,h18])],[h16,171,h17,h18]) ).

thf(173,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h15,h16])],[h14,172,h15,h16]) ).

thf(174,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h13,h14])],[h12,173,h13,h14]) ).

thf(175,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h11,h12])],[h10,174,h11,h12]) ).

thf(176,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h9,h10])],[h8,175,h9,h10]) ).

thf(177,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h7,h8])],[h6,176,h7,h8]) ).

thf(178,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h4,177,h5,h6]) ).

thf(179,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h2,178,h3,h4]) ).

thf(180,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,179,h1,h2]) ).

thf(0,theorem,
    ( ! [X1: $i,X2: $i] :
        ( ! [X3: $i] :
            ( ( in @ X3 @ X1 )
            = ( in @ X3 @ X2 ) )
       => ( X1 = X2 ) )
   => ( ! [X1: $i] :
          ~ ( in @ X1 @ emptyset )
     => ( ! [X1: $i,X2: $i,X3: $i] :
            ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
            = ( ( X3 != X1 )
             => ( in @ X3 @ X2 ) ) )
       => ( ! [X1: $i,X2: $i] :
              ( ( in @ X2 @ ( powerset @ X1 ) )
              = ( ! [X3: $i] :
                    ( ( in @ X3 @ X2 )
                   => ( in @ X3 @ X1 ) ) ) )
         => ( ! [X1: $i,X2: $i] :
                ( ( in @ X2 @ ( setunion @ X1 ) )
                = ( ~ ! [X3: $i] :
                        ( ( in @ X2 @ X3 )
                       => ~ ( in @ X3 @ X1 ) ) ) )
           => ( ( in @ emptyset @ omega )
             => ( ! [X1: $i] :
                    ( ( in @ X1 @ omega )
                   => ( in @ ( setadjoin @ X1 @ X1 ) @ omega ) )
               => ( ! [X1: $i] :
                      ( ~ ( ( in @ emptyset @ X1 )
                         => ~ ! [X2: $i] :
                                ( ~ ( ( in @ X2 @ omega )
                                   => ~ ( in @ X2 @ X1 ) )
                               => ( in @ ( setadjoin @ X2 @ X2 ) @ X1 ) ) )
                     => ! [X2: $i] :
                          ( ( in @ X2 @ omega )
                         => ( in @ X2 @ X1 ) ) )
                 => ( ! [X1: $i > $i > $o,X2: $i] :
                        ( ! [X3: $i] :
                            ( ( in @ X3 @ X2 )
                           => ~ ! [X4: $i] :
                                  ( ( X1 @ X3 @ X4 )
                                 => ~ ! [X5: $i] :
                                        ( ( X1 @ X3 @ X5 )
                                       => ( X4 = X5 ) ) ) )
                       => ~ ! [X3: $i] :
                              ~ ! [X4: $i] :
                                  ( ( in @ X4 @ X3 )
                                  = ( ~ ! [X5: $i] :
                                          ( ( in @ X5 @ X2 )
                                         => ~ ( X1 @ X5 @ X4 ) ) ) ) )
                   => ( ! [X1: $i] :
                          ( ~ ! [X2: $i] :
                                ~ ( in @ X2 @ X1 )
                         => ~ ! [X2: $i] :
                                ( ( in @ X2 @ X1 )
                               => ~ ! [X3: $i] :
                                      ( ( in @ X3 @ X2 )
                                     => ~ ( in @ X3 @ X1 ) ) ) )
                     => ( ! [X1: $i] :
                            ~ ! [X2: $i] :
                                ( ~ ( ~ ( ! [X3: $i] :
                                            ( ( in @ X3 @ X2 )
                                           => ! [X4: $i] :
                                                ( ( in @ X4 @ X3 )
                                               => ( in @ X4 @ X1 ) ) )
                                       => ~ ! [X3: $i,X4: $i] :
                                              ( ~ ( ( in @ X3 @ X1 )
                                                 => ~ ( in @ X4 @ X1 ) )
                                             => ( ! [X5: $i] :
                                                    ( ( in @ X5 @ X2 )
                                                   => ( ( in @ X3 @ X5 )
                                                      = ( in @ X4 @ X5 ) ) )
                                               => ( X3 = X4 ) ) ) )
                                   => ~ ! [X3: $i,X4: $i] :
                                          ( ~ ( ( in @ X3 @ X2 )
                                             => ~ ( in @ X4 @ X2 ) )
                                         => ( ~ ! [X5: $i] :
                                                  ( ( in @ X5 @ X3 )
                                                 => ( in @ X5 @ X4 ) )
                                           => ! [X5: $i] :
                                                ( ( in @ X5 @ X4 )
                                               => ( in @ X5 @ X3 ) ) ) ) )
                               => ~ ! [X3: $i] :
                                      ( ~ ( ! [X4: $i] :
                                              ( ( in @ X4 @ X3 )
                                             => ( in @ X4 @ X1 ) )
                                         => ! [X4: $i] :
                                              ~ ( in @ X4 @ X3 ) )
                                     => ~ ! [X4: $i,X5: $i] :
                                            ( ~ ( ~ ( ( in @ X4 @ X2 )
                                                   => ~ ( in @ X5 @ X3 ) )
                                               => ~ ! [X6: $i] :
                                                      ( ( in @ X6 @ X4 )
                                                     => ~ ( in @ X6 @ X3 ) ) )
                                           => ~ ! [X6: $i] :
                                                  ( ( in @ X6 @ X2 )
                                                 => ( ~ ! [X7: $i] :
                                                          ( ( in @ X7 @ X6 )
                                                         => ( in @ X7 @ X4 ) )
                                                   => ( in @ X5 @ X6 ) ) ) ) ) )
                       => ( ! [X1: $i > $o] :
                              ( ~ ! [X2: $i] :
                                    ( ( X1 @ X2 )
                                   => ~ ! [X3: $i] :
                                          ( ( X1 @ X3 )
                                         => ( X2 = X3 ) ) )
                             => ( X1 @ ( descr @ X1 ) ) )
                         => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                ( ( in @ X3 @ X1 )
                               => ( ( X2 @ X3 )
                                 => ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) ) ) )
                           => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                  ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                 => ( in @ X3 @ X1 ) )
                             => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                    ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                   => ( X2 @ X3 ) )
                               => ( ! [X1: $o,X2: $i] :
                                      ( ( in @ X2 @ ( prop2set @ X1 ) )
                                     => X1 )
                                 => ( ! [X1: $i] :
                                        ( ( in @ X1 @ emptyset )
                                       => ! [X2: $o] : X2 )
                                   => ( ! [X1: $i] :
                                          ~ ( in @ X1 @ emptyset )
                                     => ( ! [X1: $i] :
                                            ~ ( in @ X1 @ emptyset )
                                       => ( ! [X1: $i > $o] :
                                              ( ~ ! [X2: $i] :
                                                    ( ( X1 @ X2 )
                                                   => ~ ! [X3: $i] :
                                                          ( ( X1 @ X3 )
                                                         => ( X2 = X3 ) ) )
                                             => ~ ! [X2: $i] :
                                                    ~ ( X1 @ X2 ) )
                                         => ( ! [X1: $i,X2: $i] :
                                                ( ! [X3: $i] :
                                                    ( ( in @ X3 @ X1 )
                                                   => ( in @ X3 @ X2 ) )
                                               => ( ! [X3: $i] :
                                                      ( ( in @ X3 @ X2 )
                                                     => ( in @ X3 @ X1 ) )
                                                 => ( X1 = X2 ) ) )
                                           => ( ! [X1: $i] :
                                                  ( ! [X2: $i] :
                                                      ~ ( in @ X2 @ X1 )
                                                 => ( X1 = emptyset ) )
                                             => ( ! [X1: $i] :
                                                    ( ! [X2: $i] :
                                                        ~ ( in @ X2 @ X1 )
                                                   => ( X1 = emptyset ) )
                                               => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                      ( ( in @ X3 @ X1 )
                                                     => ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                        = ( X2 @ X3 ) ) )
                                                 => ( ! [X1: $i] :
                                                        ( ( X1 != emptyset )
                                                       => ~ ! [X2: $i] :
                                                              ~ ( in @ X2 @ X1 ) )
                                                   => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                          ( ( in @ X3 @ X1 )
                                                         => ( ( X2 @ X3 )
                                                           => ( ( dsetconstr @ X1 @ X2 )
                                                             != emptyset ) ) )
                                                     => ( ! [X1: $i] :
                                                            ( ~ ! [X2: $i] :
                                                                  ~ ( in @ X2 @ X1 )
                                                           => ( X1 != emptyset ) )
                                                       => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) )
                                                         => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                  ( ( in @ X3 @ X2 )
                                                                 => ( in @ X3 @ ( setadjoin @ X1 @ X2 ) ) )
                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                    ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                                                   => ! [X4: $o] :
                                                                        ( ( ( X3 = X1 )
                                                                         => X4 )
                                                                       => ( ( ( in @ X3 @ X2 )
                                                                           => X4 )
                                                                         => X4 ) ) )
                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                      ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                                                     => ( ( X3 != X1 )
                                                                       => ( in @ X3 @ X2 ) ) )
                                                                 => ( ! [X1: $i] :
                                                                        ( ( dsetconstr @ X1
                                                                          @ ^ [X2: $i] : ~ $false )
                                                                        = X1 )
                                                                   => ( ! [X1: $i,X2: $i] :
                                                                          ( ! [X3: $i] :
                                                                              ( ( in @ X3 @ X2 )
                                                                             => ( in @ X3 @ X1 ) )
                                                                         => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                                     => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                                                       => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                ( ( in @ X2 @ ( powerset @ X1 ) )
                                                                               => ( ( in @ X3 @ X2 )
                                                                                 => ( in @ X3 @ X1 ) ) )
                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                  ( ( in @ X2 @ X3 )
                                                                                 => ( ( in @ X3 @ X1 )
                                                                                   => ( in @ X2 @ ( setunion @ X1 ) ) ) )
                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                    ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                   => ! [X3: $o] :
                                                                                        ( ! [X4: $i] :
                                                                                            ( ( in @ X2 @ X4 )
                                                                                           => ( ( in @ X4 @ X1 )
                                                                                             => X3 ) )
                                                                                       => X3 ) )
                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                      ( ( in @ X2 @ X1 )
                                                                                     => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
                                                                                 => ( ! [X1: $i > $o] :
                                                                                        ( ~ ! [X2: $i] :
                                                                                              ( ( X1 @ X2 )
                                                                                             => ~ ! [X3: $i] :
                                                                                                    ( ( X1 @ X3 )
                                                                                                   => ( X2 = X3 ) ) )
                                                                                       => ~ ! [X2: $i] :
                                                                                              ~ ! [X3: $i] :
                                                                                                  ( ( X1 @ X3 )
                                                                                                  = ( X3 = X2 ) ) )
                                                                                   => ( ! [X1: $i] :
                                                                                          ( ( X1 != emptyset )
                                                                                         => ~ ! [X2: $i] :
                                                                                                ~ ( in @ X2 @ X1 ) )
                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                            ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                           => ( X1 = X2 ) )
                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                              ( ( X1 != X2 )
                                                                                             => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                ( ( X1 = X2 )
                                                                                               => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                  ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                 => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                    ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                   => ( ( X3 != X1 )
                                                                                                     => ( X3 = X2 ) ) )
                                                                                               => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                 => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                                                                          ( ~ ! [X3: $i] :
                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                               => ~ ( X2 @ X3 ) )
                                                                                                         => ( ( dsetconstr @ X1 @ X2 )
                                                                                                           != emptyset ) )
                                                                                                     => ( ! [X1: $i > $o,X2: $i] :
                                                                                                            ( ( in @ X2 @ emptyset )
                                                                                                           => ( X1 @ X2 ) )
                                                                                                       => ( ! [X1: $o] :
                                                                                                              ( X1
                                                                                                             => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                                                                                         => ( ! [X1: $o] :
                                                                                                                ( X1
                                                                                                               => ( set2prop @ ( prop2set @ X1 ) ) )
                                                                                                           => ( ! [X1: $i > $o] :
                                                                                                                  ( ~ ! [X2: $i] :
                                                                                                                        ~ ( X1 @ X2 )
                                                                                                                 => ( ! [X2: $i,X3: $i] :
                                                                                                                        ( ( X1 @ X2 )
                                                                                                                       => ( ( X1 @ X3 )
                                                                                                                         => ( X2 = X3 ) ) )
                                                                                                                   => ~ ! [X2: $i] :
                                                                                                                          ( ( X1 @ X2 )
                                                                                                                         => ~ ! [X3: $i] :
                                                                                                                                ( ( X1 @ X3 )
                                                                                                                               => ( X2 = X3 ) ) ) ) )
                                                                                                             => ( ! [X1: $i > $o] :
                                                                                                                    ( ~ ! [X2: $i] :
                                                                                                                          ~ ! [X3: $i] :
                                                                                                                              ( ( X1 @ X3 )
                                                                                                                              = ( X3 = X2 ) )
                                                                                                                   => ~ ! [X2: $i] :
                                                                                                                          ( ( X1 @ X2 )
                                                                                                                         => ~ ! [X3: $i] :
                                                                                                                                ( ( X1 @ X3 )
                                                                                                                               => ( X2 = X3 ) ) ) )
                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                      ( ( X1 = X2 )
                                                                                                                     => ! [X3: $i,X4: $i] :
                                                                                                                          ( ( X3 = X4 )
                                                                                                                         => ( ( in @ X3 @ X1 )
                                                                                                                           => ( in @ X4 @ X2 ) ) ) )
                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                        ( ( X1 = X2 )
                                                                                                                       => ! [X3: $i,X4: $i] :
                                                                                                                            ( ( X3 = X4 )
                                                                                                                           => ( ( in @ X3 @ X1 )
                                                                                                                              = ( in @ X4 @ X2 ) ) ) )
                                                                                                                   => ( ! [X1: $i > $o] :
                                                                                                                          ( ~ ! [X2: $i] :
                                                                                                                                ( ( X1 @ X2 )
                                                                                                                               => ~ ! [X3: $i] :
                                                                                                                                      ( ( X1 @ X3 )
                                                                                                                                     => ( X2 = X3 ) ) )
                                                                                                                         => ! [X2: $i,X3: $i] :
                                                                                                                              ( ( X1 @ X2 )
                                                                                                                             => ( ( X1 @ X3 )
                                                                                                                               => ( X2 = X3 ) ) ) )
                                                                                                                     => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                                                            ( ! [X3: $i,X4: $i] :
                                                                                                                                ( ( X3 = X4 )
                                                                                                                               => ( ( X1 @ X3 )
                                                                                                                                  = ( X2 @ X4 ) ) )
                                                                                                                           => ( ( ~ ! [X3: $i] :
                                                                                                                                      ( ( X1 @ X3 )
                                                                                                                                     => ~ ! [X4: $i] :
                                                                                                                                            ( ( X1 @ X4 )
                                                                                                                                           => ( X3 = X4 ) ) ) )
                                                                                                                              = ( ~ ! [X3: $i] :
                                                                                                                                      ( ( X2 @ X3 )
                                                                                                                                     => ~ ! [X4: $i] :
                                                                                                                                            ( ( X2 @ X4 )
                                                                                                                                           => ( X3 = X4 ) ) ) ) ) )
                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                              ( ( X1 = X2 )
                                                                                                                             => ! [X3: $i,X4: $i] :
                                                                                                                                  ( ( X3 = X4 )
                                                                                                                                 => ( ( setadjoin @ X1 @ X3 )
                                                                                                                                    = ( setadjoin @ X2 @ X4 ) ) ) )
                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                ( ( X1 = X2 )
                                                                                                                               => ( ( powerset @ X1 )
                                                                                                                                  = ( powerset @ X2 ) ) )
                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                  ( ( X1 = X2 )
                                                                                                                                 => ( ( setunion @ X1 )
                                                                                                                                    = ( setunion @ X2 ) ) )
                                                                                                                             => ( ! [X1: $i > $o] :
                                                                                                                                    ( ~ ! [X2: $i] :
                                                                                                                                          ( ( X1 @ X2 )
                                                                                                                                         => ~ ! [X3: $i] :
                                                                                                                                                ( ( X1 @ X3 )
                                                                                                                                               => ( X2 = X3 ) ) )
                                                                                                                                   => ! [X2: $i,X3: $i] :
                                                                                                                                        ( ( X1 @ X2 )
                                                                                                                                       => ( ( X1 @ X3 )
                                                                                                                                         => ( X2 = X3 ) ) ) )
                                                                                                                               => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                                                                      ( ! [X3: $i,X4: $i] :
                                                                                                                                          ( ( X3 = X4 )
                                                                                                                                         => ( ( X1 @ X3 )
                                                                                                                                            = ( X2 @ X4 ) ) )
                                                                                                                                     => ( ~ ! [X3: $i] :
                                                                                                                                              ( ( X1 @ X3 )
                                                                                                                                             => ~ ! [X4: $i] :
                                                                                                                                                    ( ( X1 @ X4 )
                                                                                                                                                   => ( X3 = X4 ) ) )
                                                                                                                                       => ( ~ ! [X3: $i] :
                                                                                                                                                ( ( X2 @ X3 )
                                                                                                                                               => ~ ! [X4: $i] :
                                                                                                                                                      ( ( X2 @ X4 )
                                                                                                                                                     => ( X3 = X4 ) ) )
                                                                                                                                         => ( ( descr @ X1 )
                                                                                                                                            = ( descr @ X2 ) ) ) ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                        ( ( X1 = X2 )
                                                                                                                                       => ! [X3: $i > $o,X4: $i > $o] :
                                                                                                                                            ( ! [X5: $i] :
                                                                                                                                                ( ( in @ X5 @ X1 )
                                                                                                                                               => ! [X6: $i] :
                                                                                                                                                    ( ( in @ X6 @ X2 )
                                                                                                                                                   => ( ( X5 = X6 )
                                                                                                                                                     => ( ( X3 @ X5 )
                                                                                                                                                        = ( X4 @ X6 ) ) ) ) )
                                                                                                                                           => ( ( dsetconstr @ X1 @ X3 )
                                                                                                                                              = ( dsetconstr @ X2 @ X4 ) ) ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                          ( ! [X3: $i] :
                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                             => ( in @ X3 @ X2 ) )
                                                                                                                                         => ( subset @ X1 @ X2 ) )
                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                            ( ( X1 = X2 )
                                                                                                                                           => ( subset @ X2 @ X1 ) )
                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                              ( ( X1 = X2 )
                                                                                                                                             => ( subset @ X1 @ X2 ) )
                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                ( ! [X3: $i] :
                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                   => ( in @ X3 @ X2 ) )
                                                                                                                                               => ( subset @ X1 @ X2 ) )
                                                                                                                                           => ( ! [X1: $i] : ( subset @ emptyset @ X1 )
                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                    ( ( subset @ X1 @ X2 )
                                                                                                                                                   => ( ( in @ X3 @ X1 )
                                                                                                                                                     => ( in @ X3 @ X2 ) ) )
                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                      ( ( subset @ X1 @ X2 )
                                                                                                                                                     => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                       => ~ ( in @ X3 @ X1 ) ) )
                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                       => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                         => ~ ( subset @ X1 @ X2 ) ) )
                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                          ( ~ ( subset @ X1 @ X2 )
                                                                                                                                                         => ( X1 != X2 ) )
                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                                                           => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                             => ( X1 != X2 ) ) )
                                                                                                                                                       => ( ! [X1: $i] : ( subset @ X1 @ X1 )
                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                ( ( subset @ X1 @ X2 )
                                                                                                                                                               => ( ( subset @ X2 @ X3 )
                                                                                                                                                                 => ( subset @ X1 @ X3 ) ) )
                                                                                                                                                           => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( setadjoin @ X1 @ X2 ) )
                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                    ( ( subset @ X1 @ X3 )
                                                                                                                                                                   => ( subset @ X1 @ ( setadjoin @ X2 @ X3 ) ) )
                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                      ( ( subset @ X1 @ X2 )
                                                                                                                                                                     => ( in @ X1 @ ( powerset @ X2 ) ) )
                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                        ( ( subset @ X1 @ X2 )
                                                                                                                                                                       => ( ( subset @ X2 @ X1 )
                                                                                                                                                                         => ( X1 = X2 ) ) )
                                                                                                                                                                   => ( ! [X1: $i] :
                                                                                                                                                                          ( ( subset @ X1 @ emptyset )
                                                                                                                                                                         => ( X1 = emptyset ) )
                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                            ( ( subset @ X2 @ X1 )
                                                                                                                                                                           => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                              ( ( in @ X2 @ ( powerset @ X1 ) )
                                                                                                                                                                             => ( subset @ X2 @ X1 ) )
                                                                                                                                                                         => ( ! [X1: $i] : ( in @ X1 @ ( powerset @ X1 ) )
                                                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                  ( ( subset @ X1 @ X2 )
                                                                                                                                                                                 => ( subset @ ( powerset @ X1 ) @ ( powerset @ X2 ) ) )
                                                                                                                                                                             => ( ! [X1: $i,X2: $i > $o] : ( in @ ( dsetconstr @ X1 @ X2 ) @ ( powerset @ X1 ) )
                                                                                                                                                                               => ( ! [X1: $i,X2: $i > $o] : ( subset @ ( dsetconstr @ X1 @ X2 ) @ X1 )
                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                       => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                            ( ( in @ X3 @ X2 )
                                                                                                                                                                                           => ( in @ X3 @ ( binunion @ X1 @ X2 ) ) )
                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i,X4: $o] :
                                                                                                                                                                                              ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                                                             => ( ( ( in @ X3 @ X1 )
                                                                                                                                                                                                 => X4 )
                                                                                                                                                                                               => ( ( ( in @ X3 @ X2 )
                                                                                                                                                                                                   => X4 )
                                                                                                                                                                                                 => X4 ) ) )
                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                ( ( in @ X3 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                                                               => ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                 => ( in @ X3 @ X2 ) ) )
                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] : ( subset @ X1 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] : ( subset @ X2 @ ( binunion @ X1 @ X2 ) )
                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                     => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                       => ( in @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                        ( ( subset @ X3 @ X1 )
                                                                                                                                                                                                       => ( ( subset @ X3 @ X2 )
                                                                                                                                                                                                         => ( subset @ X3 @ ( binintersect @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                          ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                                                                                         => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X1 )
                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                              ( ( subset @ X1 @ X2 )
                                                                                                                                                                                                             => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                                                = X1 ) )
                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                                                  = X2 )
                                                                                                                                                                                                               => ( subset @ X2 @ X1 ) )
                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                  ( ( in @ X3 @ ( binintersect @ X1 @ X2 ) )
                                                                                                                                                                                                                 => ( in @ X3 @ X2 ) )
                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                    ( ! [X3: $i] :
                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                       => ~ ( in @ X3 @ X2 ) )
                                                                                                                                                                                                                   => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                                                      = emptyset ) )
                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] : ( subset @ ( binintersect @ X1 @ X2 ) @ X2 )
                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                        ( ( subset @ X2 @ X1 )
                                                                                                                                                                                                                       => ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                                                          = X2 ) )
                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                          ( ( ( binintersect @ X1 @ X2 )
                                                                                                                                                                                                                            = X1 )
                                                                                                                                                                                                                         => ( subset @ X1 @ X2 ) )
                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                            ( ( binintersect @ X1 @ ( binunion @ X2 @ X3 ) )
                                                                                                                                                                                                                            = ( binunion @ ( binintersect @ X1 @ X2 ) @ ( binintersect @ X1 @ X3 ) ) )
                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                             => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                               => ( in @ X3 @ ( setminus @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                                               => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                  ( ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                                                 => ~ ( in @ X3 @ X2 ) )
                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                    ( ( subset @ X1 @ X2 )
                                                                                                                                                                                                                                   => ( ( setminus @ X1 @ X2 )
                                                                                                                                                                                                                                      = emptyset ) )
                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                      ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                                                     => ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                       => ( in @ X3 @ X2 ) ) )
                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                        ( ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) )
                                                                                                                                                                                                                                       => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                                         => ~ ( in @ X3 @ X1 ) ) )
                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                          ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                                         => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                            ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                                           => ~ ( in @ X3 @ ( setminus @ X1 @ X2 ) ) )
                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] : ( subset @ ( setminus @ X1 @ X2 ) @ X1 )
                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                ( ( ( setminus @ X1 @ X2 )
                                                                                                                                                                                                                                                  = emptyset )
                                                                                                                                                                                                                                               => ( subset @ X1 @ X2 ) )
                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                  ( ( in @ X3 @ ( symdiff @ X1 @ X2 ) )
                                                                                                                                                                                                                                                 => ! [X4: $o] :
                                                                                                                                                                                                                                                      ( ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                       => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                                                         => X4 ) )
                                                                                                                                                                                                                                                     => ( ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                         => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                                                           => X4 ) )
                                                                                                                                                                                                                                                       => X4 ) ) )
                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                   => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                                                     => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                      ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                     => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                                                       => ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                       => ( ( in @ X3 @ X2 )
                                                                                                                                                                                                                                                         => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                          ( ~ ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                         => ( ~ ( in @ X3 @ X2 )
                                                                                                                                                                                                                                                           => ~ ( in @ X3 @ ( symdiff @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i] : ( iskpair @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                      ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                                                     => ( subset @ ( setadjoin @ X2 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                        ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                                                       => ( in @ ( setadjoin @ X2 @ emptyset ) @ ( powerset @ X1 ) ) )
                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                         => ( in @ ( setadjoin @ X3 @ emptyset ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                            ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                                                           => ( ( X3 != X1 )
                                                                                                                                                                                                                                                                             => ( X3 = X2 ) ) )
                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                             => ! [X4: $i] :
                                                                                                                                                                                                                                                                                  ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                 => ( subset @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( binunion @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                                                                                                                    ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                   => ( in @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                 => ! [X4: $i] :
                                                                                                                                                                                                                                                                                      ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                     => ( subset @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) )
                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                   => ! [X4: $i] :
                                                                                                                                                                                                                                                                                        ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                       => ( in @ ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                         => ( in @ ( kpair @ X3 @ X4 ) @ ( powerset @ ( powerset @ ( binunion @ X1 @ X2 ) ) ) ) ) )
                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                           => ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) ) ) )
                                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                          ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                         => ~ ! [X4: $i] :
                                                                                                                                                                                                                                                                                                ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                                               => ! [X5: $i] :
                                                                                                                                                                                                                                                                                                    ( ( in @ X5 @ X2 )
                                                                                                                                                                                                                                                                                                   => ( X3
                                                                                                                                                                                                                                                                                                     != ( kpair @ X4 @ X5 ) ) ) ) )
                                                                                                                                                                                                                                                                                     => ( sP5
                                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                              ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                                                                                                                                                                                                                             => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                   => ~ ( in @ X2 @ X3 ) ) )
                                                                                                                                                                                                                                                                                         => ( ! [X1: $i] : ( subset @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) @ X1 )
                                                                                                                                                                                                                                                                                           => ( ! [X1: $i] : ( subset @ X1 @ ( setunion @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                             => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                                    ( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
                                                                                                                                                                                                                                                                                                    = X1 )
                                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                                                                      ( ! [X3: $i] :
                                                                                                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                         => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                              ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                                                             => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                                                                               => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                                                                 => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                                                                                                     => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                             => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                                                                                                       => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                                              ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                             => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                               != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                                                                        ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                                              ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                             => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                               != ( setadjoin @ X3 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                       => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                             => ~ ( X2 @ X3 ) ) )
                                                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                                                                                                                                                                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                         => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                                                                           => ( ! [X4: $i] :
                                                                                                                                                                                                                                                                                                                  ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                                                                 => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                                                                   => ( X4 = X3 ) ) )
                                                                                                                                                                                                                                                                                                             => ~ ! [X4: $i] :
                                                                                                                                                                                                                                                                                                                    ( ( in @ X4 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                   => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                                     != ( setadjoin @ X4 @ emptyset ) ) ) ) ) )
                                                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                                                                                                                                                                                            ( ! [X3: $i] :
                                                                                                                                                                                                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                               => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                                    ( ( in @ X4 @ X1 )
                                                                                                                                                                                                                                                                                                                   => ( ( X2 @ X3 )
                                                                                                                                                                                                                                                                                                                     => ( ( X2 @ X4 )
                                                                                                                                                                                                                                                                                                                       => ( X3 = X4 ) ) ) ) )
                                                                                                                                                                                                                                                                                                           => ( ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                                   => ~ ( X2 @ X3 ) )
                                                                                                                                                                                                                                                                                                             => ~ ! [X3: $i] :
                                                                                                                                                                                                                                                                                                                    ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                   => ( ( dsetconstr @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                                     != ( setadjoin @ X3 @ emptyset ) ) ) ) )
                                                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                              ( ( ( setadjoin @ X1 @ emptyset )
                                                                                                                                                                                                                                                                                                                = ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                                                             => ( X1 = X2 ) )
                                                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                ( ( in @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                               => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                                                           => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                                                  ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                                                                                 => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                                                        ( ( in @ X2
                                                                                                                                                                                                                                                                                                                          @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                                            @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) ) )
                                                                                                                                                                                                                                                                                                                       => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                                            @ ^ [X3: $i] : ( in @ ( setadjoin @ X3 @ emptyset ) @ X1 ) )
                                                                                                                                                                                                                                                                                                                         != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                                                                                             => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                                                    ( ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                                                          ( ( in @ X2 @ X1 )
                                                                                                                                                                                                                                                                                                                         => ( X1
                                                                                                                                                                                                                                                                                                                           != ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                   => ( in @ ( setunion @ X1 ) @ X1 ) )
                                                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                                      ( ( kfst @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                      = X1 )
                                                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                       => ( in @ ( kfst @ X3 ) @ X1 ) )
                                                                                                                                                                                                                                                                                                                   => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                          ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                                            = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                         => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                            ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                                              = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                                           => ( X1 = X3 ) )
                                                                                                                                                                                                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                                              ( ( X1 = X2 )
                                                                                                                                                                                                                                                                                                                             => ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                                                                                = ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                                                ( ( X1 = X2 )
                                                                                                                                                                                                                                                                                                                               => ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                                                  = ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                                  ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                                                    = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                                 => ( ( X3 = X4 )
                                                                                                                                                                                                                                                                                                                                   => ( X2 = X4 ) ) )
                                                                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                                    ( ( ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                                                                                                                                                                                                                                                      = ( setadjoin @ X3 @ emptyset ) )
                                                                                                                                                                                                                                                                                                                                   => ( X1 = X2 ) )
                                                                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                                      ( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
                                                                                                                                                                                                                                                                                                                                        = ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
                                                                                                                                                                                                                                                                                                                                     => ( X2 = X4 ) )
                                                                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                                        ( ( ( kpair @ X1 @ X2 )
                                                                                                                                                                                                                                                                                                                                          = ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                                                       => ( X2 = X4 ) )
                                                                                                                                                                                                                                                                                                                                   => ( ! [X1: $i] :
                                                                                                                                                                                                                                                                                                                                          ( ( iskpair @ X1 )
                                                                                                                                                                                                                                                                                                                                         => ~ ! [X2: $i] :
                                                                                                                                                                                                                                                                                                                                                ( ( in @ X2
                                                                                                                                                                                                                                                                                                                                                  @ ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                                                                    @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                                                                                                        ( X1
                                                                                                                                                                                                                                                                                                                                                        = ( kpair @ ( kfst @ X1 ) @ X3 ) ) ) )
                                                                                                                                                                                                                                                                                                                                               => ( ( dsetconstr @ ( setunion @ X1 )
                                                                                                                                                                                                                                                                                                                                                    @ ^ [X3: $i] :
                                                                                                                                                                                                                                                                                                                                                        ( X1
                                                                                                                                                                                                                                                                                                                                                        = ( kpair @ ( kfst @ X1 ) @ X3 ) ) )
                                                                                                                                                                                                                                                                                                                                                 != ( setadjoin @ X2 @ emptyset ) ) ) )
                                                                                                                                                                                                                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                                                                                                                                                                                                                            ( ( ksnd @ ( kpair @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                                            = X2 )
                                                                                                                                                                                                                                                                                                                                       => ( sP8
                                                                                                                                                                                                                                                                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                                                ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                                               => ( in @ ( ksnd @ X3 ) @ X2 ) )
                                                                                                                                                                                                                                                                                                                                           => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                                                  ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                                                 => ( in @ X3 @ X1 ) )
                                                                                                                                                                                                                                                                                                                                             => ( ! [X1: $i,X2: $i,X3: $i,X4: $i] :
                                                                                                                                                                                                                                                                                                                                                    ( ( in @ ( kpair @ X3 @ X4 ) @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                                                   => ( in @ X4 @ X2 ) )
                                                                                                                                                                                                                                                                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                                                                     => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                                                                          ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                                                                                         => ( ( kfst @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                                                                            = X3 ) ) )
                                                                                                                                                                                                                                                                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                                                                                                                                                                                                                                                       => ! [X4: $i] :
                                                                                                                                                                                                                                                                                                                                                            ( ( in @ X4 @ X2 )
                                                                                                                                                                                                                                                                                                                                                           => ( ( ksnd @ ( kpair @ X3 @ X4 ) )
                                                                                                                                                                                                                                                                                                                                                              = X4 ) ) )
                                                                                                                                                                                                                                                                                                                                                   => ! [X1: $i,X2: $i,X3: $i] :
                                                                                                                                                                                                                                                                                                                                                        ( ( in @ X3 @ ( cartprod @ X1 @ X2 ) )
                                                                                                                                                                                                                                                                                                                                                       => ( ( kpair @ ( kfst @ X3 ) @ ( ksnd @ X3 ) )
                                                                                                                                                                                                                                                                                                                                                          = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[180,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SEU664^1 : TPTP v9.2.0. Released v3.7.0.
% 0.03/0.12  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34  % Computer : n031.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Wed Oct  8 21:05:23 EDT 2025
% 0.12/0.34  % CPUTime  : 
% 0.50/0.70  % SZS status Theorem
% 0.50/0.70  % Mode: cade22sinegrackle2x6978
% 0.50/0.70  % Steps: 2939
% 0.50/0.70  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------